Optoelectronic Integrated Systems Based
`on Free-Space Interconnects with an
`Arbitrary Degree of Space Variance
`
`
`
`TIMOTHY J. DRABIK
`
`1nvited Paper
`
`It is appealing to contemplate how VLSI or wafer—scale inte-
`grated systems incorporating fi'ee~space optical interconnection
`might outperform purely electrically interconnected systems. One
`important dimension of this question concerns the limits that
`optical physics imposes on the interconnect density of these sys-
`tems: what bounds can be placed on the physical volume of an
`optical system that implements a particular interconnect? Another
`primary consideration arises when optical sources and detectors
`are integrated with circuit substrates, and the substrates are in-
`terconnected optically. Because the input and output planes of
`the optical interconnect are coincident with the substrates them-
`selves, the underlying physical optical constraints are coupled with
`new considerations driven by circuit and packaging technology;
`namely. speed, power, circuit integration density, and concurrency
`of operation. Thus the overall optoelectronic integrated system
`must be treated as a whole and means sought by which optimal
`designs can be achieved.
`This paper first provides a uniform treatment of a general
`class of optical interconnects based on a Fourier—plane imaging
`system with an array of sources in the object plane and an
`array of receptors in the image plane. Sources correspond to
`data outputs of processing “cells,” and receptors to their data
`inputs. A general abstract optical
`imaging model, capable of
`representing a large class of real systems, is analyzed to yield
`constructive upper bounds on system volume that are comparable
`to those arising from “3-D VLSI" computational models. These
`bounds, coupled with technologically derived constraints, form
`the heart of a design methodology for optoelectronic systems
`that uses electronic and optical elements each to their greatest
`advantage. and exploits the available spatial volume and power
`in the most efficient way. Many of these concepts are embodied
`in a demonstration project that seeks to implement a bit-serial,
`multiprocessing system with a radix-2 butterfly topology, and
`incorporates various new technology developments. The choice of
`a butterfly for a demonstration vehicle highlights the benefits of
`using free-space optics to interconnect high-wire-area topologies.
`
`Manuscript received February 2, 1994; revised August 23, 1994. This
`work was supported by the National Science Foundation under Grant
`MIPe9l 10276 and by the Georgia Institute of Technology Microelectronics
`Research Center.
`
`The author is with the School of Electrical and Computer Engineering
`and the Microelectronics Research Center, Georgia Institute of Technol-
`ogy, Atlanta. GA 30332-0250 USA.
`IEEE Log Number 9405791.
`
`The practice of wafer-scale integration has been hindered by
`the large area overhead required by sparing strategies invoked
`against the inevitable fabrication defects. If wafers are partitioned
`into functional circuit cells which are then interconnected strictly
`optically, then defective cells can be accommodated in a wafer-
`specific difi‘ractive interconnect. with no substrate area lost
`to
`inter-cell connectivity. The task of this interconnect is to map a
`desired network topology onto the physical set offunctional cells.
`Results of mapping regular processor topologies onto wafers with
`defective cells are given in terms of asymptotic volume complexity.
`
`I.
`
`INTRODUCTION
`
`Computational complexity theory seeks to determine
`how the resources necessary to perform a computational
`task grow as some measure of the “size" of the task
`increases [1], [2]. When integrated circuit technology be-
`came sufficient for the incorporation of entire systems on
`a single chip (integrated systems) [3], curiosity about the
`performance limitations of such systems led to a gener-
`alization of complexity theory that set formal bounds on
`the simultaneous chip area and time required to implement
`solutions to various problems [4], [5]. Further advances
`in very large scale integration (VLSI)
`technology that
`increased the number of interconnection levels available
`
`and improved the prospect of vertical integration of ac—
`tive devices [6]—[9], inspired further generalization to “3D
`VLSI” computational models that permit significant or
`unlimited stacking of active (transistor) or passive (inter—
`connect) layers [10]. Recent advances in technologies for
`integration of self~luminous sources, passive modulators,
`and high-performance detectors with complex circuitry
`have brought closer the implementation of what can be
`called optoelectronic integrated systems, Fig. 1, based on
`electronic circuitry and free—space optical interconnection.
