# Devices in Optical Network Node

Authored by: Partha Pratim Sahu

# Fundamentals of Optical Networks and Components

Print publication date:  July  2020
Online publication date:  July  2020

Print ISBN: 9780367265458
eBook ISBN: 9780429293764

10.1201/9780429293764-3

#### Abstract

Recently, Fiber-optic networks have become essential to fulfill the skyrocketing demands of bandwidth in present day’s communication networks. In these networks, flexible operations such as routing, restoration and reconfiguration are provided by the nodes, where optical matrix switches [1–4], wavelength division multiplexing (WDM) [5,6] and add/drop multiplexing (ADM) devices [7–10] are the key devices. The basic design of these optical devices has not changed for hundreds of years. They had bulky and heavy components requiring careful alignment, protection against vibration, moisture and temperature drift. In the early 1970s, in order to make them more compatible with modern technology, integrated optics concept has emerged [11]. At that time, the availability of low-loss optical fibers together with the invention of the laser caused an increasing interest in compact optical systems, in which conventional integrated circuit (IC) processing is used to miniaturize optical ICs (OIC) or photonic IC (PIC), and the wires and radio links are replaced by optical waveguides in the backbone of networks. OICs [11] would have a number of advantages compared with other bulk optical system – enhanced reliability, protection against vibration and electromagnetic interference, low loss propagation, small size, light weight, large bandwidth (multiplexing capability), low power consumption and mass-scale fabrication economy. Other than optical communication, OIC is also used for sensor technology. There are mainly three basic passive components and two basic active components in constructing the above devices. The passive components are directional coupler (DC) [11–16], multimode interference (MMI) coupler [12], [16–20], and two-mode interference (TMI) coupler [16,21–23]. The active components are Mach–Zehnder (MZ) device with phase controller and delay line coupler with phase controller (MZ with unequal arms). Apart from these, there is an array of waveguide grating components.

#### Devices in Optical Network Node

Recently, Fiber-optic networks have become essential to fulfill the skyrocketing demands of bandwidth in present day’s communication networks. In these networks, flexible operations such as routing, restoration and reconfiguration are provided by the nodes, where optical matrix switches [1–4], wavelength division multiplexing (WDM) [5,6] and add/drop multiplexing (ADM) devices [7–10] are the key devices. The basic design of these optical devices has not changed for hundreds of years. They had bulky and heavy components requiring careful alignment, protection against vibration, moisture and temperature drift. In the early 1970s, in order to make them more compatible with modern technology, integrated optics concept has emerged [11]. At that time, the availability of low-loss optical fibers together with the invention of the laser caused an increasing interest in compact optical systems, in which conventional integrated circuit (IC) processing is used to miniaturize optical ICs (OIC) or photonic IC (PIC), and the wires and radio links are replaced by optical waveguides in the backbone of networks. OICs [11] would have a number of advantages compared with other bulk optical system – enhanced reliability, protection against vibration and electromagnetic interference, low loss propagation, small size, light weight, large bandwidth (multiplexing capability), low power consumption and mass-scale fabrication economy. Other than optical communication, OIC is also used for sensor technology. There are mainly three basic passive components and two basic active components in constructing the above devices. The passive components are directional coupler (DC) [11–16], multimode interference (MMI) coupler [12], [16–20], and two-mode interference (TMI) coupler [16,21–23]. The active components are Mach–Zehnder (MZ) device with phase controller and delay line coupler with phase controller (MZ with unequal arms). Apart from these, there is an array of waveguide grating components.

#### 3.1  Basic Components of Integrated Waveguide Devices

As discussed earlier, integrated waveguide devices are based on two types of basic components passive components and active components. Here, we tried to discuss basic passive components like DC, TMI and MMI couplers and array waveguide grating components.

#### 3.1.1  Directional Coupler

Figure 3.1 shows a three-dimensional (3D) view of a typical asymmetric directional waveguide coupler consisting of two rectangular waveguides – waveguide-1 of width w 1 and thickness t 1 and waveguide-2 of width w 2 and thickness t 2, where β 1 and β 2 are the propagation constants in wave guides 1 and 2 before coupling, respectively. The refractive indices of spacing in the coupling region, core-1, core-2 and their surroundings are n 3, n 2, n 4 and n 1, respectively. The gap between two waveguides in the coupling region is h. The input powers P 1 and P 2 are incident in waveguide-1 and waveguide-2, respectively, when the output powers P 3 and P 4 are found in waveguide-1 and waveguide-2, respectively, after coupling. The coupling takes place in the 0 < z < L region in which the even and odd modes can propagate with propagation constants βe and βo. The phase shift between the even and odd modes becomes π when the propagation distance L π is given by [14]

Figure 3.1   A 3D view of an asymmetric DC of coupling length L consisting waveguide-1 and -2.

3.1a $L π = π / ( β e − β o )$

In a symmetrical DC where t 1 =t 2, n 2 =n 4 and w 1 = w 2, i.e., β 1 = β 2, considerable coupling occurs in the h < 8 μm range [18]. On the other hand, in an asymmetrical DC where t 1t 2, n 2n 4 and w 1w 2, and hence, β 1β 2, the coupling is not noticeable unless h is less than 5 μm. The power transfer due to mode coupling is generally characterized by a phase mismatch (β 1β 2) between the two waveguides, and the coupling coefficient is determined by [14]

3.1b $k = 1 2 ( β e − β o )$

To study mathematical analysis of DC, it is required to know coupled mode theory, which is discussed in the next section.

#### 3.1.1.1  Coupled Mode Theory

Coupled mode theory is a powerful tool for studying the optical waveguide coupling behavior. The concept of coupled mode theory is based on two-mode coupling theory. It is seen that when the energy is incident on one of the waveguides, then there is a periodic exchange between two waveguide-1 and 2. To explain the coupling behavior, we should know the coupled mode equations, which describe the variation of amplitude of modes propagating in each individual waveguide of the coupler.

The coupled mode equations may be written as [23]

3.2 $d a d z = − j β 1 a ( z ) − j k 12 b ( z )$
3.3 $d b d z = − j β 2 b ( z ) − j k 21 a ( z )$

The k 12 and k 21 represent the strength of coupling between two modes and are also called as coupling coefficients. In the absence of coupling, k 12 =k 21 = 0.The coupling coefficients depend on the waveguide parameters, separation between the waveguides in coupling region h and wavelength.

#### 3.1.1.2  Power Transferred between Two Waveguides Due to Coupling

In order to solve coupled mode equations, we have considered the trial solutions of equations (3.1) and (3.2) as follows [14]:

3.4 $a ( z ) = a 0 e − j β 1 z b ( z ) = b 0 e − j β 2 z }$

Substituting a(z) and b(z) in equations (3.11) and (3.12), we get

3.5 $a 0 ( β − β 1 ) − k 12 b 0 = 0$
3.6 $b 0 ( β − β 2 ) − k 21 a 0 = 0$

So, we can write from equations (3.14) and (3.15),

3.7 $β 2 − β ( β 1 + β 2 ) + ( β 1 β 2 − k 2 ) = 0$

Thus,

3.8 $β e , o = 1 2 ( β 1 + β 2 ) ± [ 1 4 ( β 1 − β 2 ) 2 + k 2 ] 1 / 2$

where

3.9 $k = k 12 k 21$

In the coupling region, there are two independent modes called as even and odd modes propagating with propagation constants β e and β o , respectively. The suffixes e and o represent even and odd modes, respectively. The general solutions are written as [14]

3.10 $a ( z ) = a e e − j β s z + a o e − j β a z$
3.11 $b ( z ) = { ( β e − β 1 ) / k 12 } a e e − j β e z + { ( β o − β 1 ) / k 12 } a o e − j β 0 z$

where a e and a o are the amplitudes of even and odd modes, respectively. Equations (3.10) and (3.11) are coupled wave fields in waveguide-1 and 2, respectively. The behavior of the coupled waves can be determined by obtaining propagation constants. Since the waves in the two waveguides are propagated in the same direction in the case of DC, the propagation constants are β 1 >0 and β 2 >0, respectively. The solutions of the coupled mode equations are rewritten as

3.12 $a ( z ) = ( a e e − j k 2 + δ ​ β 2 z + a o e j k 2 + δ ​ β 2 z ) e j β a v z b ( z ) = [ { ( β e − β 1 ) / k 12 } a e e − j k 2 + δ ​ β 2 z + { ( β o − β 1 ) / k 12 } a 0 e − j k 2 + δ ​ β 2 z ] a a e − j β a v z$

where 2δβ = β1 β 2 and 2βav = β 1 + β 2. The constants ae and ao for even and odd modes are determined by boundary conditions. We assume that at z = 0, the mode is launched in waveguide-1 with unit power and there is no power in waveguide-2. By considering boundary conditions, the power flows in waveguide-2 and 1 are given by

3.13 $P 4 / P 1 = | A ( z ) | 2 = 1 − k 2 k 2 + δ ​ β 2 sin 2 [ ( k 2 + δ ​ β 2 ) 1 / 2 z ]$
3.14 $P 3 / P 1 = | B ( z ) | 2 = k 2 k 2 + δ ​ β 2 sin 2 [ ( k 2 + δ ​ β 2 ) 1 / 2 z ]$

where $k = k 12 k 21$

The powers of waves propagating along two guides vary periodically. The maximum power transfer occurring at a distance L π is obtained as [24,25]

3.15 $P 4 , max / P 1 = 1 1 + ( δ β / k ) 2 .$

where $L π = π 2 k 2 + δ β 2$

As δβ → 0, the maximum power transfer increases. At δβ = 0 there is a complete power transfer between two waveguides. This is called as synchronous or symmetric DC (β 1 = β 2).

#### 3.1.1.3  Coupling Coefficient

The coupling coefficient of asymmetric DC with gap h between the coupling waveguides (2D model) derived by Marcuse [24] is written as

3.16 $k = | k | = 2 K 2 K 4 γ 3 e − h γ 3 k 0 2 β { ( n 2 2 − n 3 2 ) ( n 4 2 − n 3 2 ) ( w 1 + 1 / γ 1 + 1 / γ 3 ) ( w 2 + 1 / γ 1 + 1 / γ 3 ) } 1 / 2$

where

• $K 2 = n 2 2 k 0 2 − β 2 , K 4 = n 4 2 k 0 2 − β 2$
• $γ 3 = β 2 − n 3 2 k 0 2$
• $k 0 = 2 π / λ$

The propagation constants for even and odd modes are given by

3.17 $β e = β + k β 0 = β − k }$

#### 3.1.2  MMI Coupler

Figure 3.2a shows the schematic diagram of M × M MMI device in which the central structure is a multimode waveguide designed to support a large number of modes (typically ≥ 3). In order to launch light into and recover light from the multimode waveguide, a number of access waveguides (usually single-mode waveguides) are placed at its beginning and end of the central structure of width w mmi and thickness t. Such devices are generally called as M × M MMI couplers, where M is the number of input/output access waveguides. The refractive indices of MMI core and cladding are n 2 and n 1 respectively.

Figure 3.2   (a) A 3D MMI coupler with M number of input and M number of output access waveguides. (b) A 2D representation of an M × M MMI coupler.

The principle of operation of MMI is based on self-imaging by which the input field is replicated in single or multiple images periodically along the propagation direction of the waveguide. There are a number of methods to describe the self-imaging phenomena – ray-optics approach [26], hybrid methods [27], guided mode propagation analysis [28], etc. The guided mode propagation analysis is probably the most comprehensive method to analyze self-imaging in multimode waveguide, because it not only supplies the basis for numerical modeling and design but also explains the mechanism of MMI.

In MMI waveguide for wide width, the electric field is present along the Y direction in TE mode, and for TM mode the electric field is present along the X direction. This follows the field distribution of TE and TM modes in Figure 3.2b and Figure 3.3, respectively.

Figure 3.3   A schematic diagram of a TMI coupler of coupling length L.

#### 3.1.2.1  Guided Mode Propagation Analysis

The self-imaging phenomena should be analyzed by 3D M × M multimode structures as shown in Figure 3.2b. As the lateral dimensions are much larger than the transverse dimensions, it is justified to assume that the modes have the same transverse behavior everywhere in the waveguide. So, the problem can be analyzed using two-dimensional (2D) (lateral and longitudinal) structures, as shown in Figure 3.2b. The analysis based on 2D representation of the multimode waveguide can be obtained from the actual 3D physical multimode waveguide by effective index method [11].

The input field profile H(y, 0) incident on MMI coupler is summation of mode field distribution of all modes in 2D approximation as follows [29],

3.18 $H ( y , 0 ) = ∑ i b i H i ( y )$

where b i is the mode field excitation coefficient which can be estimated using overlap integrals based on the field orthogonality relations and H i (y) = mode field distribution of the ith mode.

