Analysis of hexagonal array geometry for free-space optical interconnects with improved...

Analysis of hexagonal array geometry for free-space opticalinterconnects with improved signal-to-noise ratio

Feng-Chuan F. Tsai, Christopher J. O’Brien, Novak S. Petrovic, and Aleksandar D. Rakic

The effect of transmitter and receiver array configurations on the performance of free-space opticalinterconnects (FSOIs) was investigated. Experimentally measured, spectrally resolved, near-field imagesof vertical-cavity surface-emitting laser (VCSEL) transverse modes were used as extended sources in oursimulation model and combined with laser relative intensity noise and the receiver noise to determine theoptimal array geometry. Our results demonstrate the importance of stray-light cross talk in both squareand hexagonal configurations. By changing the array lattice geometry from square to hexagonal, weobtained an overall optical signal-to-noise ratio improvement of 3 dB. We demonstrated that the opticalsignal-to-noise ratio is optimal for the hexagonal channel arrangement regardless of the transverse modestructure of the VCSEL beam. We also determined the VCSEL drive current required for the bestperformance of the FSOI system. © 2007 Optical Society of America

OCIS codes: 200.4650, 200.2610.

1. Introduction

The ever-increasing demand for bandwidth is test-ing the capabilities of electrical interconnects. The in-herent capacitance and inductance of metallic wireslimits the maximum potential rate of data transfer;high clock speed and thermal effects introduce clockskew and threaten the fidelity of timing signals insynchronous circuits; the drive for higher densitychannels causes pin congestion and electrical crosstalk.1,2 High-bandwidth, long-distance communica-tion schemes primarily employ optical transmission,and a similar design philosophy is becoming attrac-tive for communication over shorter data links.Optical interconnects have an enormous aggregate-bandwidth advantage and competitive power con-sumption in comparison with electrical interconnectsat the chip and board levels. In addition to theirtransmission characteristics, free-space implementa-tions of optical interconnects (OIs) promote the devel-opment of novel VLSI designs and reconfigurable

systems.3–5 Furthermore, recent developments in theintegration of vertical-cavity surface-emitting laser(VCSEL) arrays and photodetector arrays with com-plementary metal-oxide semiconductor (CMOS) elec-tronic circuitry have increased the practical potentialof optical interconnects.6,7

Several OI designs based on 2D VCSEL arrayshave been proposed.8–13 From these studies it is ev-ident that one of the major factors that determine themaximum channel density and bit-error ratio is theoptical cross-talk noise within the system. The ma-jority of proposed OI designs employ microlenses andother small-diameter optical elements to producecompact optical systems (microchannel architecture).Through the process of miniaturization, the micro-lens diameter will decrease to allow for higher chan-nel density; consequently the performance of thesystem will become increasingly dominated by dif-fraction.

The generic implementation of a parallel free-spaceoptical interconnect (FSOI) system (shown in Fig. 1below) consists of a VCSEL array and two microlensarrays, employed to collimate and subsequently focusthe laser beams onto an array of photodetectors. Theoptical power transmitted to its intended receiver isthe signal, and the optical power trespassing ontothat receiver from neighboring channels is referred toas optical cross-talk noise. The type of cross talk con-ventionally considered in FSOI modeling is diffraction-caused cross-talk noise (DCCN). Following a numberof studies,14–16 DCCN is modeled as the power incident

The authors are with the School of Information Technology andElectrical Engineering, The University of Queensland, St. LuciaQLD 4072, Brisbane, Australia. A. D. Rakic’s e-mail address [email protected].

Received 5 September 2006; revised 21 December 2006; accepted22 December 2006; posted 22 December 2006 (Doc. ID 74781);published 9 April 2007.

0003-6935/07/132434-09$15.00/0© 2007 Optical Society of America

2434 APPLIED OPTICS � Vol. 46, No. 13 � 1 May 2007

on unintended receiver microlenses due to diffractionat the transmitter microlenses and the spread of thelaser beam between the transmitter microlens arrayand the receiver microlens array. In a recent paper17

the authors demonstrated that stray-light cross-talknoise (SLCN), the fraction of the optical power imagedby the neighboring transmitter microlens to otherchannels, possibly far from the intended one, can con-tribute significantly to the level of optical noise in thesystem and can lead to serious degradation in signal-to-noise ratio (SNR).

