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Preface& P0 y, N6 X# h M8 o6 h# [
Optical filters whose frequency characteristics can be tailored to a desired response7 I1 v- x& d! Y/ q1 O
are an enabling technology for exploiting the full bandwidth potential of optical0 m. Q# l( f& {" A
fiber communication systems. Optical filter design is typically approached with
4 Y `% _9 G3 r5 `, eelectromagnetic models where the fields are solved in the frequency or time domain.$ {" X. }8 @0 _+ n3 J7 [7 m! O. b4 W5 h
These techniques are required for characterizing waveguide properties and individual2 G& R0 _4 J" ^/ }4 e
devices such as directional couplers; however, they can become cumbersome
. H* C8 j/ ~! m# s6 h9 R# i9 s( Hand non-intuitive for filter design. A higher level approach that focuses on the
* ?( H4 m& q7 N. S5 Zfilter characteristics providing insight, fast calculation of the filter response, and
; `9 m7 G% ]3 a+ \# a7 Weasy scaling for larger and more complex filters is addressed in this book. The important
9 n% P& Q( `* x# a M5 |- Gfilter characteristics are the same as those for electrical and digital filters.
9 f% V/ k$ e! {For example, passband width, stopband rejection, and the transition width between' h- r- ~; \ S5 ^3 e
the passband and stopband are all design parameters for bandpass filters. For high$ c0 \2 T! C. R2 }
bitrate optical communication systems, a filter’s dispersion characteristics must also
- P' V" u/ l" O( P5 L' X( ?be understood and controlled. Given the large body of knowledge about analog and
5 E0 B3 |3 ^/ Y& d8 Fdigital filter design, it is advantageous to analyze optical filters in a similar manner.
& X4 v( }4 w( u- H( L4 gIn particular, this book is unique in presenting digital signal processing techniques
# y/ E V6 c, d) U! Q" A% Z Mfor the design of optical filters, providing both background material and theoretical; b" |( j1 g3 ]6 N
and experimental research results.
. \7 L) A" g1 }% r4 l0 cThe optical filters described are fundamentally generalized interferometers' w1 \# a: n# ]( K! j% v; |3 p, ^: Y
which split the incoming signal into many paths, in an essentially wavelength independent
% R% d" I3 D' D+ Z/ z5 ~! `$ O3 m' Gmanner, delayed and recombined. The splitting and recombining ratios, as: n4 m* ~* W/ J, `( m
well as the delays, are varied to change the frequency response. With digital filters,
% W$ W7 i% _0 v: b4 U! xthe splitting and recombining are done without concern for loss or the required
L6 ~; M+ Y+ ]* Pgain; whereas, filter loss is a major design consideration for optical filters. The delays4 r) P* m. b) a. h# Q i
are typically integer multiples of a smallest common delay. A well-known
& I# B5 u/ V4 s* _# z9 x% u: ]example is a stack of thin-film dielectric materials where each layer is a quarterxi# s, d; b; _2 ]7 o( G' y/ c
wavelength thick. In this case, the splitters and combiners are the partial reflectances4 L6 d$ D8 P; j9 b( Y1 I
at each interface. Just as capacitors, inductors, and resistors have underlying
$ B/ m+ q; D& S f' W7 y% A. H0 Kelectromagnetic models but are treated as lumped elements in analog filter designs,
! h4 f v% Y0 Weach splitting and combining element is modeled from basic electromagnetic8 h# j" ?* L3 P, H7 M. d
theory and then treated as a lumped element in the optical filter design.
; G7 c! P7 G3 a8 d; i" pAnother similarity with analog filters, but a major difference from digital filters,
+ k4 L. F- V$ y: E- X; wis the level of precision and accuracy that can be achieved in the design parameters
) ~( A S. k$ J- Ifor optical filters. For example, analog electrical components and optical components' M E5 |0 G }' O5 k
cannot be specified to the tenth decimal place; whereas, such numerical precision
# |0 S, _7 w# u9 ^' g' [is commonplace for digital filters. Thus, a filter’s sensitivity to variations in the) x3 k' E1 s2 N" M' h: z( {
design parameters must be considered. In addition, measurement and analysis techniques
4 |! C# S2 Q1 D! F! O# ~are needed to identify where variations have occurred in the fabrication4 R% k& N: o& c" t
process and what parameters are causing a filter to deviate from its nominal design.