The composite mode field profile at a distances inside a multimode coupler can be represented in 2D representation as a super position of all guided modes [29]:

3.19 $H ( y , z ) = ∑ i = 0 m − 1 b i H i ( y ) exp [ j ( β 0 − β i ) z ]$

where m is the total number of guided modes and βi is the propagation constant of the ith mode. For high index contrast, it is approximately written as [28]

3.20 $β i ≈ k 0 n r − ( i + 1 ) 2 π λ 4 n r w e 2$

where

3.21 $w e = w m m i + w p = equivalent width or effective width$

w mmi = physical width of MMI coupler

3.22 $w p = λ π ( n 1 n r ) 2 σ ( n r 2 − n 1 2 ) − 1 / 2 = lateral penetration depth related to Goos-Hahnchen shift$

n r is the effective index of the MMI core, w mmi is the width of the multimode waveguide, n 1 is the refractive index of multimode wave guide cladding is the wavelength and k 0 = 2π/λ. σ = 0 for TE mode and σ = 1 for TM mode. Defining Lπ as the beat length of the two lowest order modes, it is given in Ref. [28] as

3.23 $L π = π β 0 − β 1 ≈ 4 n r w e 2 3 λ$

where β 0 = propagation constant of fundamental mode and β 1 = propagation constant of first-order mode.

#### 3.1.2.2  Power Transferred to the Output Waveguides

At the end of the MMI section, optical power is either transferred to the output waveguide or lost out at the end of the multimode waveguide. Again, the mode field at the access waveguide of same width, w is assumed to be mode 0. Each mode of the MMI coupler contributes to mode 0 at the output access waveguide. The mode field of the output waveguide is the sum of the contribution of all the modes guided in the MMI section. So, the mode field at the Mth waveguide can be written as [29,30]

3.24 $H M ( y , L ) = ∑ i = 0 M − 1 c M , i H i ( y ) exp [ j i ( i + 2 ) π L 3 L π ]$

where cM, i = measure of field contribution of ith mode to Mth output waveguide. The cM, i is evaluated from a simple sinusoidal mode analysis [30].

In MMI coupler, there are two types of interference – general interference and restricted interference. In the case of general interference, the self-imaging mechanism is independent of modal excitation and the single image is formed at a distance [28]

3.25 $L = p ( 3 L π )$

where p = even for direct image and p = odd for mirror image. The multiple images are formed at

3.26 $L = p 2 ( 3 L π )$

In the case of restricted interference, there is a restriction of excitation of some selected modes. There are two types of restricted interference – paired and symmetric. In the case of paired interference [28], and N-fold images are formed at a distance, $L = p N ( L π )$ where p ≥ 0 and N ≥1 are integers having no common divisor. In the case of symmetric interference and N-fold images are formed at a distance $L = p N ( 3 L π / 4 )$ , where p ≥ 0 and N ≥ 1 are integers having no common divisor. The N images are formed with an equal spacing of w mmi /N. The N-way splitter can be realized using this principle [31]. The transition from DC to MMI structure with Ridge structure by reducing etch depths in between two coupling waveguides of DC is reported by Darmawan et al. [15].

#### 3.1.3  TMI Coupler

Figure 3.3 shows the schematic diagram of a TMI coupler consisting of two single-mode entrances of core width w and thickness and exit waveguides of same size and a TMI core of width 2w and length L. The operating principle of the TMI coupler is based on TMI in the coupling region. When light is incident on one of the input waveguides, only fundamental and first-order mode with propagation constants β 00 and β 01, respectively, are excited in the coupling region [16,22]. These two modes interfere with each other while propagating along the direction of propagation. Depending on the relative phase differences Δφ at the end of the coupling region, the light powers are coupled into two output waveguides.

#### 3.1.3.1  Power Transferred to Output Waveguides

Like DC, in the case of TMI DC, we have to use the same coupled mode equations for the calculation of power transfer to the output waveguides. So, the powers coupled into two single-mode identical waveguides of TMI coupler are approximately given by [16]

3.28 $P 3 P 1 = sin 2 ( Δ φ / 2 )$
3.29 $P 4 P 1 = cos 2 ( Δ φ / 2 )$

where

3.30 $Δ φ = Δ β . L , L = length of multimode region and Δ β = β 00 − β 01$

The coupling length for getting maximum power transfer from waveguide-1 to -2 is found to be

3.31 $L c o = π n / Δ β = n L π$

where is an odd integer and

3.32 $L π = π / Δ β$

#### 3.1.4  Array Waveguide Grating

Figure 3.4 shows a schematic structure of Array waveguide grating (AWG) [32,33] having N × N input star coupler and N × N output star coupler. It has two passive-star couplers connected to each other by a grating array. The first star coupler consists of N inputs and N′ outputs, (where NN′), whereas the second one has N′ inputs and N outputs. The inputs to the first star are alienated by an angular distance of a and their outputs are estranged by an angular distance. The grating array has N′ waveguides, with lengths l 1, l 2, … l N , where, l 1 <l 2 < … < l N. The difference in length between any two adjacent waveguides is a constant Δl. In the first star coupler, a signal on a given wavelength entering from any of the input ports is split and transmitted to its N′ outputs which are also N′ inputs of the second star coupler. The signal transmitted through the grating array obtaining a different phase shift in each waveguide depends on the length of the waveguides and the wavelength of the signal. The constant difference in the lengths of the waveguides makes a phase difference of β Δl in adjacent waveguides, where β = 2πn eff /λ is the propagation constant in the waveguide, n eff is the effective refractive index of the waveguide and λ is the wavelength of the light. At the input of the second star coupler, the phase difference in the signal shows that the signal will constructively recombine only at a single output port. Signals of different wavelengths coming into an input port will each be separated to a different output port. Also, different signals using the same wavelength is simultaneously incident on different input ports, and still not interfere with each other at the output ports.

Figure 3.4   Array waveguide grating.

Two signals of same wavelength coming from two different input ports do not interfere with each other in the grating because there is an additional phase difference obtained by the distance between the two input ports. The two signals will be joint in the grating but is separated out again in the second star coupler and directed to different outputs. This phase difference is given by kR(pq)αα′, where k is a propagation constant which is not a function of wavelength, where R is the constant distance between the two foci of the optical star, p is the input port number of the router and q is the output port number of the router. The total phase difference is given by

3.33 $ϕ = 2 π Δ l λ + k R ( p − q ) α α ′$

The transmission power from a particular input port p to a particular output port q is maximum when the phase difference is equal to an integral multiple of 2π. Thus, for only one wavelength λ, ϕ is satisfied with an integral multiple of 2π, and this λ is transmitted from input port p to output port q. Alternately, for a given input port and a given wavelength, the signal is transmitted to the output port.

#### 3.1.5  MZ Active Device

Figure 3.5 shows a 2 × 2 MZ active device [34–36] consisting of an MZ section of equal arm length with phase controllers and two 3-dB DCs of coupling lengths L 0 and L 1. The phase controller is a device that changes the phase of the wave using external power P. The input power P 1 is incident in waveguide-1 when the output powers P 3 and P 4 are obtained as cross and bar states, respectively. The 3-dB coupler consists of two waveguides having a small gap h between them. The core width of waveguide is w. The refractive index of core and cladding are n 2 and n 1 respectively.

Figure 3.5   A schematic diagram of a planar waveguide-type TOMZ switching unit with 3-dB DC and a heater of length L H .

The coupling section of DC can be described with the coupled mode equations of DC with a small gap as follows:

3.34 $d A d z = − j K B and d B d z = − j K A$

where A and B are the normalized electric fields in the upper and lower waveguides, K = coupling coefficient of DC. There are two orthogonal polarization modes propagating in the planar waveguide of thermooptic MZ (TOMZ) device – TE and TM polarization modes.

#### 3.1.5.1  TE Polarization

In the case of TE polarization modes, analytical solution of equation (3.63) following equations (3.21) and (3.22) for each individual (kth) coupler of the length L k (k = 0, 1) is given by

3.35 $A ( L k ) = A ( 0 ) cos ( K T E L k ) − j B ( 0 ) sin ( K T E L k )$
3.36 $B ( L k ) = B ( 0 ) cos ( K T E L k ) − j A ( 0 ) sin ( K T E L k )$

where A(Lk) and B(Lk) are amplitudes of coupling waveguide-1 and 2, respectively, with length L k . K TE is the coupling coefficient of TE mode for DC with a small coupling gap. In calculating K TE by using Marcuse’s equation [30], the propagation constant is determined from dispersion equations for TE mode [18]. Equations (3.35) and (3.36) represent the coupled electric fields in the upper and lower waveguides after coupling in the coupling region of length L k . In matrix form, equations (3.35) and (3.36) can be written as

3.37 $( A ( L k ) B ( L k ) ) = T k ( A ( 0 ) B ( 0 ) ) = ( C k T E − j S k T E − j S k T E C k T E ) ( A ( 0 ) B ( 0 ) )$

where $S k T E = sin ( K T E L k )$

3.38 $C k T E = cos ( K T E L k ) and T k = ( C k T E − j S k T E − j S k T E C k T E )$

The MZ section is a phase shifter in which phase changes with heating power P applied on the device via a thin film heater. In the case of TE mode, this phase change occurs mainly due to thermooptic effect with application of heating power [10]. The electric fields in the upper and lower waveguides are written as

3.39 $A ( Z ) = A ( 0 ) exp ( − j Δ ϕ ( P / 2 ) ) B ( Z ) = B ( 0 ) exp ( j Δ ϕ ( P ) )$

In matrix form, we can write [37]

3.40 $( A ( Z ) B ( Z ) ) = T M Z T E ( A ( 0 ) B ( 0 ) ) = ( exp ( − j Δ φ ( P ) / 2 ) 0 0 exp ( j Δ φ ( P ) / 2 ) ) ​ ( A ( 0 ) B ( 0 ) )$

where

3.41 $T M Z T E = ( exp ( − j Δ φ ( P ) / 2 ) 0 0 exp ( j Δ φ ( P ) / 2 ) )$

ϕ(P) = thermooptic phase change obtained with the application of heating power P for TE mode

3.42 $= 2 π λ d n d T Δ T c L H$
• L H = heater length,
• $d n d T$ = thermooptic refractive index coefficient
• λ = wavelength and ∆T c = temperature difference between two cores.

The transfer matrix of MZ coupler for TE mode is written as

3.43 $T = T 1 T E T M Z T E T 0 T E$

The output electric field $A o u t T E$ and $B o u t T E$ for upper and lower waveguide scan be expressed as

3.44 $( A o u t T E B o u t T E ) = T 1 TE T M Z T E T 0 T E ( A i n T E B i n T E )$
3.45 $= ( T 21 T E − T 22 T E * T 22 * T 21 T E * ) ( A i n T E B i n T E )$

where $A i n T E$ and $B i n T E$ are the input fields of TE mode in upper and lower waveguides, respectively. $T 21 T E$ and $T 22 T E$ are the matrix elements with relation $| T 21 T E | 2 + | T 22 T E | 2 = 1$ . From equation (3.73), we can write

3.46 $A o u t T E = T 21 T E A i n T E − T 22 T E * B i n T E$
3.47 $B o u t T E = T 22 T E A i n T E + T 21 T E * B i n T E$

Considering input field $B i n T E$ in lower waveguide only, we can write equations (3.46) and (3.47) as follows:

3.48 $A o u t T E = − T 22 T E * B i n T E$
3.49 $B o u t T E = T 21 T E * B i n T E$

The cross-state transmitted power function for TE mode is written as

3.50 $( P 3 / P 1 ) T E = | T 22 T E | 2 = | a 0 T E | 2 + | a 1 T E | 2 + 2 a 0 T E a 1 T E cos [ Δ ϕ ( P ) ]$

where $a 0 T E = C 0 T E S 0 T E$ and $a 1 T E = S 0 T E C 1 T E$ . Considering 3-dB couplers of same coupling length (L 0 = L 1) in both sides of the MZ section, we get $a 0 T E = a 1 T E = 0.5$ . The cross- and bar-state transmitted powers of TE mode can be written as

3.51 $( P 3 / P 1 ) T E ~ cos 2 [ ( Δ ϕ ( P ) / 2 ) ]$
3.52 $( P 4 / P 1 ) T E ~ sin 2 [ ( Δ ϕ ( P ) / 2 ) ]$

Similarly, the cross- and bar-state powers of TM mode are written as

3.53 $( P 3 / P 1 ) T M ≈ cos 2 [ ( Δ ϕ ( P ) T M / 2 ) ]$
3.54 $( P 4 / P 1 ) T M ≈ sin 2 [ ( Δ ϕ ( P ) T M / 2 ) ]$

The phase change is obtained due to the application of external power P. Two types of external power can be applied – thermooptic and electrooptic powers. Due to these powers, there are two types of MZ devices – TOMZ device and electrooptic MZ (EOMZ) device. The details of these devices are discussed later in this chapter.

#### 3.2  Wavelength Division Multiplexer/Demultiplexer-Based Waveguide Coupler

The wavelength multiplexer/demultiplexer can be developed using basic waveguide coupler components such as DC), TMI coupler and MMI coupler. The multiplexing is achieved by cross coupling of one wavelength and bar coupling of the other wavelength, and in the case of demultiplexing, it is vice versa. There are different types of wavelength multiplexer/demultiplexer – DC-based, TMI-based and MMI-based multiplexer/demultiplexer [5,6,14]. Figure 3.6a shows the basic structure of a four-channel wavelength multiplexer/demultiplexer based on a waveguide coupler in which there are two waveguide couplers of L π for wavelength λ 1 in the first level and one coupler with beat length 2L π. The figure also shows the working of multiplexing wavelengths λ 1, λ 2, λ 3 and λ 4. It is seen that wavelength multiplexing/demultiplexing made by using TMI coupler is more compact than that using DC and MMI coupler.