FSOI designs are typically evaluated by consider-ing propagation from point sources or uniform sur-face emitters. However, VCSELs tend to operate inseveral transverse modes simultaneously; the pres-ence of higher-order transverse modes, depending onthe modal structure of the VCSEL beam can signifi-cantly alter the spot size and consequently the noiselevels in the microchannel systems. Second, the non-optimal square-lattice arrangement of channels is typ-ically considered when investigating the performanceof the FSOI systems, as was pointed out earlier.18

Here we comprehensively address, for what we be-lieve to be the first time, the effect of channel geometryon the SNR in microchannel FSOI systems. A combi-nation of experimental and comprehensive numericalsimulation modeling has been used to optimize thechannel geometry and accurately predict the maxi-mum channel densities and interconnect distancesachievable in VCSEL-based systems.

We demonstrate that by departing from the square-lattice geometry employed by most FSOI architec-tures, the performance of the FSOI system can besubstantially improved. We show that by using theoptimal, hexagonal-lattice, VCSEL array geometry,one can significantly reduce the total optical cross-talk noise and improve the SNR of the FSOI systemby approximately 3 dB. The use of experimentally

determined mode profiles, as extended sources in ouroptical simulations, and the use of experimentallymeasured laser noise in our system analysis yieldedrealistic and accurate estimates of the overall FSOIperformance as a function of channel geometry, laserbias current, and the laser beam modal structure.

In Section 2 we develop the FSOI simulation model.Experimental procedures used to obtain the modalcontent, spectrally resolved beam profiles of the coex-isting VCSEL modes, and measure relative intensitynoise (RIN) are described in Section 3. These experi-mental findings are used in the simulation model toexamine the effect of array geometry on the FSOIperformance and optimize the system geometry inSection 4. The paper is concluded with a discussion inSection 5.

2. Microchannel FSOI Design Description

A. Design Outline

Figure 1 shows the basic architecture used in thesimulations: a microchannel FSOI constructed fromtwo microlens arrays, a VCSEL array and a photo-detector array. The VCSEL array is located at z � 0,and the first microlens array is situated at z � d1.The second microlens array is at a distance of d2� d3, away from the first microlens array, and thephotodetector array is positioned at d4 � d1 awayfrom the second microlens resulting in a symmetricalconfiguration. Distances d2 and d3 are the distancesof the intermediate beam waist from the transmittingto the receiving microlens arrays, respectively. Thepitch of the system is �, and the diameter of themicrolens is D. Fill factor � is defined as the ratio ofthe microlens diameter to the array pitch: � � D��.Two metrics frequently used to assess interconnectperformance are the maximum achievable channeldensity, 1��2, and the interconnect distance, L � d1� d2 � d3 � d4. The optical SNR (OSNR) is defined asfollows:

OSNR � 10 log10

SN � 10 log10

SSLCN � DCCN, (1)

where S, the signal power, is the fraction of the op-tical power emitted by a given VCSEL that is col-lected by its corresponding photodetector. The sum ofSLCN and DCCN, or the noise power N, representsthe total optical power emitted by all other VCSELsin the system that is incident upon the same detector.

To obtain accurate performance indicators, electri-cal noise components need to be included. We identifythe VCSEL RIN and the photodetector and pream-plifier noise as the most significant sources of electri-cal noise. The complete SNR for a given channel canbe written as19,20

SNR � 10 log10

X2�RS�2

RIN�RS � RN�2B � 2q�RS � RN � Id�B � �4kBT�Req�BFt � X2�RN�2. (2)

Fig. 1. (Color online) Schematic of a microchannel free-space op-tical interconnect.

1 May 2007 � Vol. 46, No. 13 � APPLIED OPTICS 2435

In Eq. (2), R is the photodiode responsivity, RIN is theVCSEL relative intensity noise, B is the receiverbandwidth, Id is the photodetector dark current, Ft isthe preamplifier noise figure, q is the electron charge,kB is Boltzmann’s constant, T is the operating tem-perature, and Req is the equivalent resistance of thephotodetector load and the preamplifier. X is themodified extinction ratio defined by X � �ER � 1��ER � 1�. The extinction ratio ER is a measure of theamplitude of the digital modulation on the opticalcarrier and is defined as the ratio of the averageoptical power in logic one pulse and the average op-tical power in logic zero pulse.20