+ ^ E2 N: @3 s4 Z+ ~% H- {These issues, which are characteristic of optical filters, are addressed in detail.0 N6 ]+ p! M* r7 R0 o7 ]
This book is intended for researchers and students who are interested in optical
- D+ x" Q) W' _% n& y1 A' yfilters and optical communication systems. Problem sets are given for use in a graduate# t% W/ ]+ U/ T) g+ o
level course. The main focus is to present the theoretical background for various; T( Z. G9 K0 g+ @+ W: S8 D7 m3 o
architectures that can approximate any filter function. Planar waveguide devices1 i6 G3 H V; _# m' k( p4 o
realized in silica are used as examples; however, the theory and underlying design
% v U! X. v% u; @; G) cconsiderations are applicable to optical filters realized in other platforms such as* B) U0 E. `2 U) m# K' z) Z
fiber, thin-film stacks, and microelectro-mechanical (MEMs) systems. We are at an2 Q+ N8 E2 E5 `8 z. X( n
early point in the evolution of optical filters needed for full capacity optical communication
4 j5 R& W! \ T3 asystems and networks. Many filters need experimental investigation, so7 B- ] {! D6 h7 u" ~! \
this book should be valuable to people interested in furthering their theoretical understanding
4 E& ^) `6 H! k9 E ^2 u- F6 cas well as those who are fabricating filters using a wide range of material7 O5 j! o* R# M# X4 g4 Z7 ^2 o
systems and fabrication techniques.
9 Y5 G" `6 ]4 E: V8 _A detailed introduction to electromagnetic and signal processing theory is given
# O) T0 z) C4 K3 g. R$ ?in Chapter 1. In Chapter 2 on electromagnetic theory, a complete discussion is provided
' y9 U9 f# Z9 E* x" pon waveguide modes, coupled-mode theory, and dispersion. In Chapter 3 on+ Z% ^6 H+ \2 F3 B0 K. ~8 g
signal processing theory, Fourier transforms, Z transforms, and digital filter design9 h' [$ x' Q5 e* s; V5 z
techniques are discussed. The next three chapters (Chapters 4–6) cover optical filters8 a* U( ^5 ?7 Q* d) j
and include design examples that are relevant to wavelength division multiplexed) L: y' F3 t* t) s# B8 l; @
(WDM) optical communication systems. The examples include bandpass filters,
7 ~& K* N3 `/ F( l' f! k# Vgain equalization filters for compensating the wavelength dependent gain of( K! u" W% |- U( `, G
optical amplifiers, and dispersion compensation filters. A particularly important filter
+ C0 s6 }: ]* f" ], P0 rfor WDM systems is the waveguide grating router (WGR), which is fundamentally5 H( Z: P# F( J% _8 Z0 F
an integrated diffraction grating, because it filters many channels simultaneously.
+ ~( k. }- z9 I. OIts operation is examined using Fourier transforms to provide insight into its/ H6 o7 b- I6 R
periodic frequency and spatial behavior. Filters using thin-film dielectric stacks,$ e/ K9 n- ^. Y2 C, E4 l2 t
Bragg gratings, acousto-optic coupling, and long period gratings are also examined.
$ Z$ A6 z$ W9 H+ xFilters with a large number of periods such as Bragg and long period gratings are
& n) X+ @& G' T$ l& Mtypically analyzed using coupled-mode theory. We include the coupled-mode solutions
% T6 P D1 o# E* x: Q) w8 gfor these filters, thus offering the reader a comparison between signal processing
' r) h2 s- p( }techniques and the coupled-mode approach. Measurement techniques and filter
* f0 l1 F# ^8 Y3 ?9 ]6 p1 Sxii PREFACE4 ]% P& S. q1 E2 B! O) a9 t
analysis algorithms, which extract the filter’s component values from its spectral or
2 K( d5 F) d0 B, Otime domain response, are addressed in Chapter 7. Finally, areas that are expected to; t. d7 |( R" W Q* q; E
have a dramatic effect on the evolution of optical filters are highlighted./ U6 D) B8 a1 G
The authors gratefully acknowledge the review and suggestions provided by G.5 J! r) Z7 a! [# ]6 G2 K2 a
Lenz, Y. P. Li, W. Lin, D. Muelhner, and A. E. White of Bell Laboratories Lucent
L+ F( i% V/ t2 }; A0 ~1 jTechnologies, S. Orfanidis of Rutgers University, B. Nyman of JDS Fitel, and T. Erdogan. m$ y9 X$ Q8 x
of the University of Rochester.2 k+ e- j. g. O- o8 A3 T
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