Figure 3.6   (a)Four-channel cascaded multiplexer/demultiplexer, (b) variation of coupling length with Δn (n 1 =1.447, V = 2.4).

#### 3.2.1  WDM-Based TMI Coupler

For TMI coupler-based multiplexing/demultiplexing of two wavelengths λ 1 and λ 2, we have to consider four guided propagation constants $β 00 λ 1 , β 01 λ 1 , β 00 λ 2 and β 01 λ 2$ , and the required coupling length can be approximately written as [6]

3.55 $L c = π Δ β | λ 1 − Δ β | λ 2$

where

3.56 $Δ β | λ 1 = ( β 00 λ 1 − β 01 λ 1 ) , Δ β | λ 2 = ( β 00 λ 2 − β 01 λ 2 )$

These propagation constants are determined by using an effective index method [18] where $β 00 λ 1 , β 01 λ 1 , β 00 λ 2 and β 01 λ 2$ are ~6.0556, 5.9807, 5.974 and 5.9023 (μm)−1, respectively, for the wavelengths λ 1 =1.52 μm and λ 2 =1.54 μm, of the coupler with Δn = 5%. L c is calculated as 980 μm, which is about six times less than that of the TMI coupler with Δn =0.6%, using Ti:LiNbO3 [20].

Keeping the normalized frequency ~2.4 for single-mode waveguide access of TMI coupler, we have determined the variation of coupling length of multiplexer/demultiplexer with Δn for wavelengths 1.52 and 1.56 μm using equation (3.17) as shown in Figure 3.6b. The experimental result of TMI multiplexer using Ti:LiNbO3 reported in Ref. [31] is represented by a black rectangle showing the almost agreement with theoretical value. The black circle represents L c obtained experimentally by us with Δn ~2% and 5%, showing almost close to theoretical value [14]. The curve in the figure has two slopes – slope-1 which represents the compact TMI multiplexer region where L c > 980 μm and its corresponding Δn <5% and slope-2 which represents the ultra compact TMI multiplexer region, where L c < 980 μm and its corresponding Δn >5%. It is evident from the figure that L c in slope-2 decreases slowly with Δn in comparison with slope-1.

Figure 3.6a shows the block diagram of a four-channel multiplexer/demultiplexer consisting three TMI couplers – having two couplers of the same coupling length L c and other one of 2L c . For the four-channel multiplexer/demultiplexer with Δn =5%, considering λ 1 =1.52, λ 2 =1.54, λ 3 =1.56 and λ 4 =1.58 μm, the device length can be obtained approximately as ~5 mm.

#### 3.3  Optical Switching

Optical switching is required to change the optical signal path from one input fiber to the other fiber or from one direction to the other. The concept to switch in originated from electronics field. In case of switching, two basic types are circuit switching and cells witching [38]. In an optical field, circuit switching provides wavelength routing, and cell switching gives optical packet switching and optical burst switching. For the transparency of signals considered here, there are two types of switching: opaque and transparent. The switching devices are of two types: logic and relational switching.

Logic switching is carried out by a device where the data (or the information-carrying signal) launched into the device makes the control over the state of the device in such a way that some Boolean function, or a combination of Boolean functions, is carried out on the inputs. In a logic device, form at and rate of data are changed or converted in intermediate nodes; thus, logic switching provides opaque switching. Further, some of its components perform the change of states or it switches as fast as or faster than the signal bit rate. Based on the logic device and ideal performance in electronic field, logic switching is used in an electronic field. But, traditional. optical–electronic–optical (o–e–o) conversion in optical networks is still widely applied due to having lack of proper logic devices operated in the optical domain. The most current optical networks use electronic processing and consider the optical fiber only as a transmission medium. Switching and processing of data are carried out by converting an optical signal back to its “native” electronic form. Such a network relies on electronic switches, i.e., logic devices. It shows a high degree of flexibility in terms of switching and routing functions for optical networks; however, the speed of electronics is not able to deal with the high band width of an optical fiber. Also, an electro optic conversion at an intermediate node in the network produces extra delay and cost. These factors make motivated toward the development of all-optical networks where optical switching components switch high-bandwidth optical data stream switch out electro optic conversion. Relational switching is used to set up a relation between inputs and outputs. The relation function depends on the control signals applied to it and is independent of the contents of the signal or data inputs. In switching devices, the control of the switching function is performed electronically, with the optical stream being transparently routed from a given input of the switch to a given output. Such transparent switching permits the switch to be independent of the data rate and format of the optical signals. Thus, the strength of a relational device permits signals at high bit rates to pass through it. Due to the limits of optical hardware, various kinds of optical switching devices basically use relational switching, which provides more advantages for optical networks in terms of optical hardware limits.

There are different optical/photonic switches – TOMZ switch [36], TMI switch [39], X-junction type switch [40], MMI switch [41,42], etc.

#### 3.3.1  MZ Switch

MZ switch consists of a 3-dB coupler and an MZ section of equal arms. The 3-dB coupler divides signal equally into two output access waveguides when power is incident into one of the input waveguides. Due to 3-dB effect, without phase change, within MZ section signal will be transferred to cross-state output waveguide. Through thermooptic or electrooptic effects, the path difference between two arms of MZ section can be changed. While the phase difference between signal of two arms is π, then the signal will be transferred into the bar-state output waveguide. There are different types of MZ switch – TOMZ switch and EOMZ switch. In TOMZ switch, the phase change in MZ arms is controlled by thermooptic effect via a thin film heater, whereas in EOMZ switch, the phase change in MZ arms is controlled by electroooptic effect via an electrode placed on one of the MZ arms. The 3-dB couplers are made of either DC or MMI coupler or TMI coupler.

#### 3.3.1.1  TOMZ Switch-Based DC

Figure 3.7 shows a TOMZ switch consisting of an MZ section of equal arm length with thermooptic phase controllers and two 3-dB DCs of coupling lengths L 0 and L 1. The thermooptic phase controller is a thin film heater, which changes the phase of the wave via thermooptic effect. The input power P 1 is launched into waveguide-1, and the output powers P 3 and P 4 are obtained as cross and bar states, respectively. The 3-dB coupler consists of two waveguides having a small gap h between them. The core width of the waveguide is w. The refractive index of core and cladding are n 2 and n 1 respectively.

Figure 3.7   A schematic diagram of a planar waveguide-type TOMZ switching unit with 3-dB DC and a heater of length L H .

There are two orthogonal polarization modes propagating in the planar waveguide of TOMZ device – TE and TM polarization modes.

#### 3.3.1.2  TE Polarization

The cross- and bar-state transmitted powers of TE mode obtained from equations (3.51) and (3.52) are rewritten as

$( P 3 / P 1 ) T E ~ cos 2 [ ( Δ ϕ ( P ) T E / 2 ) ]$
$( P 4 / P 1 ) T E ~ sin 2 [ ( Δ ϕ ( P ) T E / 2 ) ]$

where ∆ϕ(P) TE =thermooptic phase change due to application of heating power P for TE mode

3.57 $= 2 π λ d n d T Δ T c L H$
• L H =heater length,
• $d n d T$ = thermooptic refractive index coefficient
• λ = wavelength and ΔT c = temperature difference between two cores.

Similarly, the cross- and bar-state powers of TM mode obtained from equations (3.53) and (3.54) are rewritten as

$( P 3 / P 1 ) T M ≈ cos 2 [ ( Δ ϕ ( P ) T E / 2 + Δ ϕ s / 2 ) ]$
$( P 4 / P 1 ) T M ≈ sin 2 [ ( Δ ϕ ( P ) T E / 2 + Δ ϕ s / 2 ) ]$

where [Δϕ(P) TM = Δϕ(P) TE + Δϕs ]. The phase change with applying heating power arises not only due to isotropic thermooptic effect but also by an anisotropic stress optic effect when the waveguide is heated by a thin film heater locally [39,41]. This is called as secondary stress optical effect. When the waveguide is heated locally via the heater, the glass (SiO2) can expand freely to the Si substrate. But it cannot expand freely in the parallel direction, because it is surrounded by other glass (SiO2). So, a compressive stress occurs only in the parallel direction, and it mainly induces a refractive index increase in the TM mode. The refractive index increase due to stress optic effect provides an extra phase change Δϕ S in TM mode apart from the thermooptic phase change with application of heating. The extra stress optic phase change in TM mode is given by

3.58 $Δ ϕ S = 2 π λ d ( n T M − n T E ) d T Δ T c L H$

where $d ( n T M − n T E ) d T = temperature rate of birefringence produced by heater$ .

The cross-and bar-state powers are obtained as a function of heating power applied on the MZ section of the device. Since both sides of MZ section 3-dB couplers are used, the TOMZ device shows a cross state where signal will be fully transferred to the other waveguide. As the heating power applied on MZ section increases, the power transferred to cross state decreases, and at a particular heating power, the power will remain in parallel state waveguide and the transferred power to cross state becomes almost zero. The state is called as bar state. The heating power required to obtain bar state is called as bar state power, and at bar sate, the thermooptic phase Δϕ(P) is π. It is seen that due to anisotropic thermooptic effect, the stress optic phase is included in TM mode apart from the thermooptic phase as mentioned earlier. At bar state, a slight amount of power is transferred to cross state via TM mode. This provides a crosstalk of the switch. To reduce crosstalk, it is required to release the stress developed in the silica waveguide due to anisotropic thermooptic effect. Figure 3.8b shows an 8 × 8 optical matrix switch consisting of a 64 TOMZ device (Figure 3.8c) which has a switching power and response time of ~ 360 mW and 4.9 ms, respectively.

Figure 3.8   (a) Layout of an 8 × 8 optical matrix switch demonstrated by Kasahara et al. [2] using SiO2/SiO2-GeO2 waveguide. (b) Arrangement of eight switching units in each stage.

#### 3.3.1.3  EOMZ-Based DC

The balanced bridge interferometer switch (Figure 3.9) comprises an input 3-dB coupler having two input waveguides and at middle electrodes to allow changing the effective path length over the two arms, and a final 3-dB coupler [11]. Light incident on the upper waveguide is divided into half by the first coupler. With no voltage applied to the electrodes, the optical path length of the two arms enters the second coupler in phase. The second coupler acts like the continuation of the first, and all the light are crossed over to the second waveguide to provide the cross state. To achieve the bar state, voltage is applied to an electrode, placed over one of the interferometer arms to electrooptically produce a 180° phase difference between the two arms. In this case, the two inputs from the arms of the interferometer combine at the second 3-dB coupler out of phase, with the result that light remains in the upper waveguide.

Figure 3.9   An EOMZ-based 3-dB DC.

#### 3.3.1.4  MMI Coupler-Based MZ Switch

Figure 3.10 shows a 4 × 4 MMI coupler-based 4 × 4 optical switch [43] having five TOMZ structures. The switch-based SOI waveguide has length of 50 mm, response time of 30 μs and heating power of 330 mW. Each switching element uses two 3-dB MMI coupler on both sides of MZ section with a thermooptic phase changer. There is no heating in the MZ section, the switch is in cross state and when the heating power is applied to get thermooptic phase of π, then the switch is in cross state.

Figure 3.10   Architecture of an SOI 4 × 4 optical matrix switch demonstrated by Wang et al. [43] (L P = length of input/output waveguide, L = length of 3-dB coupler, L MZ = MZ section length = L H = heater length, L S = length of 4 × 4 optical matrix switch).

#### 3.3.1.5  TMI Coupler-Based MZ Switch

Figure 3.11 shows single MZ optical switching element [39] having two 3-dB TMI coupler on both sides of the MZ section with a thermooptic phase changer. There is no heating in the MZ section, the switch is in cross state and when the heating power is applied to get thermooptic phase of π, then the switch is in cross state. In cross state of the switch, P 4 ~0 and in bar state, P 3 ~ 0.

Figure 3.11   A schematic diagram of a TOMZ switch with a thin film heater of length L H , transition region of length L T and 3-dB TMI couplers of length L.

#### 3.3.2  X-Junction Switch

Figure 3.12a shows an X-junction switch structure [40] in which for a small intersection angle θthe symmetric X junction can be treated as a zero-gap DC with branches 1 and 4 forming the top waveguide and branches 2 and 3 the bottom waveguides. The actual pattern of the X junction is approximated by a staircase configuration along the direction of propagation. In the symmetric X junction, there is no mode conversion, and therefore there is no phase shift at the steps. For each lateral input mode two modes of equal amplitude (even and odd) existed in the symmetric junction. For the sake of simplicity, we restrict ourselves to the two fundamental TE modes of the waveguide system. Under these conditions, coupled mode equations are easily shown to be

Figure 3.12   An X-junction switch architecture.

3.59 $A i 1 = c i A i 0$

where A i1, A i0 are mode amplitudes before and after the step, respectively (i =1 for even and i =0 for odd mode). The coupling coefficient is given by

3.60 $c i = 2 β i 0 β i 1 β i 0 + β i 1 I i 0 , i 1 ( I i 0 , i 0 ⋅ I i 1 , i 1 )$

β i0 and β i1 are the local normal mode propagation constants before and after the steps. Overlap integrals are defined as

3.61 $I i m , i n = ∫ − ∞ ∞ E i m ( x ) ⋅ E i n ( x ) ⋅ d x$

where m, n = 0, 1. For simple field distributions, E im (x) and E in (x) are given by sinusoidal and exponential functions and overlap integrals are analytically obtainable. This prevents the need for the time-consuming numerical simulation.