B. Design Geometries

We assume that the 2D arrays of VCSELs, the trans-mitter microlenses, the receiver microlenses, and thephotodetectors are all arranged at the nodes of thesame type of grid. The usual square grid configura-tion used in most microchannel architectures is de-picted in Fig. 2(a). The shaded circular aperturedepicts the central channel of the FSOI system. Analternative arrangement can be achieved by offset-ting each of the outer two rows with respect to thereference row as indicated by the arrows in Fig. 2(b).The reference row can be taken to be the one thatcontains the center channel. The displacement of theadjacent rows with respect to the reference can bemeasured by the value of the offset, where 100% offsetcorresponds to the displacement of half of the arraypitch ��2�. The configuration for which the offsetvalue reaches 100% can be referred to as the hexag-onal grid configuration. Each channel in the squareconfiguration has eight neighboring channels; chan-nels in the hexagonal arrangement have only sixneighbors.

C. Diffraction-Caused Cross Talk

For each channel, we consider a laser beam ofbeam waist �0 emitted from the transmitter planethrough its corresponding transmitter microlens andimaged to the intermediate beam waist located atdistance d2 from the transmitter microlens plane.The beam propagates from the intermediate beamwaist to the intended receiver microlens. Owing tothe diffraction-caused spreading of the laser beamsand the finite diameter of the transmitter microlens,the beam radius at the receiver microlens sometimes

exceeds the radius of the receiver microlens. There-fore a fraction of the transmitted power will fall onthe microlenses adjacent to the intended microlensand will be focused onto unintended photodetectors[Fig. 3(a)] introducing cross-talk noise. This noise isusually assumed to be the only component of theoptical cross-talk noise. Here we refer to this as theDCCN. Therefore the DCCN is defined as the opticalpower that propagates through the intended trans-mitter microlens but falls onto an adjacent receivermicrolens and is focused onto photodetectors forwhich it was not intended.

D. Stray-Light Cross Talk

Here we consider a different type of optical cross talkcaused by the overfill of the transmitter microlensand which will be referred to as SLCN throughoutthis article.17 Let us consider an arbitrary channelwithin the microchannel architecture, [Fig. 3(b)]. Inthis case we concentrate on the fraction of poweremitted by the VCSEL that falls on the transmittermicrolenses adjacent to the intended transmitterlens. Due to the curvature of the microlenses, thebeam is refracted away from the intended channel asshown in Fig. 3(b). As it propagates through the sys-tem, the beam will further expand until it reachesthe receiver microlens plane. Unlike the diffraction-caused cross talk, where most of the noise can beattributed to the adjacent channels, in this case thebeam can be redirected to photodetectors far fromthe intended channel. Therefore, in our simulations

Fig. 2. Structure of the transmitter and the receiver microlensarrays in (a) square configuration and (b) hexagonal configuration.

Fig. 3. (Color online) Schematic of a free-space optical intercon-nect showing (a) diffraction-caused cross talk and (b) stray-lightcross talk.


we depart form the usual analysis in which a channelwill contribute noise only to its nearest neighbors. Inthis study we demonstrate that, once stray-light crosstalk is properly accounted for, significant cross talkcan be introduced to a receiver by non-neighboringchannels.

To calculate the cross-talk noise present in the cen-tral channel, we consider the noise induced on a cen-tral photodetector by all the channels surrounding it.However, the same result can be obtained by calcu-lating the optical power falling on the surroundingphotodetectors from the central channel. In this man-ner, the computational complexity of calculating thesignal and noise powers can be greatly reduced byconsidering the transmission of a single beam over alarge area, instead of the propagation of a large num-ber of beams into a localized area.

3. VCSEL Transverse Modes and the ExperimentalResults

A. Higher-Order Modes

While the output of a VCSEL is limited to one longi-tudinal mode, it typically lases in several transversemodes. The fundamental mode has a Gaussian inten-sity profile, while higher-order transverse modes arecharacterized by spatial distributions that can be de-scribed by either the Hermite–Gaussian (HG) orLaguerre–Gaussian (LG) notations. Either family oforthogonal functions can be used to describe any laserbeam, but for the purpose of this work, the LGmodes (expressed in cylindrical coordinates) are themost appropriate. An arbitrary laser beam is aweighted combination of LG modes, each of whichcan be described by21

� LGnm�r, �, z�LGnm*�r, �, z�� Knm� r�2

w�z�m

Ln�m�� 2r2

w�z�2� exp� �r2

w�z�2 � jkr2

2R�z��cos�m��sin�m��,

(3)

where,

Knm � AnmNnm, (4)

Anm � exp�j�2n � m � 1�arctan�z � zs�

ws2

� k�z � zs��, (5)

Nnm �2

w�z��1 � �om� n!

