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Preface6 R& M' f) l# i: t% s4 g! l n
Optical filters whose frequency characteristics can be tailored to a desired response
: G! g- [0 z" s' `are an enabling technology for exploiting the full bandwidth potential of optical, B B1 V b( O/ ?) c, K3 x( A1 i
fiber communication systems. Optical filter design is typically approached with7 C7 l7 Q8 k/ d/ m, b1 Y
electromagnetic models where the fields are solved in the frequency or time domain.+ Y. M2 u$ S) {5 |2 m/ B6 I/ t
These techniques are required for characterizing waveguide properties and individual" x/ b8 s% `0 _- ^
devices such as directional couplers; however, they can become cumbersome7 J. T0 g( `' x9 ?
and non-intuitive for filter design. A higher level approach that focuses on the
4 i& q7 P; X3 D* q+ A) Gfilter characteristics providing insight, fast calculation of the filter response, and! Y! ]+ g$ t. R5 `3 b
easy scaling for larger and more complex filters is addressed in this book. The important4 _2 @7 y; L) B' n
filter characteristics are the same as those for electrical and digital filters.. e7 Q2 M6 P9 i+ n; ]
For example, passband width, stopband rejection, and the transition width between
3 ]; m. a1 ?! I! r1 r" ethe passband and stopband are all design parameters for bandpass filters. For high0 x e! r; X0 {+ ]- f9 R
bitrate optical communication systems, a filter’s dispersion characteristics must also8 y5 v2 M4 x7 N0 ~0 j
be understood and controlled. Given the large body of knowledge about analog and
! s# H7 g& _) a6 r* Idigital filter design, it is advantageous to analyze optical filters in a similar manner.
) I1 \# u& A3 }) b. I3 r- m8 TIn particular, this book is unique in presenting digital signal processing techniques
3 e5 I3 {; O5 N: Kfor the design of optical filters, providing both background material and theoretical+ \# S+ ?: ?; F8 r
and experimental research results.& L. M: U/ q" h$ J: Q
The optical filters described are fundamentally generalized interferometers7 ?4 _0 m0 ^2 R
which split the incoming signal into many paths, in an essentially wavelength independent
; L/ f: y* Y- c: |* K; j$ Tmanner, delayed and recombined. The splitting and recombining ratios, as6 Y$ e/ o7 a; o7 I( q" u
well as the delays, are varied to change the frequency response. With digital filters,
4 I) f: \( f$ Bthe splitting and recombining are done without concern for loss or the required. H! g5 K0 k% R; B& Q1 e
gain; whereas, filter loss is a major design consideration for optical filters. The delays& z3 |, @$ G$ z& E) ]3 ?6 F+ o- I
are typically integer multiples of a smallest common delay. A well-known
) q/ _5 D5 Z0 t9 h# jexample is a stack of thin-film dielectric materials where each layer is a quarterxi
n7 D+ G2 g: |4 n6 O3 Y+ Twavelength thick. In this case, the splitters and combiners are the partial reflectances( A8 o8 {1 }" ~
at each interface. Just as capacitors, inductors, and resistors have underlying1 @, @' i& S( ?2 L( j' N1 A
electromagnetic models but are treated as lumped elements in analog filter designs,
0 E/ z2 v, D% G) c0 ]" g- Y. oeach splitting and combining element is modeled from basic electromagnetic1 N+ r9 O# b' C- h m& o; v
theory and then treated as a lumped element in the optical filter design.* i, b5 ?5 p) I& M( O l
Another similarity with analog filters, but a major difference from digital filters,* j* h$ Z' X, G( P! v9 O6 m
is the level of precision and accuracy that can be achieved in the design parameters7 N8 B% Y, [3 I4 S4 G& |1 h4 n
for optical filters. For example, analog electrical components and optical components- f, R. m4 m+ X$ A2 Q; w
cannot be specified to the tenth decimal place; whereas, such numerical precision
, p( C# e( v2 U3 l: F* `( X! ?is commonplace for digital filters. Thus, a filter’s sensitivity to variations in the9 V# r, u4 y* s+ ?/ I$ x
design parameters must be considered. In addition, measurement and analysis techniques
$ V3 i3 M0 m0 u; U8 xare needed to identify where variations have occurred in the fabrication
