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`\
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`XLNX—1009 / Page 1 of 9
`’\ "/
`-'
`_
`'W
`_
`\
`u
`
`"
`
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`

`

`Copyright © 1992 by Saunders College Publishing
`A Harcourt Brace Jovanovich College Publisher
`
`All rights reserved. No part of this publication may be reproduced or transmitted in any form or
`by any means, electronic or mechanical, including photocopy, recording, or any information
`storage and retrieval system, without permission in writing from the publisher.
`
`Requests for permission to make copies of any part of the work should be mailed to Copyrights
`and Permissions Department, Harcourt Brace Jovanovich, Publishers, 8th Floor, Orlando,
`FL 32887
`
`Text Typeface: Times Roman
`Compositor: Tapseo, Inc.
`Senior Acquisitions Editor: Barbara Gingery
`Assistant Editor. laura Shur
`Managing Editor: Carol Field
`Project Editor. Janet B. Nuciforo
`Copy Editor. Merry Post
`Manager of Art and Design: Carol Bleistine
`Art Director: Doris Bruey
`Text Designer. Rita Naughton
`Cover Designer: Lawrence R. Didona
`Text Artwork: Vantage Art
`Production Manager. Charlene Squibb
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`
`THIS BOOK IS PRINTED ON ACID-FREE, RECYCLED PAPER
`
`Printed in the United States of America
`
`GUIDED-WAVE PHOTONICS
`
`ISBN 0-03-033354-7
`
`Library of Congress Catalog Card Number: 9l-050888
`
`1234
`
`039
`
`987654321
`
`XLNX—1009 / Page 2 of 9
`
`

`

`250
`
`GUIDEDWAVE MODULATORS, SWITCHES. AND INFORMATION-PROCESSING DEVICES
`
`such as the one shown in Figure 1.2. This allows a degree of parallel processing
`that is exploited in each of the devices described below.
`
`7.3.2 Guided-Wave Real-Time Spectrum Analyzer (13)
`
`With electronic computation, obtaining the power spectrum of a received signal
`requires sampling a large number ofpoints and then calculating a different integral
`for each frequency at which a value for the power spectrum is desired. Since
`each calculation occurs in sequence in a conventional electronic computer, the
`entire spectrum of a wideband signal takes a long time to generate. The device
`shown in Figure 7.13 generates the power spectrum much faster. Light from a
`CW laser is butt-coupled into the slab waveguide, before entering the two-di-
`mensional lens, L1, which collimates the guided wave into a “beam” in the slab,
`with a width W. This beam interacts with the surface acoustic wave produced
`at the transducer. The geometry of this interaction is the same as that in Figure
`7. 10( a). Neglecting any Doppler shift in the light frequency in Equation (7-71)
`requires that
`
`wi = COD
`
`(7-76)
`
`which means that the incident and diffracted modes will differ only in direction
`and not in propagation constant, or
`
`in Equation (7-70). The vector momentum conservation diagram in Figure
`7.10(b) is thus an isosceles triangle, with the diffraction angle 0 given by
`
`IBil = IBDI
`
`(7-77)
`
`K Slab waveguide
`
`Detector array
`
`Incoming
`signal
`
`‘05
`
`
`
`
`Local
`oscillator
`
`Figure 7.13 Schematic of a guided-wave real time spectrum analyzer.
`
`XLNX—1009 / Page 3 of 9
`
`In idew of Equation (
`(7-78 ). The surface
`acoustic frequency r
`
`which is just the gene
`wave. Solving 15th
`(7-78) produces the
`angle
`
`Before being appliec
`is mixed with a sin:
`that the SAW fi‘equ
`
`Actually, the incom
`yielding diffracted g
`lens, L2, collimates
`’detector in the arra:
`
`signal component a
`calculated by subsfi
`guided mode powei
`the corresponding c
`the array that is pn
`centered at (05.
`To see this mm
`
`Figure 7.13, magni
`incoming signal be
`angle 6c shown in 1
`from the interacti01
`at one detector of VI
`detector of width L
`
`Differentiating Eqi
`gives
`
`