�n � m�!�1�2

. (6)

In Eqs. (3)–(6), the wavenumber k � 2�, and theRayleigh range is given as zR �

12 kws

2, where ws is the

beam waist and is located at z � zs � 0. The beamradius at any distance along the propagation axis isgiven as

w�z� � ws�1 � � zzR2

, (7)

and the radius of curvature is

R�z� � z1 � �zR

z 2�. (8)

Equation (3) describes the beam’s phase shift withmode order �2n � m�, which is referred to as the Guoyshift. This phase shift is of particular interest whenconsidering laser resonators, as it reduces the effec-tive length of a laser cavity and causes higher-order�n, m � 0� modes to lase at shorter wavelengths. Thespatial extent and divergence of a laser beam is alsodictated by its modal structure. The modal composi-tion of a VCSEL beam is, therefore, an importantconsideration when aiming to calculate the cross-talknoise in an optical interconnect.

Experiments were performed on a commerciallyavailable VCSEL (Mode 8085-2008) to determine itsmodal content. These measurements were furtherused in optical simulations to examine the effect oftransverse modes on optical cross talk. Using thesetup shown in Fig. 4 a series of VCSEL spectra wasmeasured, as the drive current was gradually in-creased to 7 � Ith, where Ith is the laser thresholdcurrent. At approximately this VCSEL current �7 �Ith� the total emitted optical power starts to decreasewith further increasing drive current, and we consid-ered it to be the practical limit in all our simulationsand experiments alike.

VCSEL spectra exhibit a series of peaks corre-sponding to transverse modes lasing at that current.The magnitude of all the spectral peaks was recordedfor currents between Ith and 7 � Ith, and used toconstruct a modally resolved light–current curve.

Within the context of cross-talk analysis in free-space optical interconnects, the variation in spatialprofile of the transverse modes is far more importantthan their spectral separation. To determine thetransverse mode structure of the VCSEL beam an

Fig. 4. Experimental setup used to measure the VCSEL opticalspectrum and the spectrally resolved and polarization-resolvedbeam profiles. Spatial scanning of the beam profile in the XY planewas implemented using a single-mode fiber and an actuator.


actuator controlled fiber probe was used to scan across section of the magnified near field. At each pointof a 15 � 15 grid, the spectrum was recorded, and thespectral peaks associated with transverse modes wereisolated. From these measurements we determinedthe optical power associated with each individual modeat each spatial pixel of the grid. This spectrally, spa-tially, and polarization-resolved data were used to re-create the spatial profile of each coexisting transversemode. From these transverse mappings, the dominantlasing modes of this VCSEL can be identified as LG00,LG01, LG02, and an LG10 � LG02 combination. Theresults have been summarized in Table 1. It can beseen that with the increasing current the fractionof the optical power corresponding to higher ordermodes is increasing; this consequently leads to theincrease in the beam spot size and optical noise.

B. Laser Noise and Modal Structure

The RIN refers to the stochastic variation observed inlaser output power, even when driven by a perfectlystable source.22 The total RIN can be calculated bythe ratio of the mean square of the laser power fluc-tuation �P�t� to the square of the average power P:

RIN ��P2

�P 2 . (9)

The RIN spectrum was measured at four differentcurrents using the setup shown in Fig. 5. The VCSELwas driven by the Newport 8000 modular controller,which also maintained the device temperature at 298K. The light was coupled into a Newport D-100-FChigh-speed photodetector. The average optical powerwas measured directly, and the noise component wastransmitted through a DC block and two microwavelow-noise amplifiers (JS2-00100800-17-0A and AFS3-00100800-32-L-N, Miteq, Hauppauge, New York) toa microwave spectrum analyser (Hewlett Packard8565E). The frequency response of the detector, am-plifiers, and the spectrum analyzer’s noise floor arenumerically removed from these data to obtain thenoise component of the VCSEL output. The result-