`It
`is a pressing question whether VLSI or wafervscale
`integrated (WSI) systems incorporating free-space optical
`interconnection might not in some ways outperform purely
`electrically interconnected systems. An important dimen—
`
`PROCEEDlNGS OF THE IEEE, VOL. 82, NO. 11, NOVEMBER [994
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`1595
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`0018—9219/94$04.00 (9) 1994 IEEE
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`This paper introduces an approach to the study of optical
`interconnect complexity, that yields practically applicable
`criteria to facilitate the design of optoelectronic integrated
`systems that efficiently use the primary resources of power
`and physical volume.
`The first half of the paper provides a uniform treatment
`of a general class of optical
`interconnects based on a
`Fourier-plane imaging system with an array of sources in
`the object plane and an array of receptors in the image
`plane. The sources correspond to data outputs of processing
`“cells,” and the receptors to their data inputs. Intercon-
`nection may be thought of as a mapping—one-to—one, or
`possibly one-to—many‘from the set of sources to the set of
`receptors. In Sections II and III, an abstract optical imaging
`model is defined that
`is sufficiently general to represent
`a large class of real systems. Section IV relates elements
`of this canonical system to practical imaging systems, dif-
`fractive elements, detectors, modulators or selfeluminous
`sources, and microlens arrays. In Section V, bounds are
`computed for the overall system volume and for other
`important parameters, in terms of certain characteristics of
`the interconnect pattern, and for an arbitrary number of
`cells. These are not fundamental lower bounds, but rather
`
`that
`upper bounds determined by constructive example.
`are consistent with such practical systems constraints as
`maintaining a constant signal-to-noise ratio and numerical
`aperture. Section VI uses these results to derive meaningful
`bounds on the physical volume of optical implementations
`of specific regular interconnection networks.
`In the second half of the paper, results of the first half are
`applied to the design of optoelectronic integrated systems.
`Section VII introduces a methodology for the design of
`optoelectronic integrated systems based on planar arrays of
`electronic processing cells. Cells are interconnected opti—
`cally by means of integrated light modulators or sources,
`and detectors, and an external optical
`routing network.
`This methodology establishes requirements on cell area
`and on the speed—power characteristics of optical sources.
`modulators. and detectors, and gives rise to guidelines
`for optimizing designs of regularly interconnected arrays.
`Many of the concepts discussed above are embodied in a
`design for a prototype system described in Section VIII, for
`a bit-serial. pipelined processor array. The design incorpo—
`rates electrooptic and optomechanical technology building
`blocks recently developed through the author’s research
`collaborations. Finally. Section IX demonstrates how the
`functioning physical processing cells on an optoelectronic
`substrate with defects can be interconnected as a regular
`array with no need for onrwal‘er redundancy or reconfigura—
`tion circuitry. The effect of wafer defects on the complexity
`of the optical interconnect required to accomodate them is
`determined for a useful topology: the 2D mesh.
`
`11. GENERAL ASPECTS OF TIIE Two—HOLOGRAM
`FOURIER»PLANF. INTERCONNECT
`
`Before proceeding with the rigorous descriptions and
`definitions needed to support
`the complexity analysis of
`Section V. it is beneficial to discuss informally the optical
`
`PROCEEDINGS OF THE lEEE. VOL. 82. NO. 11. NOVEMBER 1994
`
`Fig. l. Optoelectronic integrated systems concept: electronic sub-
`strate with electrical-optical transduction elements. interconnected
`optically.
`
`sion of this question concerns the limits that optical physics
`imposes on the physical size of these systems: what bounds
`can we place on the volume of an optical system that
`implements a particular interconnect? We expect intuitively
`that optoelectronic systems with many optical signal paths
`will
`take up more space than those with fewer optical
`connections, just as planar VLSI layouts with many distinct
`electrical nets require more area than those with fewer
`wires. Further, VLSI complexity theory has revealed a
`strong connection between the communication efficiency
`of a network, as quantified in terms of graph—theoretical
`measures of connectivity, and the area required for its
`planar layout. Thus we also expect the required optical
`system volume to depend on topological aspects of the
`interconnect pattern.
`It
`is desirable to find interconnect structures that offer
`
`high computational performance and lead as well to optical
`systems with low complexity. A treatment of optical
`in-
`terconnect capacity that applies to a large class of systems
`could serve as a tool to identify such structures and perhaps
`determine what attributes of interconnect structure lead to
`
`small volume requirements.