' X! M2 j' p% gprocess and what parameters are causing a filter to deviate from its nominal design.2 z) X) H5 @. ^- d |% d2 z
These issues, which are characteristic of optical filters, are addressed in detail.0 T: E$ R7 S" N4 M$ ~8 Y( V+ J( }
This book is intended for researchers and students who are interested in optical
" p/ {3 y7 ^- _5 @# Wfilters and optical communication systems. Problem sets are given for use in a graduate4 }3 l6 g2 r$ E
level course. The main focus is to present the theoretical background for various2 y7 ?7 j) j6 D: N* A% h6 X2 F
architectures that can approximate any filter function. Planar waveguide devices
$ |8 X! {: J0 j) t8 d4 e4 Jrealized in silica are used as examples; however, the theory and underlying design8 ~# a2 i+ f1 h0 D, ^
considerations are applicable to optical filters realized in other platforms such as1 c) P+ X8 C4 A
fiber, thin-film stacks, and microelectro-mechanical (MEMs) systems. We are at an
# y7 U- y( Z) D. Hearly point in the evolution of optical filters needed for full capacity optical communication8 `9 W# W b/ |9 `, E
systems and networks. Many filters need experimental investigation, so" a* e1 ~3 `1 m8 d% `8 \: p) ~
this book should be valuable to people interested in furthering their theoretical understanding
" V5 m- F8 B2 ]( H5 e4 t/ b& _6 Sas well as those who are fabricating filters using a wide range of material
5 ]2 a0 ?0 n3 I5 t; Y$ zsystems and fabrication techniques.3 l% m9 q i+ \0 K6 F
A detailed introduction to electromagnetic and signal processing theory is given# `* V. S6 R- g
in Chapter 1. In Chapter 2 on electromagnetic theory, a complete discussion is provided# G+ F/ t& L8 d) O
on waveguide modes, coupled-mode theory, and dispersion. In Chapter 3 on# s+ X4 J! k% b
signal processing theory, Fourier transforms, Z transforms, and digital filter design
6 s, ^2 s: i) jtechniques are discussed. The next three chapters (Chapters 4–6) cover optical filters
+ D0 F8 J! ~9 M ?; M; F3 Iand include design examples that are relevant to wavelength division multiplexed
1 w$ H, ~& M8 h( }5 L(WDM) optical communication systems. The examples include bandpass filters,
- M0 t/ c2 A9 T* D/ Mgain equalization filters for compensating the wavelength dependent gain of6 e; O- ^* I7 \9 H, X A$ g6 n: A
optical amplifiers, and dispersion compensation filters. A particularly important filter7 x) G7 e7 n+ s
for WDM systems is the waveguide grating router (WGR), which is fundamentally, c; Y' a6 P- I4 Q
an integrated diffraction grating, because it filters many channels simultaneously.9 r+ v; M) a6 s8 r) B
Its operation is examined using Fourier transforms to provide insight into its6 W- }) I9 [# q5 s
periodic frequency and spatial behavior. Filters using thin-film dielectric stacks,- F- L) U$ a: _$ H, @! w: T: a
Bragg gratings, acousto-optic coupling, and long period gratings are also examined.
' K$ c2 _* p/ p: _( Q$ n" `1 F HFilters with a large number of periods such as Bragg and long period gratings are" ]) g' d) W$ v0 E, ~8 i) W5 k
typically analyzed using coupled-mode theory. We include the coupled-mode solutions; V; l, n" Q; }- G2 u1 [" H. K! k# e
for these filters, thus offering the reader a comparison between signal processing; F1 t( p0 j7 v' g# M
techniques and the coupled-mode approach. Measurement techniques and filter6 V8 h0 ]5 N! ?3 G) _2 p7 }
xii PREFACE
! O+ @4 l" p: h; ?9 w/ ?analysis algorithms, which extract the filter’s component values from its spectral or0 {1 [* q" q3 P- G. d3 g0 [& g
time domain response, are addressed in Chapter 7. Finally, areas that are expected to; L; P u4 |, |2 m# c3 x P
have a dramatic effect on the evolution of optical filters are highlighted.
# j3 }: B0 P9 ~: ]) ` h7 ^ uThe authors gratefully acknowledge the review and suggestions provided by G.: _* v4 W% L) P% M
Lenz, Y. P. Li, W. Lin, D. Muelhner, and A. E. White of Bell Laboratories Lucent
2 W7 Z2 F k6 w) KTechnologies, S. Orfanidis of Rutgers University, B. Nyman of JDS Fitel, and T. Erdogan
/ o& u% K8 |* ?' t$ k9 nof the University of Rochester.3 }! a7 P% _3 H& W4 L7 J
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