The propagation of modes from one step to the other adds a phase factor Δz βim . There is also radiation at the steps. This radiation is modeling loss caused by the waveguide taper. The steps are appropriate approximations to the photomasks made by electron beam stair step raster scanning process. Since the propagation constants of even β e and odd modes β o are different (the difference Δβ (z) = β e β o ), their interference provides an optical power at each step. For a small intersection angle θthe symmetric Junction can be treated as a zero-gap DC with branches 1 and 4 forming the top waveguide and branches 2 and 3 the bottom waveguide. We get top and bottom waveguide optical powers as follows:

3.62 $P t ( z ) = ( A e − A o ) 2 + 2 A e A o cos 2 [ Δ β ( z ) z / 2 ]$
3.63 $P b ( z ) = ( A e − A o ) 2 + 2 A e A o sin 2 [ Δ β ( z ) z / 2 ]$

where z is the distance from the input plane z = ∑Δz, P t and P b are the optical powers in the top and bottom waveguides, respectively. Repeating this procedure, the power distribution is tracked along the device. For multimode operation each input mode must be considered separately. Corresponding even and odd modes give power distribution for this input mode. The total power distribution is the superposition of all the modes at each step. Rapid changes at the intersecting points are caused by coupling between converging guides and radiation losses. As a result, the power coupled to the top and bottom waveguides of output section of X-junction depends on an intersecting angle θ. The X junction is taken as an intersecting waveguide switch shown in Figure 3.13. The properly fabricated electrode is shown in the figure, where both cross and bar states can be electrooptically achieved with good crosstalk.

Figure 3.13   An X-junction electrooptic switch.

In this X-junction switch, Δβ(z) depends on the electric field E applied on the electrode. The X-junction device can be used as a thermooptic switch in which waveguide material is thermooptic materials and thermooptic heaters are used instead of electrodes [40].

#### 3.3.3  DC-Based Electrooptic Switch

Figure 3.14a shows a DC-based electrooptic switch [11,44] consisting of a pair of optical channel waveguides that are parallel and in close proximity over a finite interaction length. Light incident on one of the waveguides is transferred to the second waveguide through evanescent coupling. The coupling strength depends on the interwaveguide separation, and the waveguide mode size also depends on the optical wavelength and confinement factor of the waveguide. If the two waveguides are indistinguishable, complete coupling between the two waveguides is obtained at a beat length which is related to the coupling strength. However, by placing electrodes over the waveguides, the difference in propagation constants of the waveguides is sufficiently increased so that no light couples between the two waveguides. Therefore, the cross state is obtained with the application of no voltage, and the bar state is obtained with the application of a switching voltage. Unfortunately, the interaction length is required to be accurate for good isolation, and these couplers are wavelength specific.

Figure 3.14   A DC-based electrooptic switch.

Switch fabrication tolerance, as well as the ability to achieve good switching for a relatively wide range of wavelengths, is overcome by using the so-called reversed delta-beta coupler (Figure 3.14b). In this device, the electrode is split into at least two sections. The cross state is obtained by applying equal and opposite voltages to the two electrodes.

Figure 3.15   Switches based on amplifier gates.

Other types of switches include the mechanical fiber-optic switch and the thermooptic switch. These devices show slow switching (about milliseconds) and is used in circuit-switched networks. One mechanical switch has two ferrules, each with polished end faces that can rotate to switch the light appropriately. Thermooptic waveguide switches, on the other hand, are fabricated on a glass substrate and are operated by the use of the thermooptic effect. One such device uses a zero-gap DC configuration with a heater electrode to increase the waveguide index of refraction.

#### 3.3.4  Gate Switches

In the N × N gate switch-based amplifier gates [45], each input signal first passes through a 1 × N splitter. The signals then pass through an array of N 2 gate elements and are then recombined in N × combiners and sent to the N outputs. The gate elements can be implemented using optical amplifiers that can either be turned on or off to pass only selected signals to the outputs. The amplifier gains can compensate for coupling losses and losses incurred at the splitters and combiners. A 2 × 2 amplifier gate switch is shown in Figure 3.15. A disadvantage of the gate switch is that the splitting and combining losses limit the size of the switch.

#### 3.4  Optical Crossconnect (OXC)

An optical crossconnect (OXC) makes switching operation of wavelength having optical signals from input to output ports with rout specified for destination [43]. It is based on an optical matrix switch. As per input and output ports in OXC, the number of inputs and outputs of optical matrix switch is selected. The optical matrix switch is based on basic switch elements, and for N × N optical matrix switch, the number of switch elements/units is 2N − 3. These elements are usually considered to be wavelength insensitive, i.e., incapable of demultiplexing different wavelength signals on a given input fiber. A basic crossconnect element is a 2 × 2 crosspoint element which is shown in Figure 3.16. There are two states of 2 × 2 crosspoint element – cross and bar states. In cross state, the signal from the upper input port is routed to the lower output port, and the signal from the lower input port is routed to the upper output port. In the bar state, the signal from the upper input port is routed to the upper output port.

Figure 3.16   A 2 × 2 crossconnect element.

There are two types of OXC architectures demonstrated using two types of technologies:

1. the generic directive structure where light is physically transmitted to one of two different outputs.
2. the gate switch structure in which optical amplifier gates are made to select and filter input signals to specific output ports.

Different types of switching elements are already discussed earlier. These switching elements are based on DC, X-branching structure, MMI coupler, TMI coupler, MZ structure, etc.

#### 3.4.1  Architecture-Based Crossconnect

Figure 3.17 shows OXC crossconnect based on Clos architecture [46]. It is used for building multistage TDM switching systems. The advantage is that it implements the fewest switching crosspoints for providing a large range of scalability that provides strict or rearrangeably non-blocking traffic paths.

Figure 3.17   A 3-stage Clos architecture.

In the figure, the number of second-stage switches is dependent on blocking: in fully non-blocking, k ≥ 2n − 1; in rearrangeably non-blocking, kn [47]. Crossconnect Switch Architecture up to 2048 × 2048 ports and 10 Gbps per port are also reported.

#### 3.4.2  Micro Electro Mechanical Systems (MEMS)

Recently, micro electro mechanical systems (MEMS) is one of the most promising approaches for large-scale OXCs. Optical MEMS-based switches are either mirrors and membranes based or planar moving waveguides based [46,48]. MEMS-based switches follow two major approaches – 2D and 3D approaches. The 3D optical MEMS based on mirror is more preferred for compact, large-scale switching fabrics. This type of switch has high application flexibility in network design due to low insertion loss and low wavelength dependency under various operating conditions. Furthermore, this switch shows minimal degradation of optical signal-to-noise ratio caused by crosstalk, polarization-dependent loss (PDL), and chromatic and polarization mode dispersions.

Figure 3.18 shows the basic unit of a 3D MEMS optical switch. The optical signals passing through the optical fibers at the input port are switched independently by the gimbal-mounted MEMS mirrors with two- axis tilt control and are then focused onto the optical fibers at the output ports. In the switch, any connection between input and output fibers is accommodated by controlling the tilt angle of each mirror. As a result, the switch can handle several channels of optical signals directly without costly optical–electrical or electrical–optical conversion. The 3D MEMS-based 0–0–0 switch is built in sizes ranging from 256  × 256 to 1000 × 1000 bidirectional port machines [48]. In addition, 8000 × 8000 ports may be fabricated within the foreseeable future. The port count is only one dimension to the scalability of a 0–0–0 switch. All-optical switch based on this type is bit-rate and protocol independent. The combination of thousand ports and bit-rate independence may provide unlimited scalability.

Figure 3.18   A schematic diagram of a 3D MEMS optical switch.

Optical MEMS approach provides miniature devices with optical, electrical, and mechanical functionalities at the same time, fabricated using batch process techniques as derived from microelectronic fabrication. Optical MEMS provides intrinsic characteristics for very low crosstalk, wavelength insensitivity, polarization in sensitivity and scalability.

Optical ADM (OADMs) provide capability to add and drop wavelength traffic in the network like synchronous optical network (SONET) ADMs. Figure 3.19 shows a generic ADM placed at network nodes connecting one or two (bidirectional) fiber pairs and making a number of wavelength channels to be dropped and added. This reduces the number of unnecessary optoelectronic conversions, without affecting the traffic that is transmitted transparently through the node.

An OADM is employed in both linear and ring network architectures operating in either fixed or reconfigurable mode [9,10]. In fixed OADMs, the add/drop and through channels are predetermined, and the adding and dropping of wavelength channels are not tuned by external arrangement. In reconfigurable OADMs, the channels that are added/dropped pass through the node with dynamically reconfigured external arrangement as required by the network. Thus the reconfigurable OADMs are more complex but more flexible as they provide on-demand provisioning without manual intervention.

Reconfigurable OADMs are classified into two categories – partly reconfigurable and fully reconfigurable architectures [9,10,49]. In partly reconfigurable architectures, there is a capability to select the predetermined channels to be added/dropped, with a predetermined connectivity matrix between add/drop and through ports, restricting the wavelength-assignment function. Fully-reconfigurable OADMs provide the ability to select all the channels to be added/dropped, but they also offer connectivity between add/drop and through ports, which enables flexible wavelength assignment with the use of tunable transmitters and receivers. Reconfigurable OADMs have two main generations. The first is mainly applied in linear network configurations and support no optical path protection, while the second provides optical layer protection.

Two types of fully reconfigurable OADMs are – wavelength-selective (WS) and broadcast-selective (BS) architectures [43], which are shown in Figure 3.20. The WS architecture has wavelength demultiplexing/multiplexing and a switch fabric interconnecting express and add/drop ports, whereas the BS has passive splitters/couplers and tunable filters. The overall loss obtained by the through path of the BS is noticeably lower than that of the WS approach, significantly improving the optical signal-to-noise ratio (OSNR) of the node, and therefore its performance is better in a transmission link or ring. In addition, the BS provides superior filter concatenation performance, features such as drop and continue, and good scalability in terms of add/drop percentage.

Figure 3.20   Fully reconfigurable BS OADM architectures.

The theory and applications of cascaded MZ (CMZ) filters consisting of delay lines (MZ coupler with unequal arms) are already reported by different authors [9,10,49,50], in which Y symmetry CMZ filter is chosen for add/drop filter application, because of lower pass band in comparison to point symmetry CMZ couplers [9]. Figure 3.21 illustrates 2 × 2 N-stage Y symmetry CMZ coupler having N number of delay line section with arm lengths L A and L B (where path difference between two arms ΔL = L A L B ), thin film heater of length L H (L H L A ) and width W H on the curved arm of MZ section and N +1 number of TMI) couplers of width 2w (where w = width of single-mode access waveguide). The core and cladding are chosen to be SiON and SiO2 respectively, due to availability of wide index contrast, compatibility with conventional silicon-based IC processing, high stability, etc. In the figure, the couplers of the device are considered to act as one long coupler with total coupling length L distributed in different ways over all individual couplers of the circuit, where $L = ∑ k = 0 N L i$ and L i is the length of the ith coupler (i = 0, 2, 3, … N). The coupling length distribution which controls transmission characteristics of the filter is discussed later. Each TMI coupler consists of a two-mode coupling region in which only fundamental and first-order mode with propagation constants β 00 and β 01, respectively, are excited in the coupling region [11], and coupling coefficient (k T ) of TMI coupler is represented by (β 00β 01)/2. From the geometry of the figure length of each delay line section is obtained as L B H 2L, where H is the height of the delay line section. The refractive indices of the core and its cladding are n 1 and n 2 respectively. The input power P 1 is launched into lowermost waveguide and the output powers P 3 and P 4 are cross-and bar-state powers, respectively. The normalized cross-state power of N-stage Y symmetric CMZ coupler is derived as [10]

Figure 3.21   N-stage Y symmetric CMZ circuit using TMI coupler and thin film.

3.64 $P 3 P 1 = { ∑ k = 0 N | a k | 2 + 2 ∑ i = 0 N a i ∑ k = i + 1 N a k cos [ ( k − i ) Δ ϕ ( λ , Δ L , P ) ] } e − N α L B$

where α is bending loss coefficient function of bending radius [10,18]. The coefficients a k of normalized cross-state power are estimated from the coupling coefficient k T of TMI couplers [10]. Δϕ(λ, ΔL, P) is the phase difference for the length difference between two arms of delay line section plus the phase shift obtained by heating the curved arm with heating power P and is written as[10]

3.64 $Δ φ ( λ , Δ L , P ) = 2 π [ φ ( Δ L ) + φ ( P ) ] { 1 − λ − λ r e f λ r e f }$

where $φ ( Δ L ) = n e f f Δ L λ$ , n eff is the effective index at wavelength λ and λ ref is the reference wavelength.