`Analyses have investigated the capacity of numerous
`optical interconnect configurations in contexts of varying
`generality. Particularly, Feldman and Guest [11] established
`upper bounds on the area of computer—generated holograms
`required to implement
`the type of arbitrary connection
`patterns with fan-out that characterize signal paths in VLSI.
`Barakat and Reif [12] placed optical interconnect systems
`into the context of computational complexity theory by
`using arguments based on Gabor’s theorem [13] to derive
`fundamental bounds on interconnect capacity of systems
`with optical sources and detectors lying on a bounding
`surface. and thereby enabled the direct theoretical compar—
`ison of optical interconnects with 3D VLSI circuitry. This
`analysis was generalized by Ozaktas and Goodman [14]
`to accommodate sources and detectors placed arbitrarily
`within a system‘s volume.
`Along with these fundamental treatments have arisen var
`ious studies that incorporate aspects of structure or regular-
`ity of the interconnect, to derive constructive or engineering
`bounds [lS]—[24]. and recent, ever more comprehensive and
`general analyses have deepened understanding ol~ the utility
`of optical interconnection in computing [[4], [25]—[27].
`
`1596
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`

`

`ARRAY OF
`
`SOURCES ARRAY 0F
`
`RECEPTORS
`
`Fig. 2. Optical interconnection with a Fourieriplane imaging system and beam-deviating elements.
`
`system on which this work is based. The system is a re-
`finement of the hybrid “basis-set” interconnection originally
`described by Jenkins and Strand [28] and Jenkins et al. [29],
`[30]. The functional objective is to communicate optical
`signals in a space—variant way from a plane (9 containing
`sources to a plane I containing receptors, Fig. 2. In order
`that light from a given source be directed to the desired
`receptors,
`it must be possible to change the direction of
`a beam of light as it leaves the object plane (9, and as it
`passes through the Fourier plane 7-" of the imaging system.
`These deviations can be realized with diffractive elements.
`For convenience, all elements causing beam deviation or
`splitting will be referred to as holograms, in the spirit of
`[31]'.
`The high interconnect capacity of the system described
`in this work derives from the shift invariance (or space
`invariance) of Fourier-plane spatial filtering: angular de-
`flection of a beam as it passes through the Fourier plane
`results in equal displacements of each feature in the image
`plane relative to that feature’s location in the absence
`of the deflection. A single region of H; that causes a
`specific angular beam deflection can thus be used to send
`light from many different sources through identical relative
`displacements.
`In this way, a large number of regular
`interconnections (involving a small total number of distinct.
`relative displacements) can be realized optically in a small
`volume.
`
`Figure 2 illustrates how the required beam direction is
`accomplished with two segmented holographic elements.
`Beams of light
`leave the sources and are,
`in general,
`deflected or split upon passing through holographic element
`H O. which is in direct contact with the sources in the object
`plane 0. Holograms that perform deflection act on the light
`traversing them as do triangular prisms. The paths through
`the lenses of the rays representing the beams” centers, are
`described by the theory of geometric optics. Both HO
`and H f are partitioned into independently programmed
`regions. A region in HO serves to “point" the light leaving
`a source toward one or more of the regions in Hf. A
`region of Hf receiving light imparts an angular deflection
`(or splits the light into multiple. differently deflected beams)
`that causes the resulting spot in the image plane I to suffer
`a particular relative displacement (or to be replicated into
`
`1"‘When I use a word.‘ Humpty Dumpty said. in a rather scomful tone.
`'it means what I choose it to mean ineither more, nor less.” [3]].
`
`multiple, differently displaced spots). This way, light from
`different sources can be differently directed to receptors
`in the image plane. The behavior of this optical system is
`described comprehensively by Fourier opticsz.
`As Ozaktas and Goodman have shown [14], the optical
`interconnect capacity of a system with sources and receptors
`on the convex hull of its volume is generally less than that
`of a system whose sources and receptors are allowed to
`lie anywhere within its volume. However, the former may
`serve as a building block for the latter in an obvious way
`[26] and, we will show, can attain desirable performance
`levels with low optomechanical complexity.
