Optical Networks: A Practical Perspective - Part 26 ppsx

The phase change induced by each amplifier on the probe is different be- cause different amounts of signal power are present in the two amplifiers.. Referring to Figure 3.78, where we pl

220 COMVONrNTS

3.8.3

The advantage of CGM is that it is conceptually simple However, there are several drawbacks The achievable extinction ratio is small (less than 10) since the gain does not really drop to zero when there is an input 1 bit The input signal power must be high (around 0 dBm) so that the amplifier is saturated enough to produce a good variation in gain This high-powered signal must be eliminated at the amplifier output by suitable filtering, unless the signal and probe are counterpropagating Moreover, as the carrier density within the SOA varies, it changes the refractive index as well, which in turn affects the phase of the probe and creates a large amount of pulse distortion

Interferometric Techniques

The same phase-change effect that creates pulse distortion in CGM can be used

to effect wavelength conversion As the carrier density in the amplifier varies with the input signal, it produces a change in the refractive index, which in turn mod- ulates the phase of the probe~hence we use the term cross-phase modulation for this approach This phase modulation can be converted into intensity modulation

by using an interferometer such as a Mach-Zehnder interferometer (MZI) (see Sec- tion 3.3.7) Figure 3.78 shows one possible configuration of a wavelength converter using cross-phase modulation Both arms of the MZI have exactly the same length, with each arm incorporating an SOA The signal is sent in at one end (A) and the probe at the other end (B) If no signal is present, then the probe signal comes out unmodulated The couplers in the MZI are designed with an asymmetric cou- pling ratio ?' -r 0.5 When the signal is present, it induces a phase change in each amplifier The phase change induced by each amplifier on the probe is different be- cause different amounts of signal power are present in the two amplifiers The MZI translates this relative phase difference between its two arms on the probe into an intensity-modulated signal at the output

This approach has a few interesting properties The natural state of the MZI (when no input signal is present) can be arranged to produce either destructive or constructive interference on the probe signal Therefore we can have a choice of whether the data coming out is the same as the input data or is complementary The advantage of this approach over CGM is that much less signal power is required to achieve a large phase shift compared to a large gain shift In fact, a low signal power and a high probe power can be used, making this method more attractive than CGM This method also produces a better extinction ratio because the phase change can be converted into a "digital" amplitude-modulated output signal

by the interferometer So this device provides regeneration with reshaping (2R) of

Figure 3.78 Wavelength conversion by cross-phase modulation using semiconductor optical am- plifiers embedded inside a Mach-Zehnder interferometer

the pulses Depending on where the MZI is operated, the probe can be modulated with the same polarity as the input signal, or the opposite polarity Referring to Figure 3.78, where we plot the power coupled out at the probe wavelength versus the power at the signal wavelength, depending on the slope of the demultiplexer, a signal power increase can either decrease or increase the power coupled out at the probe wavelength Like CGM, the bit rate that can be handled is at most 10 Gb/s and is limited by the carrier lifetime This approach, however, requires very tight control of the bias current of the SOA, as small changes in the bias current produce refractive index changes that significantly affect the phase of signals passing through the device

We have seen above that the CPM interferometric approach provides regenera- tion with reshaping (2R) of the pulses As we saw earlier, while 2R cleans up the signal shape, it does not eliminate phase (or equivalently timing) jitter in the signal, which would accumulate with each such 2R stage In order to completely clean up the signal, including its temporal characteristics, we need regeneration with reshap- ing and retiming (3R) Figure 3.79 shows one proposal for accomplishing this in

222 COMPONENTS

Figure 3.79 All-optical regeneration with reshaping and retiming (3R) using a combination of cross-gain modulation and cross-phase modulation in semiconductor optical amplifiers (After [Chi97].)