When the waveguide is heated through the thin film heater, the glass (SiO2) can expand freely to the Si substrate. But it cannot expand freely in the parallel direction, because it is surrounded by other glass (SiO2). So, a compressive stress is developed in the parallel direction, and it mainly induces a refractive index increase in the TM mode. In the case of TM mode φ(P), phase change due to application of heating power P occurs not only due to isotropic thermooptic phase φ T (P), $φ T ( P ) = d n d T Δ T c ( P ) L H λ$ , where $d n d T$ = thermooptic index coefficient, ΔTc (P) is the temperature difference between two cores) but also by an anisotropic stress optic phase φ S (P). The anisotropic stress optic phase change for the temperature difference ΔT c (P) between two cores obtained by heating via heater is written as [10]

$φ S ( P ) = d ( n T M − n T E ) d T Δ T c ( P ) L H λ$

where $d ( n T M − n T E ) d T$ = temperature rate of increase of birefringence depending on stress optical coefficient $δ ( n T M − n T E ) δ S$ and Young’s modulus $δ S δ V$ , and thermal expansion coefficient $δ V δ T$ is expressed as [10]

3.65 $d ( n T M − n T E ) d T = ∂ ( n T M − n T E ) ∂ S ⋅ ∂ S ∂ V ∂ V ∂ T$

In the case of TE mode, the phase change with the application of heating power ϕ(P) is only an isotropic phase change ϕT (P)s.

#### 3.5.1  Thermooptic Delay Line Structure

Considering the above polarization-dependent characteristics and reduction structure of polarization dependence, a thermooptic delay line structure is shown in Figure 3.22. The structure consists of four sides or boundaries – top surface (side-A), bottom surface (side-B), left surface (side-C) and right surface (side-D). The thermal analysis of conventional and low-power thermooptic device structure with silicon trench at the bottom surface are already studied [9,10] and optimized the parameters such as heater width, total cladding width, and trench width. Like these structures, the delay line structure has two waveguides with the addition of a groove of width W G and depth H G made in between two waveguide cores at its top surface for release of stress anisotropy, inducing mainly a refractive index increase in the TM polarization [10]. It has an air medium in which the temperature is taken to be ambient temperature of air medium which is close to room temperature T I . The bottom and right-side surfaces of the silicon trench, made just below the heater in the proposed structure, are attached to the substrate, whereas left-side surface of the trench is attached to the heat insulator. The position of waveguide cores and their sizes, heater size and its position, upper cladding thickness W oc and total cladding thickness W c , and trench width and thickness are the same as those of the conventional structure. Both side surfaces of the proposed structure are taken as heat insulator for suppressing lateral heat diffusion. The temperature gradient obtained from the temperature profiles by using implicit finite difference temperature equations [10] is an important factor for study of stress release groove in which, for more magnitude of these values, the stress release is also more.

Figure 3.22   Cross-sectional view of the proposed thermooptic delay line structure consisting of single stress releasing grooves of depth H G and width W G and a silicon trench of trench height H T and width W T (Cladding width = W c , upper cladding width = W oc , and device width = W wg ).

The implicit temperature equations are made at discrete points. The first step in this method is to find these points. The temperature distribution of the waveguide region is made with a heat flux of q 0 via heater and is divided into several small regions of same width, same length and height of Δx and assigning to each reference point that is at its center. This reference point is termed as a nodal point or node. Two types of nodes – interior nodes, which are situated inside the thermooptic structure, and surface nodes/exterior nodes, which are situated on the surface or boundary of the thermooptic structure as shown in Figure 3.22. For computation, these equations of the nodes in short form are written using implicit temperature equations as [10]

3.66 $a i , i T i p + 1 + ∑ a i , j T j p + 1 = b i$

Where superscript p indicates the time t (t = pΔt, where Δt =(Δx)2/4α). The first subscript i of coefficients a i,I shows the equation number, and second subscript i states the node number. Similarly, the first subscript i of coefficients a i,j indicates the equation number, and the second subscript j denotes the neighboring node number of the ith node. $T i p + 1$ and $T j p + 1$ are denoted as the temperatures of ith node and its neighboring node j, respectively. The coefficients of the temperature equations for all interior and surface nodes are derived easily from implicit temperture equations.

temperature equations [10] and are as follows [10,11]:

• a i,i = 8 for all interior nodes, silicon trench nodesand air-exposed top surface nodes,
• = 1, for side surface nodes (side-C and -D) andbottom surface nodes attached to the substrate and stress releasing groove nodes,
• = 3, for heater-exposed top surface nodes.
• a i,j = −1, for all interior nodes, side surface nodes (j = i + 1 for side-C and j = i−1 for side-D), heater exposed to top surface nodes (j = i + m, m = total number of nodes in a row of the device) and air-exposed top surface nodes (j = i ±1), silicon trench nodes and stress releasing groove nodes.
• = −2, for air-exposed top surface nodes (  j = i + m)
• = 0, otherwise.
• $b i = 4 T l p$ , for all interior nodes.
• = $2 T l p + q 0 Δ x / k$ , for heater-exposed top surface nodes.
• = 0, for side surface nodes (side-C and -D).
• = T I , for bottom surface nodes.
• = T α , for stress relieving groove nodes.
• = $4 T l p + 2 B i T α$ , for air-exposed top surface node and stress relieving groove nodes.
• k = thermal conductivity of waveguide medium.
• Bi = Biot’s number.

After keeping the initial temperature of all nodes at room temperature, the heat flux q 0 of the heater is set at a value, and the old temperatures of all the nodes are updated with new tempertures by putting p = p + 1 till t is equal to time to get the required temperature difference between the cores.

Figure 3.23 represents the polarization-independent tunable transmission characteristics of 5-stage Y symmetric CMZ filter based on the proposed thermooptic delay line structure with Δn = 5%, λ ref = 1.55 µm, cladding index = 1.447, waveguide core width w =1.5 µm, ΔL =20.5 µm and L B = 462 µm. The difference between transmission characteristics of TE and TM polarization for the structure having groove is lesser than that of the conventional structure having no groove. The shift of resonant wavelength due to heating the curved arm of delay line section by heater is the same in both TE and TM polarization because anisotropic stress developed by the temperature difference between two cores (showing additional phase difference in TM polarization) is relieved by the groove. The reduction of peak normalized cross-state power is obtained due to bending loss which is approximately 0.1 dB per MZ section. The heating power (H) needed per delay line section to obtain $Δ T c ( P )$ of 6°C and 12°C for tuning of ADM based on CMZ coupler with conventional structure to wavelengths 1.56 and 1.57 µm from 1.55 µm is estimated by using the equation H = q 0·W H ·L H (where q 0 =heat flux to achieve these temperature difference, W H = heater width and L H = heater length) as 84.2 and 178 mW per delay line section, respectively, whereas those needed for the structure having grooves to tune to the same wavelengths are 53 and 108.4 mW, respectively.

Figure 3.23   Polarization-independent tunable transmission characteristics of 5-stage Y symmetric CMZ filter based on a proposed thermooptic delay line structure with Δn = 5%, λ ref = 1.55 µm, cladding index = 1.447, waveguide core width w =1.5 µm, ΔL =20.5 µm and L B = 462 µm.

#### 3.6  SONET/SDH

With the development of WDM optical network, it is required to increase the transmission capacity in each individual wavelength. It is seen that for accommodation of a connection request/service, we do not need this much of bandwidth to allocate a dedicated wavelength to this connection. We should have hierarchical digital time multiplexing to accommodate more number of channels for a wavelength channel. In this direction, there is a standard signal format known as SONET in North America and synchronous digital hierarchy (SDH) in other parts of the world. This section mentions the basic concepts of SONET/SDH, its optical interfaces and fundamental network implementations.

#### 3.6.1  Transmission Formats and Speeds of SONET

Several vendors throughout the world started developing standards for formats of SONET frame to interconnect different connections and services for a wavelength channel for fiber-optic communication. There is a need for the development of a common standard. In this direction, ANSI T1.105 standards are developed for SONET in North America [51] and ITU-G. 957 standards for SDH in other parts of the world [IEEE 802.17]. In fact, there is a slight difference for implementation of these standards. Figure 3.24 shows the structure of a basic synchronous transport signal (STS)-1 frame of SONET having a 2D structure consisting of 90 columns by 9 rows of bytes. There are three overloads – section overload and line overload at the beginning of the frame and path overload in the middle of the frame. Section overload connects adjacent pieces of equipment, whereas line overload connects two SONET devices [52–54]. Path overload provides complete end-to-end connection. The fundamental SONET frame has a 125 μs duration.

Figure 3.24   An STS-1 frame structure.

$Overload per frame of STS- 1 = ( 4 bytes/row ) × ( 9 r o w s / f r a m e ) × ( 8 b i t s / b y t e ) = 288 bits$
$Information bits per frame of STS- 1 = ( 86 bytes/row ) × ( 9 rows/frame) × ( 8 bits/byte ) = 6192 bits$
$Total number bits per frame of STS- 1 = 6192 bits + 288 bits = 6480 bits$

Since the frame length is 125 μs, the transmission bit rate of the basic SONET signal is given by

$STS- 1 = 6480 bits/ 125 μ s = 51.84 Mbps$
$STS- 1 = ( 90 bytes/row ) × ( 9 rows/frame ) × ( 8 bits/byte ) / ( 125 μ s/frame ) = 51.84 Mbps$

This is called an STS-1 signal where STS represents a synchronous transport signal. All other SONET signals are integral multiples of this bit rate. Figure 3.25 shows STS-N signals in which the transmitted bit rate is N × 51.84 Mbps. Each frame of STS-N has N ×90 column bytes and same 9 rows within 125 μs duration. When an STS-N signal is used to modulate an optical source, the logical STS-N signal is scrambled to avoid log strings of ones and zeros and to allow easier clock recovery at the receiver. After undergoing electrical to optical conversion, the resultant physical layer optical signal is called OC-N, where OC represented an optical carrier. The value can have range 1-192 but ANSI T1.105 standard recognizes the value of N = 1, 3, 12, 24, 48 and 192.

Figure 3.25   An STS-N frame structure.

In SDH, the basic rate is equivalent to STS-3 or 155.52 Mbps. This is called as synchronous transport module – STM-1. Higher rates can be written as an integral multiple of STM-1 × M or STM-M where M =1, 2, …, 64. The values of M supported by ITU-T recommendations are M =1, 4, 16 and 64. These are equivalent to SONET OC-N signals where N =3M. This shows compatibility between SONET and SDH. Table 3.1 shows commonly listed values of OC-N and STS-M. Figure 3.26 shows SONET STS-192 digital transmission hierarchy and its SDH equivalent. In the figure, lower-level time division multiplexer is STS-1 for SONET, whereas that for SDH is STM-1. There are five levels of hierarchy in SONET, whereas there are four levels for SDH.

### Table 3.1   STS/OC Specifications

Electrical Level

SONET Level

SDH Equivalent

Line Rate (Mbps)

STS-1

OC-1

51.84

2.304

STS-3

OC-3

STM-1

155.52

6.912

STS-12

OC-12

STM-4

622.08

27.648

STS-48

OC-48

STM-16

2488.32

110.592

STS-192

OC-192

STM-64

9953.28

442.368

Figure 3.26   A SONET STS-192 or SDH STM-64 digital transmission hierarchy multiplexer.

#### 3.6.2  SONET/SDH Rings

Normally, SONET/SDH technologies are configured as a ring architecture. This is done to create a loop diversity for uninterrupted service protection purposes in case of link or equivalent failures. This SONET/SDH rings are commonly called self-healing rings, since the traffic flowing along a certain path can automatically be switched to an alternative or backup path while failure or degradation of the link segment occurs.

There are three main features yielding eight possible combinations of ring types. First, there can be either two or four fibers running between the nodes on a ring.

#### 3.7  Optical Regenerator

As discussed in Figure 1.6, there are three optical windows of low propagation loss for optical fiber transmission characteristics – first window centered at 0.85 μm and with propagation loss ~0.82 dB/km, second window centered at 1.30 μm and with propagation loss ~0.3 dB/km and a third window centered at 1.55 μm and with propagation loss ~0.2 dB/km. Attenuation in optical fiber is due to the impurity content in glass (water vapor) and Rayleigh scattering which is caused by fluctuation in the refractive index. As lower attenuation is obtained in the third window, optical network uses this window for signal transmission. But still for long-distance communication (more than 100 km) it requires an optical regenerator/repeater. Optical regenerator mainly amplifies the signal so that it can compensate signal power loss and normally placed it at an interval of 40 km [55]. Since it has mainly optical amplifiers, it is discussed in the next section.

#### 3.7.1  Optical Amplifiers

An optical signal transmits a long distance typically 80 km at a stretch in current deployment before it needs amplification. Optical networks cover a wide area, but these networks having a diameter of covering area (specially nationwide network) beyond 87 km need all-optical amplifiers for long-distance links. All-optical amplification is different in which before amplification it needs optoelectronic conversion and after amplification electrooptical conversion. The optical amplifier acts only to amplify the power of a signal, but not to restore the shape or timing of the signal. There are three types of optical amplification – inline optical amplifier, preamplifier and power amplifier [56].

Inline amplification: There is only inline amplification without getting reshaping and retiming of the signals to compensate only the transmission loss.

Preamplification: This type of amplification is used as a front-end amplification for optical receivers. The week signal is amplified before detection, so that signal-to-noise degradation arises due to thermal noise in the receiver which can be suppressed.

Power amplification: It is placed just after the transmitter to boost the transmitted power and to increase the transmission distance without amplification. This boosting technique is used in undersea optical fiber communication where the transmission distance is 200–250 km. It is also used for compensation of coupler insertion loss and power splitting loss.