`The elegance of the basis~set system of Fig. 2 lies in
`that an arbitrary overall degree of shift-variance can be
`realized by varying the number of segments in H7 . If only
`one segment, representing a particular sum of linear phase
`factors, occupies the whole aperture of Hf , then H 0 serves
`no purpose and the interconnect is shift-invariant. At the
`other extreme, light from each source in O can be directed
`by the segment of HO in front of it to a distinct segment of
`Hf . In this case each source can be mapped independently.
`which corresponds to total shift variance.
`The degree of shift variance, represented by the number
`of segments into which Hf is divided, is directly linked
`to the physical volume required to contain the system.
`Each segment of H7: functions as a pupil in the Fourier
`plane, whose diameter determines the spatial frequency
`response of the imaging system [32]. This pupil diameter
`must be large enough to image spots of light from the
`sources with sufficient acuity to prevent crosstalk between
`adjacent sources or adjacent receptors. Thus all other things
`being held equal, an increase in degree of shift-variance
`necessitates an increase in total Fourier—plane area. If the
`focal
`lengths of lenses L1 and L2 are held constant,
`then an increase in their numerical aperture is prescribed.
`Numerical aperture is a useful measure of the cost of
`fabricating a lens, however, and it is often desirable to hold
`it constant and vary some other parameter to accommodate
`the increased demands on the imaging system. It is plain
`that the interplay of all optical system parameters must be
`
`theory and its applications is
`2A thorough treatment of this elegant
`found in Goodman [32]. The Appendix of this paper presents essential
`results of the theory, establishes notational conventions, and discusses the
`nature of diffractive elements.
`
`DRABIK: OPTOELECTRONIC [NTEGRATED SYSTEMS
`
`1597
`
`

`

`NOMINAL
`PROPAGATION
`
`
`
`Fig. 3. Canonical Fourier~plane optical system configuration and
`notational conventions. Sense of the coordinate system in Z is
`opposite that
`in 0 because of the image inversion that occurs
`upon propagation through the system.
`
`considered methodically such that the system “grows" in a
`reasonable way. This is the goal of the next section.
`
`III. A CANONICAL REPRESENTATION or
`FOURIER-PLANE-BASED OPTICAL INTERCONNECT SYSTEMS
`
`Because many physical embodiments of optical intercon—
`nects are based on a variant of the system of Fig. 2,
`it
`is sensible to define an abstract model sufficiently general
`to represent them all, both for simplicity of analysis and
`so that different systems can be evaluated comparatively.
`This canonical system, shown in Fig. 3, comprises two ideal
`lenses of equal focal length f and diameter D, arrays of
`sources in O and receptors in I, and two holographic
`elements: H0 in O. and HI in f. All elements are
`centered on a common system axis, which also pierces the
`origins of O, 7", and I.
`
`A. Sources and Receptors
`
`The nature of the physical sources and receptors being
`interconnected can vary widely across different applica-
`tions. Sources with emitting areas only a few wavelengths
`in extent. such as edge-emitting laser diodes, exhibit greater
`beam divergence than do large-area passive modulator
`cells or verticalecavity lasers, for example. Physical recep—
`tors can differ as well: an integrated pin photodetector
`might be made 10 ,am in diameter or smaller to re-
`duce parasitic capacitance and increase speed, whereas
`metal—semiconductor~metal (MSM) detectors > 100 am
`in diameter can peiform satisfactorily [33]. Numerical aper—
`ture of the receptor elements must be taken into account,
`and spacing of sources and receptors on a substrate is
`coupled to the size of the cells being interconnected.
`Different types of physical sources and receptors are ac-
`commodated by defining a simple object plane specification
`to which light from any type of emitter or modulator can be
`made to conform, and an image plane specification compat—
`ible with any type of detector: “sources" and “receptors” in
`the abstract model are simply regions that emit light or are
`sensitive to it. For ease of analysis, these regions will be
`understood to be circularly symmetrical. although elliptical
`or other shapes would better suit some dcvicc technologies.