`

`
`
`7.3 GUIDED-WAVE INFORMATION PROCESSING
`
`251
`
`
`
`IKI ]. _0 = sm '[—
`
`
`
`2 | BI
`
`In view of Equation (7-77), the i and D subscripts have been dropped in Equation
`(7-78). The surface acoustic wave propagation velocity is constant over a wide
`acoustic frequency range, and obeys the relation
`
`”SAW =
`
`(2
`—
`IKI
`
`7-79
`
`)
`
`(
`
`which is just the general wave property ( Eq. 1-1 1 ), written for the surface acoustic
`wave. Solving Equation (7-79) for IKI and substituting the result into Equation
`(7-78) produces the desired relation between acoustic frequency and diffraction
`angle
`
`a = sin" ——9
`ZUSAWIBI
`
`<7-80)
`
`Before being applied to the SAW transducer in Figure 7.12, the incoming signal
`is mixed with a single-frequency sinusoid at cum from the local oscillator, so
`that the SAW frequency is related to the incoming signal frequency, (.05, by
`
`Q = «mg + cos
`
`("I-81)
`
`Actually, the incoming signal consists of multiple components at different cos,
`yielding diffracted guided modes at multiple values of 0. The second waveguide
`lens, L2, collimates light diffracted into a particular direction onto a particular
`detector in the array at the right side of the slab waveguide in Figure 7.13. Each
`signal component at a different cos corresponds to a different diffraction angle
`calculated by substituting Equation (7-81) into Equation (7-80). Assuming the
`guided mode power diffracted into any 0 is proportional to the signal power at
`the corresponding (0;, this device yields a set of currents from each detector in
`the array that is proportional to the signal power in a narrow frequency band
`centered at ms.
`To see this more clearly, consider the region enclosed by the dashed line in
`Figure 7.13, magnified to yield Figure 7.14. Let the center frequency of the
`incoming signal be we, and the diffraction angle corresponding to we be the
`angle 0, shown in Figure 7.14. If the lens L2 is situated a focal length, f, away
`from the interaction region, all diffracted energy in the angular range A0 arrives
`at one detector of width L. For small 01 , the range of angles incident on a single
`detector of width L is given by
`
`A0 = —
`
`(7-82)
`
`Differentiating Equation (7-80) with respect to 9, and using Equation (7-81)
`gives
`
`XLNX—1009 / Page 4 of 9
`
`(7-78)
`
`
`
`

`

`252
`
`GUIDED-WAVE MODULATORS, SWITCHES. AND INFORMAIION-PROCESSING DEVICES
`
`SAW direction
`
`‘<
`
`”U:r
`o'9
`Oa.(D...
`OO..
`o"I
`
`N:
`
`1N
`
`by a controllable El
`electrical signal. 11
`structure like the c
`of the electro-OPfi‘
`linear array of 9‘31
`in Figure 7.15. T1!
`the grating period,
`in the IOSLM is
`Figure 7.15. In It
`guided mode ant
`Each cell of t
`modeled in Sectic
`electro-optic mod
`assembled into a!
`of each cell must
`from that cell do r
`
`Figure 7.14 Diffraction and focusing on the detector array in the guided-wave real time
`spectrum analyzer.
`
`9:0
`
`d0_d0_
`1
`d—Q_d—ws_2v5Aw|fll
`
`2-1/2
`
`ll_[wLo+ws]}
`205Aw|l3|
`
`(”3)
`
`Solving Equation (7-83) for do)s and substituting Equation (7-82) for A0 gives
`the channel bandwidth associated with each detector in the array as
`
`dws= 205Aw|6|[1—[
`
`wLo + cos ]2]1/2 L—
`2vSAw IBI
`f
`
`7-84
`
`’
`
`<
`
`If the array contains N detectors, the device in Figure 7.13 computes a power
`spectrum of the incoming signal over the range of (05 corresponding to the range
`of diffracted angles
`.
`
`0c—01<0<0c+01
`
`(7-85)
`
`with N-point resolution along the frequency axis. This power spectrum is com-
`puted in the time it takes for the light in the waveguide to propagate from the
`laser to the detector array. Conventional methods for computing a power spec-
`trum require many successive summations and / or integrations, each of which
`can involve considerable computation time.
`
`7.3.3 The Integrated Optic Spatial Light Modulator (IOSLM)
`
`Like the real-time spectrum analyzer, the integrated optic spatial light modulator
`(abbreviated IOSLM) operates on the principle of diffraction of a guided mode
`
`Figure 7.15 Geo
`devices are show
`second.
`
`XLNX—1009 / Page 5 of 9
`
`