In communication networks using SONET and SDH, the optical fiber is only required as a transmission medium, the optical signals are amplified by first converting the information stream into an electronic data signal, and then retransmitting the signal optically. Such a process is referred to as 3R (reamplification, reshaping and retiming).

The reshaping of the signal regenerates the original pulse shape, eliminating noise/distortion. Reshaping applies mainly to digitally modulated signals, but in some cases, it is also used for analog signals. The retiming of the signal synchronizes the signal to its original bit timing pattern and bit rate. Retiming applies only to digitally modulated signals.

Also, in a WDM system having optoelectronic regeneration, each wavelength is to be separated before being amplified electronically, and then recombined before being retransmission. Thus, in order to replace optical multiplexers and demultiplexers in optoelectronics amplifiers, optical amplifiers must boost the strength of optical signals without first converting them to electrical signals. The main problem is that optical noise is amplified with the signal. Also, the amplifier includes spontaneous emission noise, since optical amplification normally uses the principle of stimulated emission, similar to the approach used in a laser. Optical amplifiers are classified into two basic classes: optical fiber amplifiers (OFA) and semiconductor optical amplifiers (SOAs), which is mentioned in detail in the following section. In Table 3.2, comparison between OFAs and SOAs is presented. Besides, there is a new kind of optical amplifier called Raman amplifier, which is explained in detail in the following sections.

### Table 3.2   Difference of Characteristics of OFAs and SOAs

Features

OFA

SOA

Maximum internal gain

25–30

20–25

Insertion loss (dB)

0.1–2

6–10

Polarization sensitivity

Negligible

<2 dB

Saturation output power (dBm)

13–23

5–20

Noise figure (dB)

4.6

7–12

#### 3.7.2  Optical Amplifier Characteristics

The performance parameters and characteristics of an optical amplifier are gain, gain bandwidth, gain saturation, polarization sensitivity and noise amplification [52].

Gain is a ratio of the output power of a signal to its input power. The performance of amplifiers are represented by gain efficiency as a function of pump power in dB/mW, where pump power is the energy required for amplification. The gain bandwidth of an amplifier defines as a range of frequencies or wavelengths over which the amplifier amplifies effectively. In a network, the gain bandwidth provides the number of wavelength channels obtained for a given channel spacing. The gain saturation point of an amplifier states that when the input power is increased beyond a certain value, the carriers (electrons) in the amplifier are unable to output any additional light energy. The saturation power is typically defined as the output power at which there is a 3-dB reduction in the ratio of output power to input power. Polarization sensitivity refers to the dependence of the gain on the polarization of the signal. The sensitivity is measured in dB and refers to the gain difference between the TE and TM polarizations.

In optical amplifiers, the dominant source of noise is amplified spontaneous emission (ASE) arising from the spontaneous emission of photons in the active region of the amplifier. The amount of noise produced by the amplifier is a function of factors such as the amplifier gain spectrum, the noise bandwidth and the population inversion parameter which represents the degree of population inversion that has been achieved between two energy levels [52].

#### 3.7.3  Semiconductor Laser Amplifier

A semiconductor laser amplifier (Figure 3.27) is a modified semiconductor laser, which has different facet reflectivity and different device length [57]. A weak signal is sent through the active region of the semiconductor, in which stimulated emission makes it a stronger signal emitted from the semiconductor.

Figure 3.27   Semiconductor laser amplifier.

The basic structures of semiconductor laser amplifiers are the Fabry–Perot amplifier (FPA) having the Fabry–Perot cavity with partially reflective facets and traveling-wave amplifier (TWA) having non-resonant cavity with less reflective facets. The primary difference between the two is in the reflectivity of the end mirrors. FPAs have a reflectivity around 30%, whereas TWAs have a reflectivity of around 0.01%. In order to prevent lasing in the FPA, the bias current is operated below the lasing threshold current. When an optical signal enters the FPA cavity, it gets amplified as it reflects back and forth between two mirror facets until it emits at higher intensity. The amplifier gain is written as [57]

3.67 $G = P o u t P i n$

where P out and P in are the output and input powers of FPA. The higher reflections in the FPA cause Fabry–Perot resonances in the amplifier, resulting in narrow passbands of around 5 GHz. By decreasing the reflectivity, the amplification is performed in a single pass so that no resonance occurs. So the performance of TWAs is better than that of FPAs in the case of WDM networks. In TWA, the input signal gets amplified only once with the principle of semiconductor laser action during a single pass through TWA. The amplifier gain is derived as

3.68 $G = exp [ Γ ( g m − α ) L ] = exp [ g ( z ) L ]$

where Γ = optical confinement factor, g m = material gain coefficient, α = absorption coefficient, L = amplifier length and g(z) = overall gain per unit length. Semiconductor amplifiers based on multiple quantum wells (MQW) are studied by many authors. These amplifiers have higher bandwidth and gain saturation than bulk devices and also fast on–off switching times. The disadvantage is a higher polarization sensitivity. Currently, SOAs attract more interest in both research and industry fields because its advantage of semiconductor amplifiers is the ability to integrate them with other components. By turning a drive current on and off, the amplifier can act as a gate, blocking or amplifying the signal devices.

#### 3.7.4  Doped Fiber Amplifier

Doped fiber amplifier (DFA) consists of a length of fiber lightly doped with an element [58] (rare earth elements such as Erbium (Er), ytterbium (Yb), neodymium (Nd) and praseodymium (Pr)) are used to amplify light (Figure 3.28). The active medium length doped with rare earth element is nominally ~ 10–30 m. The doping concentration is ~1000 parts per million weight. The most common doping element is erbium contributing gain for wavelengths between 1525 and 1560 nm. Sometimes Yb is added with Er++ to increase pumping efficiency and amplifier gain. For amplification of 1300 nm window, the doping elements used are Pr and Nd. At the ending of the length of the fiber amplifier, a laser emits a strong signal at a lower wavelength (taken to be the pump wavelength) to backup the fiber. Figure 3.29 shows a simplified energy diagram Er3+-doped silica fiber in which metastable states and pump energy levels are 4 I 13/2 and 4 I 11/2, respectively. The metastable states have slightly longer lifetimes in comparison with that of pump energy levels. The pump energy levels, metastable energy levels and ground energy levels are actually bands of closely spaced energy levels that form manifold due to the effect known as stark splitting by broadening with thermal effects. The gap between the top of 4 I 15/2 and the bottom of the ground state band 4 I 13/2 is around 0.841 eV, which corresponds to the wavelength 1480 nm, and the energy gap between the bottom of 4 I 15/2 and the bottom of metastable band 4 I 13/2 is ~0.814 eV corresponding to the wavelength 1527 nm. This pump signal excites the doped atoms into a higher energy level. This allows the data signal to stimulate the excited atoms to release photons. Most erbium-DFAs (EDFAs) are pumped by lasers with a wavelength of either 980 or 1480 nm. The input signal power (P in ) and output

Figure 3.28   Erbium-doped fiber amplifier.

Figure 3.29   Energy level diagram of various transition processes of Er3+-doped silica.

amplified signal (P out ) of an EDFA can be expressed in terms of the principle of energy conversion [52]

3.70 $P o u t ≤ P i n + λ p λ s ⋅ P p$

where λ p and λ s is pump and signal wavelengths, respectively, and P p = pump signal power. The maximum output amplified signal power depends on the ratio λ p /λ s . For pumping, it is required to have λ p < λ s , and for getting gain, it is also necessary to have P in P p . The power conversion efficiency (PCE) is written as

3.71 $PCE = P o u t − P i n P p$

The maximum value of PCE is ~ λ p /λ s . The quantum conversion efficiency (QCE) is defined as $QCE = λ s λ p PCE$ . The maximum value of QCE is unity in which all the pump photons are converted into signal photons. The amplifier gain (G) is written as

3.72 $G = P o u t P i n ≤ 1 + λ p P p λ s P i n$

To achieve the gain G, the input power signal cannot exceed a value given by

$P i n ≤ ( λ p / λ s ) P p G − 1$

The gain of fiber-doped amplifier not only depends on pump power but also on fiber length signal emission cross-section and rare earth element concentration. The maximum gain G max is written as

3.73 $G m a x = exp ( ρ σ L )$

The maximum possible gain of DFA is written as [52]

3.74 $G ≤ min { exp ( ρ σ L ) , 1 + λ p λ s ⋅ P p P i n }$

The maximum possible output power is expressed with min of two possible values as [52]

3.75 $P o u t ≤ min { P i n exp ( ρ σ L ) , P i n + λ p λ s . P p }$

The 980-nm pump wavelength provides gain efficiencies of around 10 dB/mW and 1480-nm pump wavelength gives efficiencies of around 5 dB/mW. Typical gains are of ~25 dB. Experimentally, EDFAs have been shown to achieve gains of up to 51 dB with the maximum gain limited by internal Rayleigh backscattering (RBS), and a portion of scattered light is back reflected towards the launch end within the optical waveguide. The 3-dB gain bandwidth for the EDFA is around 35 nm and the saturation power is ~20 dBm. A wide-band EDFA with 25 dB of flat gain over 77 nm (1528–1605 nm) and dynamic gain clamping over 13 dB of input range (25–483 W) are established experimentally.

Apart from Erbium-doped fiber, there are praseodymium-doped fluoride fiber amplifier (PDFFA) and Yb-DFA. A limitation to optical amplification is unequal gain spectrum of optical amplifiers. The gain spectrum DFA with non-uniform gain at different wavelengths is shown in Figure 3.30a, and Figure 3.30b shows the EDFA gain spectrum with different inversion levels (where the inversion levels are function of concentration of rare earth doped elements). While an optical amplifier contributes gain across a range of wavelengths, it requires to amplify all wavelengths equally. Apart from this disadvantage, optical amplifiers amplify noise with signal and also the active region of the amplifier spontaneously transmits photons providing the noise and hence degrading the performance of optical amplifiers. The spontaneous noise in the EDFA is mainly due to the spontaneous recombination of electrons and holes in the active medium of EDFA. This noise is modeled as a stream of infinitely random short pulses distributed along the amplifying medium. Such a random process is characterized by a noise power spectrum. The power spectral density of spontaneous nose [52] is

Figure 3.30   (a) An EDFA gain spectrum. (b) Gain spectrum for different inversion levels.

3.76 $S S P N ( f ) = h ν n s p [ G ( f ) − 1 ] = P S P N / Δ ν o p t$

where P SPN = the spontaneous noise power in optical frequency band Δν opt . and n sp denotes population inversion between two energy levels – metastable and lower energy levels.

$n s p = n 2 n 2 − n 1$

n 2 and n 1 are populations of electrons of metastable state and lower energy levels. The presence or absence of spontaneous noise depends on whether co-directional or counter-directional pumping is used. The signal-to-noise ratio depends on input signal power P in , gain G, population inversion n sp , front-end receiver electrical bandwidth B and quantum efficiency η.

Non-uniform gain of EDFA gain equalizer makes power imbalance in an optical network. There are a number of approaches for equalizing the non-uniform gain of an EDFA. There is a notch filter (a filter that attenuates the signal at a selected frequency) centered at around 1530 nm is used to suppress the peak in the EDFA gain. If multiple EDFAs are cascaded, another peak occurs around the 1560-nm wavelength. In the network, it is required to have dynamic EDFA gain equalizer. Using this approach we can develop these dynamic gain equalizers (DGEs) that are discussed in the next section.

#### 3.7.5  Raman Amplifier

Raman amplifiers based on Raman’s effect is used for optical amplification in long-haul and ultra-long-haul fiber-optical transmission systems. It is one of the first widely commercialized nonlinear optical devices in telecommunications [59,60]. The schematic diagram of a Raman amplifier is presented in Figure 3.31. When an optical field is incident on a molecule, the bound electrons oscillate at an optical frequency. This induced oscillating dipole moment generates optical radiation at the same frequency, with a phase shift due to the medium’s refractive index’s timeously, the molecular structure is oscillate data the frequencies of various molecular vibrations. Therefore, the induced oscillating dipole moment also comprises the difference frequency terms between the optical and vibration frequencies. These terms provide Raman scattered light in the reradiated field. In a solid-state quantum-mechanical description, optical photons are in elastically scattered by quantized molecular vibrations represented by optical phonons. Photon energy is lost (the molecular lattice is heated) or gained (the lattice is cooled), shifting the frequency of the light. The components of scattered light that shifted to lower frequencies are Stokes lines, while those shifted to higher frequencies are anti-Stokes lines. The frequency shift is due to oscillation frequency of the lattice phonon that is generate do annihilated. (The anti-Stokes process is not mentioned as it is typically orders of magnitude weaker than the Stokes process in the context of optical communications, making it irrelevant.) Raman scattering occurs in all materials, but in silica glass the domain an Raman lines are due to the bending motion of the Si–0–Si bond (see bond angle in Figure 3.31). Raman scattering is stimulated by signal light at an appropriate frequency shift from a pump, making stimulated Raman scattering (SRS). In this process, pump and signal light are coherently coupled by the Raman process. In a quantum-mechanical description, shown in the energy-level diagram in Figure 3.31, a pump photon is converted into a second signal photon that is an exact replica of the first one, and the remaining energy produces an optical photon. The initial signal photon, therefore, has been amplified.