3.8.4

The two probe signals are synchronized and modulated at twice the data rate of the incoming signal Since the clock is available, the phase of the probe signals is adjusted to sample the input signal in the middle of the bit interval At the output of the first stage, the two probe signals have reduced power levels when the input signal

is present and higher power levels when the input signal is absent In the second stage, one of the probe signals is delayed by half a bit period with respect to the other At the output of this stage, the combined signal has a bit rate that matches the bit rate of the input signal and has been regenerated and retimed This signal is then sent through a CPM-based interferometric converter stage, which then regenerates and reshapes the signal to create an output signal that has been regenerated, retimed, and reshaped

Wave Mixing

The four-wave mixing phenomenon that occurs because of nonlinearities in the trans- mission medium (discussed in Section 2.4.8) can also be utilized to realize wavelength conversion Recall that four-wave mixing causes three waves at frequencies fl, f2, and f3 to produce a fourth wave at the frequency fl + f2 - f3; when fl = f2, we get a wave at the frequency 2 f l - f 3 What is interesting about four-wave mixing

is that the resulting waves can lie in the same band as the interacting waves As we have seen in Section 2.4.8, in optical fibers, the generated four-wave mixing power

is quite small but can lead to crosstalk if present (see Section 5.8.4)

For the purposes of wavelength conversion, the four-wave mixing power can be enhanced by using an SOA because of the higher intensities within the device If we have a signal at frequency fs and a probe at frequency f p , then four-wave mixing will produce signals at frequencies 2 f p - fs and 2 f s - f p , as long as all these frequencies lie within the amplifier bandwidth (Figure 3.80)

The main advantage of four-wave mixing is that it is truly transparent because the effect does not depend on the modulation format (since both amplitude and phase are preserved during the mixing process) and the bit rate The disadvantages are that the other waves must be filtered out at the SOA output, and the conversion efficiency goes down significantly as the wavelength separation between the signal

224 COMPONENTS

Figure 3.80

amplifier

Wavelength conversion by four-wave mixing in a semiconductor optical

and probe is increased We will study the conversion efficiency of four-wave mixing

in Section 5.8.4

Summary

We have studied many different optical components in this chapter Couplers, isola- tors, and circulators are all commodity components Many of the optical filters that

we studied are now commercially available, with fiber gratings, thin-film multicavity filters, and arrayed waveguide gratings all competing for use in commercial WDM systems

Erbium-doped fiber amplifiers (EDFAs) are widely deployed and indeed served

as a key enabler for WDM EDFA designs today incorporate multiple stages and gain-flattening filters and provide midstage access between the multiple stages to insert other elements such as dispersion compensating modules and wavelength add/drop multiplexers A new generation of EDFAs providing amplification in the L-band has recently emerged We are also now seeing distributed Raman amplifiers used in conjunction with EDFAs in ultra-long-haul systems

Semiconductor DFB lasers are used in most high-speed communication systems today although other single-longitudinal mode laser structures may eventually be- come viable commercially Compact semicondunctor tunable lasers are now emerg- ing as viable commercial devices High-speed APDs and pinFET receivers are both available today

Large-scale MEMS-based optical switches for use in wavelength crossconnects are now emerging as commercial devices, and a variety of technologies are avail- able to build smaller-scale switches All-optical wavelength converters are still in the research laboratories, awaiting significant cost reductions and performance improve- ments before they can become practical

described in detail in several textbooks on optics, for example, [KF86, BW99] The Stimax grating is described in [LL84] and [Gre93] See [CK94, Ben96, Kas99] for details on fiber grating fabrication and properties, and [Ven96b, Ven96a] for applica- tions of long-period gratings For a description of how dielectric thin-film multicavity filters work, see [SS96] and [Kni76] The electromagnetics background necessary to understand their operation is provided, for example, by [RWv93] Early papers on the arrayed waveguide grating are [DEK91] and [VS91] The principle behind their operation is described in [McG98, TSN94, TOTI95, TOT96] The integrated-optics AOTF is described in [SBJC90, KSHS01], and its systems applications are discussed

in [Che90]

There is an extensive literature on optical amplifiers See [BOS99, Des94] for EDFAs, [Flo00] for a summary of L-band EDFAs, and [O'M88] for a tutorial

on SOAs [Tie95, SMB00, FDW01] provide samples of some recent work on gain-clamped SOAs See [NE01, NE00] and [KK97, Chapter 7] for an overview

of Raman amplifiers

There are several textbooks on the subject of lasers alone; see, for example, [AD93] Laser oscillation and photodetection are covered in detail in [Yar97] [JQE91] is a good reference for several laser-related topics Other good tutorials

on lasers appear in [BKLW00, LZ89, Lee91, SIA92] A very readable and up-to-date survey of vertical cavity lasers can be found in [Har00] See also [MZB97] Most semiconductor lasers today make use of quantum well structures See [AY86] for

a good introduction to this subject The mathematical theory behind mode locking

is explained in [Yar89] and [Yar65] There is an extensive discussion of various mode-locking methods for fiber lasers in [Agr95] Lithium niobate external modula- tors are well described in [Woo00] and [KK97, Chapter 9], and electro-absorption modulators in [BKLW00] and [KK97, Chapter 4]