`

`
`
`7.3 GUIDED-WAVE INFORMATION PROCESSING
`
`253
`
`by a controllable grating structure formed in a slab waveguide in response to an
`electrical signal. Instead of a surface acoustic wave, an interdigital electrode
`structure like the one in Figure 7.9 forms the grating in the IOSLM, by means
`of the electro-optic effect described in Section 7.2.1. The IOSLM consists of a
`linear array of grating modulators based on Figure 7.9 with a geometry shown
`in Figure 7.15. The angle of diffraction is not adjustable in the IOSLM, since
`the grating period, A, is fixed when the device is fabricated. However, each cell
`in the IOSLM is individually addressable using the appropriate drive line in
`Figure 7.15. In this way, the intensity in each section of the broad, incident
`guided mode wavefront is modulated individually.
`Each cell of the IOSLM is an electro-optic Bragg modulator like the one
`modeled in Section 7.2.1 and can be evaluated using the criteria developed for
`electro-optic modulators earlier in this chapter. When an array of such cells is
`assembled into an IOSLM, some additional constraints apply. The width, W,
`of each cell must be large enough so that the transmitted and diffracted beams
`from that cell do not spread out appreciably from diffraction over the propagation
`
`
`
`
`Iosm2\*
`
`I
`
`IOSLM 1
`
`Figure 7.15 Geometry for an integrated optic spatial light modulator (IOSLM). Two
`devices are shown, with the diffracted output from the first serving as the input for the
`second.
`
`XLNX—1009 / Page 6 of 9
`
`
`
`

`

`254
`
`
`
`GUIDED-WAVE MODULATORS. SWITCHES. AND INFORMATION-PROCESSING DEVICES
`
`instances to the next elements (detectors or other devices) in the system.
`Wshould be much larger than the wavelength of the guided mode in the slab.
`Two or more IOSLMs placed in optical series with each other, as shown ‘
`Figure 7.15, are capable of a number of computational functions. For exam
`suppose that no light is difiracted by a cell with no applied voltage and that,
`an applied voltage Vmax, the cell diflmas essentially all of the guided m
`incident on it. Some diffraction is present for all applied cell voltages in
`range
`
`0 < Vc < Vmax
`
`0-“)
`
`Let the cell voltages in modulator 1 in Figure 7.15 be chosen to represent N
`sampled values of a function f(x), as represented in Figure 7.16. Since the
`. diffracted power from any cell is always positive, f(x) must be restricted to
`positive values only. For scaling purposes, let the maximum value off(x) be
`one. As pointed out in Section 7.2.1, the dilfracted intensity is not linear with
`Vc, but instead proportional to sin2 (aVc), where a is a constant dependent on
`electrode geometry and waveguide properties. Therefore, the diffracted power
`from each cell will be linear with f(x) if the voltage corresponding to the value
`offis
`
`V=lsin‘l f
`a
`
`(7-87)
`
`Returning again to Figure 7.15, suppose that a second function g(x) is sampled
`using the same procedure employed with f( x) and the resulting voltages placed
`on the cells of the second IOSLM. From Figure 7.15, the difl‘racted output from
`the Mth cell of the second IOSLM is clearly the product off( M)g(M). Thus,
`the intensity profile of the diffracted output of the second IOSLM is a sampled
`product off( x)g(x).
`The device in Figure 7.15 extracts an analog product of two positive functions
`very rapidly by operating on all the samples simultaneously. As such, it is another
`
`f(x)
`
`sin2(a V)
`
`f(xN) mm....................
`
`f(x1)
`
`xl xz
`
`...........
`
`xN
`
`Flguro 7.16 Representing the sampled values of a positive function fix) by a series of
`voltage levels.
`
`XLNX—1009 / Page 7 of 9
`
`
`
`
`
`
`
`
`
`
`example of the capability 1
`ations. Since the sampled
`IOSLM electronically usir
`of shifted functions, such
`Figure 7.15, a shift would
`off(x) by +P oellsjust m
`that in cell M. In convoluti
`
`is integrated over the dorn
`IOSLM outputs is mdily
`Figure 7.17. The lens perfi
`from all cells of the [OS]
`
`h(x), the integration is eq
`
`where N is the number of
`In the IOSLM mode
`
`voltage levels. The values
`for f( x) of zero or one o
`operations on the utmost
`in Figure 7.16, in pamlk
`
`
`
`7.17 Integration across the front
`
`