Figure 3.31   A schematic demonstration of Raman amplification using simulated Raman scattering with Stoke lines concept.

There is a disadvantage – requirement of more pump power, roughly tens of milliwatts per dB of gain, whereas the tenth of a milliwatt per dB is required for EDFAs for small signal powers. There are advantages that Raman amplifiers are made along the transmission fiber itself. Now, Raman amplification is an accepted technique for enhancing system performance. Raman amplification has enabled dramatic increases in the reach and capacity of lightwave systems. Novel Raman pumping schemes have recently been reported.

#### 3.8  Channel Equalizers

Optical networks are dynamic in nature due to non-uniform and unpredictable traffics in the networks. It leads the requirements for dynamic compensation of signal power with optical amplifiers. As discussed in the previous section regarding non-uniform gain spectrum of optical amplifiers, compensation is required to get flatness of amplifier gain profiles. The gain of EDFA spectrum depends on pumping power exciting Er3+ ions to the metastable state. The number of excited Er3+ ions to metastable state is increased with an increase of pumping power. It is indicated in terms of inversion level as the ratio between the number of Er3+ ions exited to the metastable state and total number of Er3+ ions in EDFA. The variation of input powers and changes of the temperature also contribute to the variation of power profile of EDFA [61]. In order to overcome the power imbalance problems, the imbalance power profile of all wavelength channels is equalized. Due to imperfections in gain-flattening filters, changes in the amplifier operating conditions and changes in channel loading, a DGE is required with a smooth, low-ripple spectral attenuation profile that is the negative of the deviations of the amplifier gain profile from the desired profile. To compensate for unequal channel powers, resulting from dropping and adding channels, one needs a dynamic channel-power equalizer (DCE), which provides a flat attenuation profile across the full bandwidth of each channel, but the attenuation for each channel can be adjusted accordingly. There are different ways of making DGE. Every channel is equalized individually by using a channel equalizer or demux/mux combination with variable optical attenuation [61]. The use of channel separation and recombination by demux and mux become lossy and expensive for a large number of channels. Single gain equalizing device is used to flatten a large number of wavelength channels simultaneously [51,62–63]. Another way of flattening is that using many EDFAs in cascade, one can flatten WDM channels. The use of many EDFAs in cascade is costly to equalize non-uniform amplified power for a large number of channels. A single gain equalizing device is preferred due to having less lossy property. One of such EDFA gain equalizer filter based on CMZ coupler [62,63] is very simple and more cost effective. The CMZ filters made up of silica on silicon waveguide flatten the bandwidth of 30 nm (from 1.53 to 1.56 micron) but gain equalization is not dynamically adjusted. As discussed earlier, in optical network, dynamic gain equalization is required because the reconfiguration and automatic wavelengths switching in optical network change the power profile dynamically. Moreover, the changes in the network load require the dynamic adjustment of equalization of EDFA spectrum. This dynamic adjustment of EDFA gain equalization is performed with tuning of gain equalizer. The tuning is obtained by building heaters into the waveguides to vary the coupling strength and phase shift in delay line coupler via thermooptic effect. The problems of these gain equalizers are large bending loss and device length due to presence of more number of stages. Figure 3.32 shows thermally tunable CMZ filter used as dynamic EDFA gain equalizer. It has an N-stage point symmetry CMZ coupler consisting of N number of delay line sections with arm lengths L A and L B (where path difference between two arms, ΔL = L A L B ), thin film heater of length L H (L H L A ) and width W H made on a curved arm of MZ section and N + 1 number of TMI couplers of width 2w.

Figure 3.32   Schematic diagram of an N-stage 2 × 2 point symmetric MZ filter consisting of N number of delay line sections with thin film heaters and (N + 1) number.

The cross-sectional view xx is a thermooptic delay line structure that has a silicon trench with optimized device parameters such as heater width, total cladding width and trench width. Like these structures, the delay line structure has two waveguides with a groove of width W G, and depth H G made in between two waveguide cores for release of stress anisotropy, which enhances mainly a refractive index increase in the TM polarization [63]. It has an air medium where the temperature is taken to be ambient temperature of air medium which is slightly more than the room temperature T I . In the proposed structure, bottom and right-side surfaces of the trench portion are attached to the substrate, whereas left-side surface of the trench is attached to the heat insulator. The position of waveguide cores and their sizes, heater size and its position, upper cladding thickness W oc and total cladding thickness W c , and trench width and thickness are kept the same as those of the conventional structure. Both side surfaces of the structure are assumed as heat insulator for suppressing lateral heat diffusion.

The couplers of the device act as one long coupler with total coupling length L, which is represented with different ways of distribution over all individual couplers of the circuit as $L = ∑ k = 0 N L i$ and L i is the length of the ith coupler (i = 0, 2, 3, …, N). The coupling length distribution controls transmission characteristics of the filter. In each TMI coupler only fundamental and first-order mode with propagation constants β 00 and β 01 respectively are excited in the coupling region [63], and the coupling coefficient (k T) of TMI coupler is represented by (β 00β 01)/2. Expanding k T (λ) to the first-order approximation to the wavelength λ is derived in terms of the reference wavelength λ ref as

3.77 $k T ( λ ) = k T ( λ r e f ) { 1 − λ − λ r e f λ r e f }$

From the geometry, horizontal length of each delay line section is obtained as L B H 2L, where H is the height of delay line section. The total length of the device is written as [63]

3.78 $L T = N ⋅ L B + L + L I$

where L I = length of input and output portion of the device. The refractive indices of the core and its surrounding cladding are n 1 and n 2 respectively. The input power P 1 is incident on the lowermost waveguide when the output powers P 3 and P 4 are obtained as cross and bar states, respectively. The normalized cross power of N-stage points symmetric CMZ coupler is given by [63]

3.78 $P 3 P 1 = { ∑ k = 0 N | a k | 2 + 2 ∑ i = 0 N a i ∑ k = i + 1 N a k cos [ ( k − i ) Δ φ ( λ , Δ L , P ) ] } e − N α L B$

where α is the bending loss coefficient depending on bending radius [17], and the coefficients a k s are determined from the coupling coefficient k T (λ) of TMI couplers (as expressed in equation (1)). Δφ(λL, P) is the phase difference obtained due to path difference between two arms of delay line section plus the phase shift introduced by heating the curved arm. Expanding to first order in wavelength, Δφ(λL, P) is derived as [66,65]

3.79 $Δ φ ( λ , Δ L , P ) = 2 π [ φ ( Δ L ) + φ ( P ) ] { 1 − λ − λ r e f λ r e f }$

where $φ ( Δ L ) = n e f f Δ L λ$ , n eff is the effective index at wavelength λ and λ ref is the reference wavelength. When the waveguide is heated locally via the heater, the glass (SiO2) can enlarge freely to the Si substrate. But it is not enlarged freely in the parallel direction, because it is surrounded by other glass (SiO2). As a result, compressive stress is built only in the parallel direction, and it mainly induces a refractive index increase in the TM mode. So, the refractive index increase due to stress optic effect gives rise to an extra phase change ϕ S (P) in TM mode apart from thermooptic phase change ϕ T (P) with the application of heating. The anisotropic stress optic phase change for the temperature difference ΔT c (P) between the two cores obtained by heating via heater is expressed as [63]

3.80 $ϕ S ( P ) = d ( n T M − n T E ) d T Δ T c ( P ) L H λ$

where $d ( n T M − n T E ) d T$ is the temperature rate of birefringence depending on stress optical coefficient $δ ( n T M − n T E ) δ S$ , Young’s modulus $δ S δ V$ and thermal expansion coefficient $δ V δ T$ is expressed as [63]

3.81 $d ( n T M − n T E ) d T = ∂ ( n T M − n T E ) ∂ S ⋅ ∂ S ∂ V ∂ V ∂ T$

So in the case of TM mode φ(P), phase change due to application of heating power P occurs not only due to isotropic thermooptic phase φT (P) $( φ T ( P ) = d n d T Δ T c ( P ) L H λ ,$ where $d n d T$ = thermooptic index coefficient, ΔTc (P)is the temperature difference between two cores) but also by an anisotropic stress optic phase φS (P). In the case of TE mode, the phase change due to the application of heating power φ(P) is only an isotropic phase change φT (P).

Figure 3.33 illustrates the equalization of EDFA gain spectrum of different inversion levels, obtained by using 2-stage point symmetric CMZ filter-based proposed structure. The solid line of the figure shows an EDFA gain spectrum of inversion levels 0.7, 0.8 and 0.9 [63], whereas the dashed and dotted lines show gain equalized spectrum of TE and TM polarization, respectively, and EDFA gain spectrum. In the figure, EDFA spectrum of inversion level 0.7 is equalized with a 2- stage point CMZ coupler by considering that central wavelength 1.55 µm and equalization of EDFA spectrum of inversion levels 0.8 and 0.9 are obtained by shifting the central wavelength to 1.555 and 1.56 µm, respectively, by making the temperature difference ΔTc (P) of 3°C and 6°C between two cores with heater on core-1. The equalized gain spectrums of TE and TM polarization of the device structure almost overlapped. So, the gain spectrums of the proposed structure are almost polarization independent. The heating power required per delay line section to obtain ΔTc (P) of 3°C and 6°C for tuning of EDFA gain equalization with conventional structure and proposed structure are estimated by using implicit finite difference method and shown in Table 3.3. In the table, the reduction of the heating power of the low-power thermooptic structure is obtained by ~1.6 times with respect to that of the conventional structure.

Figure 3.33   Equalization of an EDFA gain spectrum of inversion levels 0.7, 0.8 and 0.9 by using 2-PB CMZ circuit with ΔT c (P) = 0, 3°C and 6°C.

### Table 3.3   Heating Power of Conventional and Proposed Structures, Thickness of Waveguide (Wc) ~ 15 µm, Thickness of Upper Cladding Layer (Woc) ~ 3 µm, Heater Length L H ~ 482 µm, Heater Width W H ~ 6 µm and Wavelength λ ref = 1.55 µm

ΔT c ( P ), Temperature Difference between Two Waveguides Cores of Delay Line Section (°C)

Heating Power (mW) of Conventional Structure (Per Delay Line Section) (mW)

Heating Power (mW) of Proposed Structure (Per Delay Line Section)

(Trench Height H T ~ 12 µm, Trench Width W T = 18 µm, Groove Depth H G = 9 µm Groove Width, W G = 9 µm)

~3

42.1

26.5

~6

89

54.2

Further, for large-range EDFA gain spectrum, its equalization is made by shifting the central wavelength via thermal tuning.

In some EDFA gain equalizers, either DGE or DCE functionality is made, but the basic design parameters for these two cases are different for different device designs required to accomplish the two different functionalities. In particular, the DGE makes an important role in WDM networks because of its ability to control the power profile of the wavelength channels, hence maintaining a high quality of service (QoS) and providing more flexibility in transmission management. The key requirements of future dynamic WDM signal equalizers are low insertion loss, wide bandwidth, fast equalization speed, small size and low cost. There are dynamic WDM equalizer structures including MEMS filters, MZ interferometer (MZI) filters, acoustooptic filters, digital holographic filters and liquid-crystal modulators. These structures use few cascaded (or parallel) optical filters, whose weights are dynamically optimized to obtain a smooth spectral equalization. It is difficult to obtain channel-by-channel equalization unless the number of optical amplifiers used in an equalizer subsystem is equal to the number of WDM channels.

#### 3.9  Wavelength Conversion

In a wavelength-routed network we require the same wavelength to be allocated on all the links in the path between the source and destination station [66–68]. This requirement is known as the wavelength-continuity constraint [66]. This constraint makes the wavelength-routed network blocking calls only when there is no availability of same wavelength for all the links in the path between the source and destination. Thus, wavelength-continuity network may suffer higher blocking than a circuit-switched network.

It eliminates the wavelength-continuity constraint problem for removal of blocked connections by converting the wavelength to another wavelength available in outgoing link in the intermediate node. This technique is known as wavelength conversion in the intermediate node.

Figure 3.34 shows the wavelength converter at Node 2 employed to convert data from wavelength λ 2 to λ 1. The new lightpath between Node 1 and Node 3 is set up by using the wavelength λ 2 on the link from Node 1 to Node 2, and then by using the wavelength λ 1 to reach Node 3 from Node 2. So the same lightpath in a wavelength convertible network is converted into a different wavelength along each of the links in its path. Thus, wavelength conversion enhances the efficiency in the network by resolving the wavelength conflicts of the lightpaths reducing blocking of connections. The impact of wavelength conversion on WDM wide area network (WAN) design is further discussed later on.

Figure 3.34   Wavelength conversion in the optical network.

In wavelength convertible network, the requirements of wavelength converter are given below:

1. fast set up time of output wavelength.
2. conversion to both shorter and longer wavelengths.
3. moderate input power levels.
4. possibility for same input and output wavelengths (i.e., no conversion).
5. insensitivity to input signal polarization.
6. low-chirp output signal with high extinction ratio and large signal-to-noise ratio, and simple implementation.

Wavelength conversion techniques are classified into two types: optoelectronic wavelength conversion, in which the optical signal must first be converted into an electronic signal, and all-optical wavelength conversion, in which the signal remains in the optical domain. All-optical conversion techniques may be subdivided into techniques which employ coherent effects and techniques which use cross modulation.