There is currently significant effort toward realizing commercially viable tunable lasers We refer the reader to [Col00, Har00, AB98, Gre93, KK97] for more in-depth explorations of this subject An early review of tunable laser approaches appeared

in [KM88] The VCSEL-based tunable laser is described in [Vak99] Other types

of tunable VCSELs have been demonstrated; see, for instance, [CH00, Har00] The sampled grating laser structure is explained in [JCC93] and superstructure grating lasers in [Toh93] See [WMB92, Rig95] for details on the GCSR laser The arrayed external grating-based laser approaches were proposed in [Soo92, ZJ94, Zir96]

Input

Figure 3.81 A 3 dB coupler with the two outputs connected by a piece of fiber

The tutorial article by Spanke [Spa87] is a good review of large switch architec- tures for optical switches See also [MS88] for a good collection of papers on optical switching and [Clo53] for the original paper on the Clos switch architecture The classic book by Bene~ [Ben65] is the authoritative reference for the mathematical theory of large switch architectures developed for telephony applications

A very accessible survey of mechanical switches can be found in [Kas95, Chapter 13] Several papers [NR01, LGT98, Nei00, Ryf01, Lao99] describe MEMS-based switches The inkjet-based waveguide switch is described in [Fou00] See [WL96, PS95] for some early papers on liquid crystal switches

Surveys and comparisons of different types of wavelength converters appear in [Stu00, EM00, NKM98, Yoo96, ISSV96, DMJ+96, Chi97]

3.1

3.2

Problems

Consider the 3 dB 2 x 2 coupler shown in Figure 3.81 Suppose we connect the two outputs with a piece of fiber Assume that the polarizations are preserved through the device A light signal is sent in on the first input What happens? Derive the field transfer function for the device Assume the coupler used is a reciprocal device so that it works exactly the same way if its inputs and outputs are reversed Hint: This device is called a loop mirror

Consider a device with three ports where it is desired to send all the energy input

at ports 1 and 2 to port 3 We assume, for generality, that all ports can be used as inputs and outputs The scattering matrix of such a device can be written as

0 0 s13 )

S - 0 0 $23 9

3.4

3.5

3.6

3.7

3.8

3.9

3.10

3.11

scattering matrix of such a device can be written as

S_ (Sll s12)

0 $22 "

Show that a scattering matrix of this form cannot satisfy the conservation of energy condition, (3.4) Thus the loss occurs in the isolator because the power input at port

2 must be absorbed by it However, the power input at port 1 can be transferred to port 2 without loss

In Figure 3.10, show that the path length difference between the rays diffracted at angle 0a and traversing through adjacent slits is approximately a[sin(Oi) - sin(0d)] when the grating pitch a is small compared to the distance of the source and the imaging plane from the grating plane

Derive the grating equation for a blazed reflection grating with blaze angle ~, such

as the one shown in Figure 3.11

Derive the amplitude distribution of the diffraction pattern of a grating with N narrow slits spaced distance d apart Show that we obtain diffraction maxima when

d sin 0 - m)~ Discuss what happens in the limit as N ~ oo

Show that the resonant frequencies f~ of a Fabry-Perot cavity satisfy f ~ - f o + n A f ,

n integer, for some fixed f0 and Af Thus these frequencies are spaced equally apart Note that the corresponding wavelengths are n o t spaced equally apart

Derive the power transfer function of the Fabry-Perot filter

Derive the expression (3.13) for the finesse of the Fabry-Perot filter Assume that the mirror reflectivity, R, is close to unity

Show that the fraction of the input power that is transmitted through the Fabry-Perot filter, over all frequencies, is (1 - R)/(1 + R) Note that this fraction is small for high values of R Thus, when all frequencies are considered, only a small fraction of the input power is transmitted through a cavity with highly reflective facets

Consider a cascade of two Fabry-Perot filters with cavity lengths 11 and 12, respec- tively Assume the mirror reflectivities of both filters equal R, and the refractive index

of their cavities is n Neglect reflections from the second cavity to the first and vice