`

`
`
`7.3 GUIDED-WAVE INFORMATION PROCESSING
`
`255
`
`example of the capability optical devices have for parallel computational oper-
`ations. Since the sampled values of f(x) and g(x) can be shifted across each
`IOSLM electronically using shift registers, operations requiring multiplication
`of shifted functions, such as correlation and convolution, are also possible. In
`Figure 7.15, a shift would just reassign cell values so that, for example, a shift
`off( x) by +P cells just means that the value of Vc in cell M + P is replaced by
`that in cell M. In convolution and correlation, the product of two shifted functions
`is integrated over the domain, x, of the functions of interest. This integration of
`IOSLM outputs is readily accomplished with a guided-wave lens, as shown in
`Figure 7.17. The lens performs the integration in Figure 7.17 by converging light
`from all cells of the IOSLM onto a single detector. For a sampled function,
`h( x), the integration is equivalent to summing the outputs from all cells, or
`
`h(x)dx= 2 kg
`
`(7-88)
`
`where N is the number of samples or cells.
`In the IOSLM model developed above, the Vc are assumed to be analog
`voltage levels. The values of Vc can also be restricted to correspond with values
`for f( x) of zero or one only. In this case, the IOSLM performs bit-level logic
`operations on the zeroes or ones in each corresponding cell of the two IOSLMs
`in Figure 7.16, in parallel. For example, the diffracted output of the second
`
`Waveguide
`lens
`
`
`
`figure 7.17 Integration across the front of an IOSLM using a lens and a single
`detector.
`
`XLNX—1009 / Page 8 of 9
`
`
`
`

`

`256
`
`GUIDED-WAVE MODULATORS. SWITCHES, AND INFORMATION-PROCESSING DEVICES
`
`IOSLM is the result of a bit-by-bit logical AND of the strings of zeros and -
`in the two IOSLMs.
`
`7.3.4 Analog-io—Digital Conversion with Guided-Wave Optics (1 .
`
`
`
`
`The final example of guided-wave information subsystems that exploit the
`herent parallelism of optical processing is the analog-to-digital converter.
`conceptual similarity to the IOSLM in the preceding section will be imme 1::—
`apparent. The analog-to-digital converter described here is a parallel arrang- u
`of electro-optic switches similar to the one in Figure 7.6. Each switch corre . u
`to one bit of precision in the A-to-D conversion. The analog voltage to be ..
`
`verted is applied simultaneously to all electro-optic switches in the conv '-
`
`An example with four-bit precision is shown in Figure 7.18. The electrode 1- ..,
`for the most-significant bit (MSB) is chosen such that the maximum voltag
`
`be converted can cause a 1r phase shift in the switch for that bit. Moving d
`the structure of Figure 7.18, the electrode length doubles with each decrease
`bit significance so that, for the 4-bit example shown, the electrode length of .
`least significant bit (LSB) is eight times that of the MSB. The discrimina .
`(DISCR) that follow the detectors convert all detector outputs to discrimi. .m
`outputs, VD, which are logical zeros or ones according to the following rule:
`
`VD =
`
`[0 ;if O<P<Pmax/2
`
`: if Pmax/Z < Pmax
`
`l
`
`(7
`
`
`
`where P is the optical power incident on a detector and Pmax is the maxim .
`optical power that can be transmitted through the switch.
`Figure 7.19 illustrates the operation of the device in Figure 7.18 as an an
`
`
`
`'IIIIIIIIIIIIIIIIIIIIIIIl
`'IIIIIIIIIIIIIIIIIIIIIIIIA
`
`LSB — Waveguide
`m Electrode
`— Wire line
`
`Figure 7.18 A 4-bit guided-wave optical analog to digital converter based on four
`parallel Mach—Zehnder electro-optic switches.
`
`XLNX—1009 / Page 9 of 9
`
`
`
`
`
`0
`
`Figure 7.19 The optical trans
`each bit channelxof the A-to—l
`
`to-digital converter, assum
`discriminators. The option]
`curve, while the correspon
`The speed of this A-
`the electro-optic switches:
`tremely fast.
`
`.0 llEMS
`
`7-1 A certain electro—opti
`trodes is capable of a
`10—4 when the maxi
`effective index is 3.4!
`channel waveguide r
`on
`
`a. A Mach—Zehndel
`
`b. A coupler switch ‘
`waveguides is l c
`
`Use the analysis
`one waveguide has e
`
`