#### 3.9.1  Opto Electronic Wavelength Conversion

Figure 3.35 represents an optoelectronic wavelength converter in which the optical signal of the wavelength to be converted is first changed into the signal in electronic domain using photodetectors [64,69]. The electronic bit stream is stored in the buffer (labeled FIFO for the First-In-First-Out queue mechanism). The electronic signal is then used to drive the input of a tunable laser (labeled T) for tuning to the desired wavelength of the output. This method is used for bit rates up to 10 Gbps. However, this method is complex and requires a lot more power than the other methods which are discussed below. All information in the form of phase, frequency and analog amplitude of the optical signal may be lost during the conversion process.

Figure 3.35   An optoelectronic wavelength converter.

#### 3.9.2  Wavelength Conversion Using Coherent Effects

Wavelength conversion methods using coherent effects are based on wave-mixing properties. Wave mixing arises from a nonlinear optical response of a medium generated from mixing of more than one wave. The generated wave intensity is proportional to the product of the interacting wave intensities, which depends on both phase and amplitude information. It allows simultaneous conversion of a set of multiple input wavelengths to another set of multiple output wavelengths and accommodates signal with high bit rates. Figure 3.36 shows a nonlinear wave mixing in which the value n = 3 refers to Four- Wave Mixing (FWM) and n = 2 refers to Difference Frequency Generation (DFG).

Figure 3.36   A wavelength converter based on nonlinear wave mixing effects.

These techniques of wave mixing are described below:

• Four-Wave Mixing (FWM: FWM is a third-order nonlinearity in silica fibers, which contributes three optical waves offer quenches f i , f j , and f k (k# i,j) to interacting multichannel WDM system to produce a fourth wave of frequency: FWM is also obtained in other passive waveguides such as semiconductor waveguides and in an active medium such as SOA. FWM is used [65] for wavelength conversion in optical networks owing to its ultra-fast response and high transparency to bitrate and modulation format. In this technique a 3-dB conversion range over 40 nm (1535–1575 nm) is obtained with a flat conversion efficiency of −16 dB and a polarization sensitivity of less than 0.3 dB.

Difference Frequency Generation (DFG): DFG is a consequence of a second-order nonlinear interaction of a medium with two optical waves: a pump wave and a signal wave [64]. DFG is free from satellite signals that appear in FWM-based techniques. This technique offers a full range of transparency without adding excess noise to the signal. It is also bidirectional and fast, but it suffers from low efficiency and high polarization sensitivity. The main difficulties in implementing this technique lie in the phase matching of interacting waves and in fabricating a low-loss waveguide for high convers ion efficiency.

#### 3.9.3  Wavelength Conversion Using Cross Modulation

Figure 3.37 shows a cross-gain modulation (CGM)-based wavelength conversion, which is based on active semiconductor optical devices such as SOAs and lasers [70]. These techniques are known as optical-gating wavelength conversion. The principle of an SOA in CGM is based on intensity-modulated input signal modulating the gain in the SOA. A continuous-wave (CW) signal at the desired output wavelength is modulated by the gain variation so that it carries the same information as the original input signal. The CW signal is either incident on SOA in the same direction as the input signal (co-directional) or incident on SOA in the opposite direction as the input signal (counter-directional). The CGM scheme contributes a wavelength-converted signal inverted with respect to the input signal. The CGM scheme contributes penalty-free conversion at 10 Gbps. Its disadvantages are extinction ratio degradation for the converted signal due to inversion of the converted bit stream.

Figure 3.37   A wavelength converter using co-propagation based on SOA.

The wavelength conversion is also made by SOA in another way where the operation of a wavelength converter using SOA in cross-phase modulation (CPM) mode based on the refractive index of the SOA dependent on the carrier density in its active region. An incoming signal producing the carrier density modulates the refractive index, contributing phase modulation of a CW signal coupled into the converter. The SOA is used into an MZI so that an intensity-modulated signal format is obtained at the output of the converter. Figure 3.38 illustrates an asymmetric MZI wavelength converter based on SOA in CPM mode. With the CPM scheme, the converted output signal is either inverted or non-inverted, unlike in the CGM scheme where the output is always inverted. The CPM scheme is also more power efficient compared with the CGM scheme. A signal up-conversion utilizing a CPM effect in an all-optical SOA-MZI wavelength converter is demonstrated in which this scheme not only shows high conversion efficiency, polarization immunity and no increase in phase noise, but also linear signal up-conversion with a low optical power requirement.

Figure 3.38   An MZI-based SOA wavelength conversion.

#### 3.9.3.1  Semiconductor Laser Based Wavelength Conversion

Figure 3.39 shows a wavelength converter based on single-mode semiconductor lasers in which lasing-mode intensity is modulated by input signal light through lasing-mode gain saturation. The obtained output (converted) signal is inverted compared with the input signal. This gain suppression mechanism has been employed in a Distributed Bragg Reflector (DBR) laser to convert signals at 10 Gbps. In the method using saturable absorption in lasers, the input signal saturates the absorption of carrier transitions near the bandgap and allows the probe beam to transmit.

Figure 3.39   Semiconductor laser-based wavelength conversion.

#### 3.9.3.2  All-Optical Wavelength Conversion Based on CPM in Optical Fiber

Wavelength conversion based on CPM effect in fibers and subsequent optical filtering has been focused due to having an all-optical wavelength conversion. The principle of the new technology is based on the generation of a frequency comb through CPM in an optical fiber with subsequent optical filtering of the desired tone. When incoming data propagate through the fiber along with a sinusoidally intensity-modulated high-power optical pump signal, the data acquire a sinusoidal phase modulation from the pump through the CPM, generating multiple wavelengths spaced at the modulation frequency on both sides of the incoming signal wavelength, i.e., generating sidebands around the incoming signal wavelength. By filtering out a portion of the sidebands, converted signal of the desired wavelength at the output is obtained. Compared with other techniques, this approach has several important advantages: First stability, operability in a wide signal wavelength range and short switching window with relatively broad signal pulses. It contributes additional functions such as waveform reshaping and phase reconstruction.

#### 3.10  High-Speed Silicon Photonics Transceiver

High-speed optical transceivers are required to deal with the high demand for high data rate due to the skyrocketed increase of users and services day by day. These are generally placed the path forward to overcome these limitations, but no traditional optical technology can provide a low-cost solution. There is an opportunity for high-speed silicon photonics, where optical and electrical circuits are monolithically formed with conventional silicon-based technology.

#### 3.10.1  Silicon Photonics Transceiver Architecture

Figure 3.40 shows an architecture of silicon-based transceivers consisting of three transmitters and three receivers with WDM multiplexer and demultiplexer. There are channels having control thermally to the MZI modulator and multiplexer/demultiplexer. This is a TPM that denotes the thermal phase modulators to control these elements. It has a communication bus, digital control circuitry and a built-in self-test block for wafer of the transceiver functionality at full data rate by means of an in-house electrooptical probe station. The light sources are only external to the chip architecture having fiber coupled to the chip through grating couplers denoted as “TXn CW-in” (as shown in Figure 3.40).

Figure 3.40   An architecture of silicon-based transceivers.

The elements in the architecture are

• The high-speed MZI modulator operates with the principle of wave propagation and is a distributed-driver design based on carrier depletion in a silicon reverse-biased diode permitting high-speed, low-power operation. The MZIs consists of monitoring photo detector and low-speed phase modulators for closed-loop control at quadrature.
• Low-loss waveguides transmit signals around the chip.
• High-efficiency grating couplers put light in and out of the CMOS circuit at close to normal incidence.
• The WDM multiplexer and demultiplexer are used for three channel designs based on an interleaver architecture. The designed channel spacing is 200 GHz, with adjacent channel crosstalk of < − 17 dB. The WDM elements are made tunable to remain locked automatically to the input laser wavelengths by a closed-loop control system.
• Ge-PIN waveguide diodes integrated to the system are set for high-speed signal detection as well as providing signals for closed-loop control systems. The extremely low capacitance of the diodes is used in receiver designs with high sensitivity.
• The architecture has all the high-speed analog circuits usually found in a transceiver (limiting amp, laser drivers, modulator driver, etc.) and large digital blocks to control the system and to communicate to the outside world through a digital bus.
• High-speed electrical interfaces are used to have the standard.

#### 3.10.2  Performance

The transmitter and the receiver part of the system are important to include predict link budget margin by using a full bidirectional link with pairs of packaged transceiver devices. The tests performed demonstrated BER< 10−12 at 10 Gbps per channel for a 231 − 1 pseudo-random bit sequence over extended testing of multiple days without any temperature control, only closed-loop control systems on chip.

#### Summary

Optical network nodes consist of WDM/WDDM, optical switch, ADM/demultiplexers, traffic grooming devices, etc. In this chapter, we have discussed that all these devices used optical network nodes. Since these devices are made by using integrated optics for improved reliability, immunity to vibration and electromagnetic interference, low loss transmission, small size, light weight, large bandwidth (multiplexing capability), low power consumption and batch fabrication economy, we have discussed basic components such as DC, TMI coupler, MMI coupler, MZ devices, and AWG used in the above integrated optical devices. We have also discussed optical amplifier used for amplification signal in wide-area optical backbone. Since optical amplifier makes non-uniform amplifications over all wavelength channels used in WDM optical network, we have also mentioned tunable gain equalizer for uniform optical power of wavelength channels. We have discussed the different types of wavelength converter used in an optical network.

#### Exercises

3.1

Suppose we want to design a system with 16 channels, each channel with a rate of 1 Gbps. How much bandwidth is required for the system?

3.2

Suppose we have a fiber medium with a bandwidth of about 20 nm. The center wavelength is 0.82 µm. How many 10 GHz channels can be accommodated by the fiber? Calculate the maximum number of channels for a center wavelength of 1.5 µm.

3.3

Consider an optical communication system in which the transmitter tuning range is from 1450 to 1600 nm, and the receiver tuning range is from 1500 to 1650 nm. How many 1 Gbps channels can be supported in the system?

3.4

Consider a WDM passive-star-based network for N nodes. Let the tuning range of the transmitters be 1550–1560 nm, and let the tuning range of the receivers be 1555–1570 nm. Assume that the desired bit rate per channel is 1 Gbps. Also assume that a channel spacing of at least 10 times the channel bit rate is needed to minimize crosstalk on a WDM system. Find the maximum number of resolvable channels for this system.

3.5

Find the converted wavelength of a wavelength converter based on FWM in which the input wavelength and pumping wavelengths are 1.52 and 1.53 µm.

3.6

Four-stage point symmetric cascaded delay line filter with uniform distribution acts as an EDFA gain equalizer. Find the total length of the filter with delay line path difference ΔL = 10 µm and height of 50 µm if the input and output waveguide length, coupling length of each coupler and central wavelength are 200, 20 and 1.55 µm, respectively.

3.7

Find population inversion of an EDFA gain equalizer when the population of Er++ ions in metastable and lower energy levels are 3 × 1010 and 1.6 × 1010.

3.8

A 5-stage Y symmetric cascaded delay line filter with uniform distribution acts as ADM. Find the total length of the filter with delay line path difference ΔL = 5 µm and height of 30 µm if the input and output waveguide length, coupling length of each coupler and the dropping wavelength are 500, 12 and 1.55 µm, respectively.

3.9

An optical amplifier delivers an output power in response to input power P in described by

$P o u t = A [ 1 – exp ( − b P i n ) ]$

where A and b are constants.

• What is the saturation power of the amplifier?
• Find the power gain of the amplifier for small input power.

3.10

How many channels can be accommodated/groomed in STS-192 SONET if each channel requires a data speed of 1.25 Gbps.

3.11

Find STS SONET if an optical link requires to have four channels of 625 Mbps and two channels of 1250 Mbps channels.

3.12

Find the minimum coupling length required for an MMI coupler to get cross and bar states if the propagation constants for fundamental mode, first-order mode and second-order mode are 6.542 (µm)−1, 6.531 (µm)−1 and 6.231 (µm)−1 respectively.

3.13

Find the minimum coupling length required for a TMI coupler to get cross and bar states if the propagation constants for the fundamental and first-order modes are 6.572 (µm)−1 and 6.541 (µm)−1, respectively.

3.14

Find the length of wavelength multiplexer-based TMI coupler to multiplex wavelength channels λ 1 = 1.53 µm and λ 2 = 1.55 µm, respectively. The propagation constants $β 00 λ 1$ , $β 01 λ 1 ,$ and $β 01 λ 2$ are ~ 6.0556, 5.9807, 5.974 and 5.9023 (μm)−1, respectively and the input and output waveguide lengths are 200 and 210 µm, respectively.

3.15

Find the length of TOMZ switch having a heater length of 3 mm, and a coupler with beat length of 100 µm and transition length of 250 µm.

3.16

If each channel has a bit rate of B Gbps and 2B GHz bandwidth requiring for encoding and modulation efficiency of 2 Hz/bps and a channel spacing requiring six times channel rate, prove that the maximum number of resolvable channels of the network is given by

$W = Δ f + 6 B 8 B$

3.17

If WDM has a central wavelength λ and tuning range of receiver/transmitter is Δλ, find the frequency range.

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