`We will consider a processing elements or cells P0,
`P1. -
`~
`-
`. P,,_1, each of which contains a collection of
`
`1598
`
`sources and receptors. These may be arranged identically
`within all cells, but this is neither essential to the analysis
`nor always desirable. Figure 4(a) shows a typical cell PJ-
`populated with 7" sources, or outputs 09—0371 and m
`receptors, or inputs I?—I;"_1. Sources and receptors have
`diameter d, and the cell has area a2. Although pictured as
`squares in Fig. 4, cells may assume any appropriate shape.
`With these conventions established, an interconnection
`can then be characterized by a (possibly multivalued)
`mapping from the sources to the receptors
`
`M 1 {(917}
`J
`
`Ie{o,m,r—i) 4t{11} temp-Apr).
`}
`]e{0.-~-.n—1)
`:(0 mil
`J
`
`(l)
`
`Because of the underlying physical context of electronic
`substrates populated with emitters and detectors, the sources
`and receptors in a given cell are physically tied to it.
`However, we will conceptually separate all sources into
`plane 0 and all receptors into plane I, to conform to the
`linear nature of the canonical imaging system. The source
`and receptor planes thus appear as in Fig. 4(b). The mutual
`spatial relationships among the sources themselves, and
`among the receptors themselves, are undisturbed. Folding
`the system back on itself with reflective elements upon
`translation to a physical embodiment (Section lV-E), will
`reunite sources and receptors corresponding to each Pi.
`Sources emit monochromatic, collimated light of free-space
`wavelength /\ normally from plane 0; sources and receptors
`may not overlap, and the cell area 0,2 must be large enough
`to accomodate them. It is useful to define the dimensionless
`
`quantity
`
`u
`
`d
`7]::;<1
`
`(2)
`
`7] can be
`:2" indicates definition or assignment;
`where
`thought of as a spatial duty cycle. Let the object plane di-
`ameter we be defined as the maximum center-to-center dis-
`tance between two sources, and the image plane diameter
`1111 as the maximum center-to-center receptor separation,
`as in Fig. 4.
`
`B. Holographic Elements
`
`H O is an array of r X n subholograms abuttcd directly to
`the sources in 0. Each subhologram H3 intercepts all light
`from exactly one Of. Hf is an array-of K subholograms
`located in the Fourier plane. Beams intercepted by the H ,f
`undergo angular deflections that result in the spatial image
`plane shifts required to implement the mapping M. The
`function of each H3 is to broadcast the spot of light from
`O; to the correct subset of the K available subholograms
`H,f . The required complex transmittance functions are
`equivalent to sums of linear phase functions
`
`tilts y) = 5a Z 8””‘W3J‘Ht’i'yl
`l
`
`(3)
`
`for (1:, y) belonging to the region occupied by H19, where
`constant 61-5 accounts for the decimation of light power
`
`PROCEEDINGS OF THE lEEE, VOL. 82, NO,
`
`ll, NOVEMBER I994
`
`

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`
`
`CELL P,- \ .019
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`C, Fourier Plane
`
`The K subholograms HL}— can be placed arbitrarily in
`f, because they need not align with other physical compo
`nents. Let the Fcurler-plane diameter 11)}- be the diameter
`of the smallest disk centered at the origin of F that covers
`all the Hf. If circles are packed hexagonally, as suggested
`in Fig. 3, then X circles of diameter It fit inside a circle
`of diameter
`
`(7)
`to; = him—l
`where [1'] denotes the smallest integer not less than a real
`number T.
`
`D. Lenses
`
`L1 and L2 are ideal Fourier transforming lenses of focal
`length f. In order to capture all light from the source plane
`and avoid vignetting [34], the diameter D1 of L1 must at
`least equal the sum of the object plane and Fourier plane
`diameters
`
`D1 2 w} + we.
`
`(3)
`
`Likewise, the diameter of L2 must at least equal the sum
`of 11)]: and w;
`
`02 2 ‘llly‘ + U1].
`
`(9)
`
`For simplicity, both lenses are assigned diameter D, where
`
`[)1 ED2EDI=1UJS+maX(LUZ.UlO).
`
`(10)
`
`(b)
`
`(a) Source and receptor configuration in canonical cell.
`Fig. 4.
`(bl Separation of all sources into object plane 0 and receptors
`into image plane I.
`
`caused by fan—out. Similarly
`’v.
`..
`.