Table 1. Parameter Values Used in the Simulation

Parameter Names Parameter ValuesSystem pitch � � 160, 190, 220, 250 �mWavelength � � 850 nmBeam waist ws � 3 �mBeam position zs � 0Focal length f � 800 �mMicrolens fill factor � � 0.95 (95%)Microlens input distance d1 � f � Rayleigh range � 833 �mModified extinction ratio X � 0.4Photodiode responsivity R � 0.6 A�WReciever bandwidth B � 10 GHzElectron charge q � 1.60218 � 1019 CPhotodiode dark current Id � 10 nABoltzmann’s constant kB � 1.3807 � 1023 J�KOperating temperature T � 290 KEquivalent resistance of

photodetector load andpreamplifier

Req � 50

Preamplifier noise figure Ft � 3 dBLaser threshold current Ith � 2.5 mA

VCSEL bias current 4 mA 6 mA 8 mA 12 mA 16 mA

Relative intensity noise (dB�Hz) 114.5 126.4 130.6 135.7 138.2

Total VCSEL output power (mW) 0.25 0.62 1.44 3.44 4.17VCSEL output power in each

mode (mW)LG00 0.25 0.62 1.15 0.04 0LG01 0.29 3.24 1.5LG10 � LG02 0.16 2.67

Fig. 5. Experimental setup for RIN measurement.


ant noise spectra are shown in Fig. 6; average noiselevels of approximately �114, �126, �130, and�136 dB�Hz were extracted for currents of 4, 6, 8,and 12 mA, respectively. An obvious noise peak, cor-responding to the relaxation resonant frequency, cannormally be identified for the VCSEL operating in thesingle-mode regime. At high drive currents, up tothree families of coexisting modes are lasing, andtheir noise characteristics are superimposed result-ing in typical multipeak RIN spectra.22 Figure 6 alsoindicates the well-known trend: RIN decreases withthe increase of laser current. However, as we haveseen in Subsection 3.A, the fraction of the opticalpower contained in the higher-order modes will besignificantly increased with laser current. Clearly,these two processes will have the opposite effect onthe noise level in an FSOI system: optical cross-talknoise will increase, while the laser noise (RIN) willdecrease with laser current. Both types of noise needto be included in the model to optimize the FSOIarchitecture.

4. Simulation Model and Results

Simulation package Code V was used to simulateboth the SLCN and the DCCN. The design parame-ters used for simulation are listed in Table 1. Thesimulation was performed on a 2D lattice microlensarray consisting of 64 � 64 channels. The large sizeof the microlens array ensures a realistic estimate ofoptical noise in the system. Both the SLCN and theDCCN are measured by the total optical power in-cident upon unintended receiver microlenses. All thesimulation parameters are given in Table 1.

Optical interconnect designs are typically evalu-ated by considering propagation from point sources oruniform surface emitters. To determine the effect ofhigher-order transverse modes on FSOI performance,we propagate a 2D beam profile through the opticalsystem. The extended sources used in our simula-tions are based on the experimentally determinedmodal structure of the VCSEL beams. The parame-ters of the LG modes were obtained by fitting theanalytical expressions to mode profiles experimen-

tally determined in Section 3. The final beam profilewas formed by the weighted combination of the fol-lowing LG modes: LG00, LG01, LG10, and LG02. Theintensity distributions and the orientations of themodes relative to the receiver lens grid that wereused in simulations are shown as insets in Figs. 7(a)–7(d). The relative power attributed to each mode wasdetermined from the modal light current curves andis indicated in Table 1.

For each mode the calculated transverse profilewas mapped onto a 101 � 101 point computationalgrid used as the beam definition for the diffraction-based beam propagation. A combination of geometricray tracing and diffraction-based propagation tech-niques implemented in Code V is used to propagate thebeam through the optical interconnect. Geometric raytracing is used when a beam encounters an opticalsurface; the field distribution is converted into raysthat are traced across the optical interface. Once therays have been traced across the interface, they areconverted back into a field distribution, and the beamis propagated using the beam-propagation method.

To determine the optimal channel configuration wesimulated the OSNR for each individual mode whilechanging the lattice offset from 0% to 100%. Figure 7shows the change of OSNR as the lattice structureevolves from the square to the hexagonal grid config-uration. Simulations were performed for a channelpitch of 250 �m and an interconnect distance of 12mm. For all the transverse modes, the hexagonalgeometry provides the optimal OSNR. Furthermoreit can be seen in Fig. 7 that the OSNR with DCCNonly overestimates the performance of the intercon-nect and the degree of overestimation worsens forhigher-order transverse modes. Therefore the inclu-sion of stray-light cross talk is vital for obtainingaccurate modeling of the FSOI performance espe-cially when using a VCSEL that operates in a higher-order mode.