228 ' C O M P O N E N T S

3.12

3.13

3.14

3.15

3.16

3.17

versa What is the power transfer function of the cascade? If 11/12 - - k / m , where k and m are relatively prime integers, find an expression for the FSR of the cascade Express this FSR in terms of the FSRs of the individual filters

Show that the transfer function of the dielectric slab filter shown in Figure G.l(b) is identical to that of a Fabry-Perot filter with facet reflectivity

~ / ~ - n2 - n l

n 2 + n l assuming n3 = n 1

Consider a stack of 2k alternating low-index (nL) and high-index (n/4) dielectric films Let each of these films have a quarter-wave thickness at )~0 In the notation of Section 3.3.6, this stack can be denoted by (HL) ~ Find the reflectivity of this stack as

a function of the optical wavelength )~ Thus a single-cavity dielectric thin-film filter can be viewed as a Fabry-Perot filter with wavelength-dependent mirror reflectivities Derive the power transfer function of the Mach-Zehnder interferometer, assuming only one of its two inputs is active

Consider the Mach-Zehnder interferometer of Section 3.3.7

(a) With the help of a block diagram, show how a 1 x n demultiplexer can be constructed using n - 1 MZIs Assume n is a power of two You must specify the path length differences AL that must be used in each of the MZIs (b) Can you simplify your construction if only a specific one of the signals needs

to be separated from the rest of the n - 1 ? Consider the Rowland circle construction shown in Figure 3.26 Show that the differences in path lengths between a fixed-input waveguide and any two successive arrayed waveguides is a constant Assume that the length of the arc on which the arrayed waveguides are located is much smaller than the diameter of the Rowland circle Hint: Choose a Cartesian coordinate system whose origin is the point of tangency of the Rowland and grating circles Now express the Euclidean distance between an arbitrary input (output) waveguide and an arbitrary arrayed waveguide in this coordinate system Use the assumption stated earlier to simplify your expression Finally, note that the vertical spacing between the arrayed waveguides is constant

In the notation of the book, this shows that 8i - - d sinOi, where d is the vertical separation between successive arrayed waveguides, and Oi is the angular separation

of input waveguide i from the central input waveguide, as measured from the origin Derive an expression for the FSR of an AWG for a fixed-input waveguide i and a fixed-output waveguide j The FSR depends on the input and output waveguides But show that if the arc length of the Rowland circle on which the input and output

3.19

3.20

3.21

3.22

3.23

function as the wavelength router depicted in Figure 3.25 Assume that the angular spacing between the input (and output) waveguides is constant Use the result from Problem 3.16 that c~ i = d sin Oi

Design an AWG that can multiplex/demultiplex 16 WDM signals spaced 100 GHz apart in the 1.55 #m band Your design must specify, among other things, the spacing between the input/output waveguides, the path length difference between successive arrayed waveguides, the radius R of the grating circle, and the FSR of the AWG Assume the refractive index of the input/output waveguides and the arrayed wave- guides is 1.5 Note that the design may not be unique, and you may have to make reasonable choices for some of the parameters, which will in turn determine the rest

of the parameters

Show that the FWHM bandwidth of the acousto-optic filter is ~ 0.8)~2/1An

Explain how the polarization-independent acousto-optic tunable filter illustrated in Figure 3.28 acts as a two-input, two-output wavelength router when both its inputs are active

Calculate the acousto-optic interaction length that would be required for the AOTF

to have a passband width (FWHM) of 1 nm at an operating wavelength of 1.55 #m

Assume An = 0.07

Consider a 16-channel WDM system where the interchannel spacing is nominally

100 GHz Assume that one of the channels is to be selected by a filter with a 1 dB bandwidth of 2 GHz We consider three different filter structures for this purpose Fabry-Perot filter: Assume the center wavelengths of the channels do not drift What is the required finesse and the corresponding mirror reflectivity

of a Fabry-Perot filter that achieves a crosstalk suppression of 30 dB from each adjacent channel? If the center wavelengths of the channels can drift

up to 4-20 GHz from their nominal values, what is the required finesse and mirror reflectivity?

[] Mach-Zehnder interferometer: Assume a cascade of MZIs, as shown in Fig- ure 3.21(c), is used for this purpose and the same level of crosstalk suppres- sion must be achieved What is the path length difference AL and the number

of stages required, when the channel center wavelengths are fixed and when they can drift by +20 GHz?