`'
`’2
`.7:
`hem-711): 6k: :6] misfittT-rutiy)
`L
`
`(4)
`
`Finally, the f-number F is declared to be a fixed parameter
`f'—E'.
`D
`F
`
`11
`()
`
`for (,1). 1/) within Hf. In the canonical system, Hf and H0
`have zero physical thickness.
`Source plane subholograms Hfl need only have diameter
`d because they are in direct contact with the 05. Spots
`from the O; spread as they propagate to the Fourier plane
`because of diffraction, and an Hk7 must be able to intercept
`some large fraction of the power in a beamlet directed
`toward it from the source. Light falling outside the intended
`ka can fall on other Fourier—plane subholograms and
`be misdirected, and is therefore a systematic source of
`crosstalk even under the assumption of ideal holographic
`elements. Let the H{- be circular with diameter It. If h, is
`given the functional dependence
`
`mm
`d
`
`(5)
`
`where q is a form factor, then the fraction of intercepted
`power is independent of focal
`length [see (A6b)]. If (1
`is chosen as a constant, a fixed fraction of the power
`intended for a given HK is actually intercepted and properly
`directed. However, as explained in Section V. q must some
`times grow as n increases in order to maintain a constant
`overall signal—to-noise ratio (SNR). Thus in general
`
`q 3 Qinl-
`
`(6)
`
`The f—number is linked closely to the cost and difficulty
`of making a lens and also relates to the minimum fringe
`spacing required in the holographic elements. Fixing F
`permits evaluation of system growth at a fixed level of
`technological effort.
`
`The above definitions of abstract sources, holograms.
`lenses and receptors. their attributes and capabilities. and
`their admissible configurations, collectively constitute the
`canonical representation or canonical model of all optical
`systems in this paper. This idealized abstraction is amenable
`to analysis of its volume complexity as well as to the
`establishment of correspondences between its constituent
`parts and real optical components. It is therefore a vehicle
`through which optically interconnected systems may easily
`be described.
`
`IV.
`
`PHYSICAL EMBODIMENTS OF THE CANONICAL MODEL
`
`that
`to the extent
`is meaningful
`The canonical model
`the demands on its idealized constituents can be met by
`the physical sources, receptors, beam-deviating elements,
`and focusing elements that comprise real systems. Details
`of realizing these components are treated in this section.
`Investigation of physical elements and their nonidealities
`establishes the conditions under which conclusions drawn
`from the canonical model have practical meaning.
`
`DRABIK: OPTOELECTROMC INTEGRATED SYSTEMS
`
`L599
`
`

`

`A. Importance of Lenslet Arrays
`In the context of optoelectronic integrated systems, phys—
`ical sources should be made small because they share
`substrate area with functional circuitry, and because small
`size generally implies lower drive requirements. In general,
`sources such as edge-emitting diode lasers typically have
`emitting areas not many wavelengths in extent. If the canon-
`ical source is identified directly with the small output face
`of such a physical source. then at is very small compared to
`the souree-to-souree spacing a, and n is small, a condition
`that leads to a large system volume requirement. A positive
`lenslet placed in front of each source to collimate the
`divergent beam from the small output face, has the effect of
`making a small source appear large, with an accompanying
`reduction in beam divergence and spot size in F. The
`plane (9 is then coincident with the plane of the lenslets,
`not of the actual sources. With lenslet arrays, sources
`can be packed “shouldeHo—shoulder;” lenslet arrays are
`therefore essential to high-performance free-space optically
`interconnected systems [17], [35].
`Many technologies now exist with which satisfactory
`lenslet arrays can be realized. Gradient index arrays exploit
`the diffusion properties of metal ions in glass [36]; mass-
`transport techniques based on melting and surface tension
`have produced high-quality refractive arrays [37]—[39];
`the formidable repertoire of synthetic diffractive optics
`[40]—[42] has yielded planar diffractive lenslets with suf-
`ficient efficiency and numerical aperture for application
`within a system [43].
`Given a multiplicity of satisfactory alternatives for
`achieving the required bare functionality, a choice of
`lenslet
`technology can be made largely on the basis of
`optomechanical compatibility with the physical design of
`the system,
`in other words, on the basis of packaging
`considerations. This will be borne out in the sections that
`follow.