Figure 8 compares the OSNR for two extreme cases:a square grid and a hexagonal grid geometry. TheOSNR as a function of interconnect density for severaltransverse modes was examined. The interconnectiondistance of 12 mm was maintained as the intercon-nect density was increased, and several transversemodes were propagated through the interconnect.The hexagonal arrangement clearly offers better per-formance than the square geometry by at least 2 dBin OSNR for all transverse modes. Figure 9 examinesthe dependence of the OSNR on interconnect dis-tance. Again, we consider the two extreme channelarrangements: the square grid and the hexagonalgrid configuration. In this case, the channel pitch of250 m was maintained as the interconnection dis-tance was increased. For longer interconnection dis-tances, the DCCN becomes the dominant source ofoptical noise, and as the beam spreads out furtherdue to diffraction, it covers a larger area of the re-ceiver microlens array, hence reducing the effect ofthe array geometry on the OSNR. On the other hand,for short interconnection distances, owing to thecloser spacing of the transmitter and receiver micro-

Fig. 6. Measured RIN spectra for VCSEL drive currents between4 and 12 mA.


lens arrays, the area of the receiver microlens arrayilluminated by the beam is consequently smaller.Therefore significant change in the OSNR is notedwhen the configuration is changed from square tohexagonal. The marked improvement in the OSNR is

evident especially for the LG01 mode. Owing to thevertical orientation of the bowtie mode �LG01� used inour simulations, the OSNR for this mode in the hex-agonal lattice surpasses even that for the LG00 forinterconnect distances shorter than 8 mm. When av-

Fig. 7. Comparison of the optical SNR including DCCN only and a combined noise of DCCN and SLCN with increasing array geometryoffset value. Different transverse modes are shown: (a) LG00, (b) LG01, (c) LG10, (d) LG02.

Fig. 8. Optical SNR ratio with increasing interconnect density�channels�mm2� for different transverse modes.

Fig. 9. Optical SNR with increasing interconnection distance fordifferent transverse modes.


eraged over the azimuthal angle �, the OSNR for theLG01 in the hexagonal lattice is consistently abovethat for the OSNR for the same mode in the squarelattice, and close to but below the values for the OSNRof the LG00 mode even for the short interconnect dis-tances. This suggests that the extent to which thechannel arrangement affects the OSNR depends onthe modal composition of the VCSEL beam and forsome lower order modes on the azimuthal mode ori-entation as well.

Figure 10 shows the system SNR (including bothoptical and electrical noise sources) with increasingVCSEL bias current and for receiver bandwidths of2.5 and 10 GHz. As already mentioned in Section 3,laser intensity noise and optical cross-talk noise asfunctions of laser drive current have opposite trends.At lower laser currents, electrical noise dominatesthe system performance especially for architectureswith channel pitch above 200 m. With an increasein laser current, the fraction of the optical powercontained in the higher-order modes increases signif-icantly, and optical noise becomes dominant. There-fore the decline in SNR at higher laser currents inFig. 10 is mainly attributable to the optical noise andcould be checked by reducing the relative contribu-tion of higher-order modes or by increasing the pitchof the system. From the dependence of the electricalnoise (RIN and the noise equivalent power) on thereceiver bandwidth, one may conclude that the posi-tion of the peak SNR will shift to higher laser cur-rents as the receiver bandwidth increases. For theFSOI systems analyzed in Fig. 10, it can be seen thatto obtain the best system performance in terms ofSNR, VCSEL has to be driven with currents between6 and 7 mA. This holds for a range of geometries withchannel pitch ranging between 160 and 250 �m.

5. Conclusion

We have addressed comprehensively, for what webelieve to be the first time, the effect of channel ge-ometry on the SNR in microchannel free-space opti-

cal interconnect systems. We have demonstrated thatthe VCSEL and photodetector array configurationstrongly affect the overall system SNR. For allVCSEL transverse modes, the optical SNR was foundto be optimal when a hexagonal configuration wasused. In addition, we have shown the importance ofincluding the stray-light cross talk in the simulationmodel especially when the VCSELs operate at higherdrive currents. The level of improvement gained byusing the optimal hexagonal geometry is dependenton the modal structure of the incident beam; SNRimprovements close to 3 dB were observed for themajority of modes. For the VCSEL array used in thisstudy, the optimal VCSEL drive current required forthe maximum SNR was found to be between 6 and 7mA, which is approximately 2.5 times the VCSELthreshold current.

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Analysis of hexagonal array geometry for free-space optical interconnects with improved...

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