`
`B. Dififractive Elements as Beam Deflectors and Splitters
`The natural physical component to realize simple optical
`deflection is a prism or tilted mirror. In practice, arrays
`of prisms are hard to fabricate and not often suited to
`the planar nature of evolving micro—optics
`technology.
`Blazed gratings and quantized-phase approximations to
`them [40]—[42], represent compatible and fairly mature
`technologies. Because of the phase-only nature of elements
`associated with simple deflection, efficiency of spurious
`diffracted orders can be systematically reduced. It is also
`possible to fit
`the combined lenslet and beam-deflection
`functionality within a single diffractive element; an off-axis
`diffractive lenslet results. The element is still phase—only,
`but
`its feature size shrinks as lenslet numerical aperture
`grows. Thus integrated foeusing~deflection elements are
`somewhat more demanding of fabrication processes than
`plain linear-phase elements.
`Elements for beam—splitting exhibit transmittance func-
`tions with varying amplitude, and are not a straightforward
`match to phaseionly fabrication techniques. However, mod—
`
`1600
`
`cm coding techniques [44], [45] permit spurious diffracted
`light (noise) to be directed to areas in the angular spectrum
`where it has no ill effect.
`
`Despite advances in design techniques, phase quanti-
`zation inevitably gives rise to some amount of spurious
`diffracted light. This light, which can be considered as
`excess noise, must augment the systematic noise associated
`with the clipping of diffraction patterns in the Fourier
`and image planes (see Section V—Al). Excess noise due
`to spurious diffraction, scattering, and other mechanisms
`that generate stray light within the system, will be seen to
`establish the noise floor of optical interconnects.
`
`C. Optoelectronic Integration
`1) Self—Luminous Sources: There are now many ap-
`proaches to populating integrated circuit substrates with
`self-luminous sources. Although circuits can certainly be
`fabricated on III—V substrates, silicon is desirable because
`of the greater circuit complexity possible and the wide range
`of mature processing techniques available, not only for elec—
`tronic elements, but also for guided-wave and micro—optic
`components. Heteroepitaxy on silicon involves growing
`a single—crystal epitaxial layer of a III—V compound on
`bulk silicon by molecular beam epitaxy (MBE) or metal-
`organic chemical vapor deposition (MOCVD) [461—[50]. Of
`primary concern in this research area is the improvement of
`lattice matching and thereby the elimination of dislocation
`defects that lead to low carrier mobilities and high laser
`threshold currents.
`
`An alternative to heteroepitaxy that has been demon—
`strated recently is
`lift—off hybridization of
`III—V thin
`films onto flat substrates of practically arbitrary materials
`[51]—[57].
`In principle,
`no degradation of material
`characteristics need be suffered in the course of transferring
`devices from the bulk to a foreign substrate, and, indeed.
`Myers et al. have transferred a thin AlGaAs film bearing
`a depletion-mode, strained-quantum-well FET with ie/tm
`gate length to a glass slide without observing a decrease in
`maximum transconductance [52].
`Given that the outlook for obtaining high—quality III—V
`films on silicon is promising, surface-emitting laser tech—
`nology suitable for application in optoelectronic integrated
`systems have had a fruitful course of development. Surface—
`emitting lasers are of two basic types: vertical—cavity lasers
`whose light path through the gain medium is normal to the
`substrate [58]—[62], and more conventional
`lateral—cavity
`lasers whose output is directed out of the wafer by a slanted
`reflector [63] or out of a waveguiding layer by a grating
`coupler [64], [65].
`2) Passive Light Modulators: The alternative to self—
`luminous sources in optoelectronic integrated systems is the
`use of cells that modulate an externally supplied beam of
`light. Passive modulator types compatible with logic circuit
`technology are multipleAquantum—well (MQW) electroab—
`sorption or electrorefraction modulators [66]—[7l], Pockel
`or Kerr cells using organic [72] and ceramic [73]—[75]
`electrooptic materials, and surface—stabilized ferroelectric
`liquid crystal (FLC) cells [76], [77]. The question of inte—
`
`PROCEEDINGS OF THE IEEE, VOL. 82. NO. 11. NOVEMBER 1994
`
`

`

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`
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