IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, VOL. 12, NO. 4, JULY/AUGUST 2006 767
Optimization of VCSEL Spatiotemporal Operation inMMF Links for 10-Gb Ethernet
Asghar Gholami, Zeno Toffano, Member, IEEE, Alain Destrez, Sebastien Pellevrault,Mathias Pez, and Francois Quentel
Abstract—A complete model of the spatiotemporal behaviorof multimode vertical-cavity surface-emitting lasers (VCSELs),through static and dynamic response, noise, thermal effects, andits coupling to multimode fibers (MMF) has been investigated inlow-cost 10-Gb Ethernet (10-Gb E) prototype optoelectronic pack-ages using GaAs VCSEL arrays coupled to MMF ribbons forshort-distance optical links. Eye diagram simulations comparedto measurements allow the analysis of critical parameters, such aslaunching conditions, in order to maximize the MMF bandwidth aswell as VCSEL static and dynamic conditions. A new bit error rate(BER) estimation method is proposed by taking into account notonly the Q-factor but random and deterministic jitter and digitalpattern effects. Global system optimization is discussed for a BERless than 10−12 for an aggregate link speed of 120 Gb/s over 300 mof a 12-fiber MMF ribbon.
Index Terms—Bit error rate (BER), fiber coupling, gigabit eth-ernet (GbE), laser beams, optical interconnections, thermal mod-eling, vertical-cavity surface-emitting lasers (VCSELs).
I. INTRODUCTION
V ERTICAL-CAVITY surface-emitting lasers (VCSELs)are the best adapted optical sources for high-capacity
applications in short-distance fiber communications as speci-fied in the 10-Gb Ethernet (10-Gb E) standard (IEEE-803.2ae:10GBASE-SR, 850-nm Serial LAN PHY) [1]. These systemsshould potentially achieve an aggregated speed of 120 Gb/swhen using 12 VCSEL arrays coupled to ribbons of multimodefibers (MMF) and with PIN photodiode array receivers. Thegoal is to obtain a maximum transmission distance of 300 m.However, due to the limited overfilled launch bandwidth of typi-cal MMF, optimization of the spatial multimode VCSEL outputand of its launching into the MMF are necessary in order toachieve the specified performances of 10 Gb/s per channel [2].
There has been much work undertaken separately onVCSEL behavior and on the propagation through an MMF.To our knowledge, no complete analysis of the coupling of thespatial multimode VCSEL output to the MMF and the propa-gation on the MMF in the time domain, including noise, hasbeen carried out [2]–[10]. We propose a complete spatiotempo-ral VCSEL model enabling the calculation of near- and far-fieldstatic and dynamic intensity profiles. The model also permitsthermal analysis. These profiles allow modeling the VCSEL tofiber coupling. The resulting MMF bandwidth is then calculated
Manuscript received August 25, 2005; revised February 21, 2006.A. Gholami, Z. Toffano, A. Destrez, and S. Pellevrault are with the De-
partment of Telecommunication, Ecole Superieure d’Electricite, F-91192 Gif,Cedex, France (e-mail: [emailprotected]).
M. Pez and F. Quentel are with D-Lightsys S.A., F-91461 Marcoussis Cedex,France.
Digital Object Identifier 10.1109/JSTQE.2006.876330
under different launching and mode conditions. The output atthe receiver level is analyzed by “eye diagram” simulations andcompared to measurements. A new method to estimate the biterror rate (BER) extracted from the eye diagrams taking intoaccount the Q-factor, jitter, and the digital modulation patterneffects is also proposed.
The optoelectronic packages measured here use non-thermally stabilized 850-nm VCSEL arrays coupled to graded-index MMF and are manufactured by D-Lightsys. The researchon the modeling of these systems has been initiated under theFrench RMNT SHAMAN project [3]. These low-cost integratedoptoelectronic packages (emitters and receivers), specified inthe temperature range −40◦C/ + 85◦C are expected to performat an aggregated speed of 120 Gb/s over 300 m of 12-MMFribbons.
Simulation results are based on the resolution of ordinarydifferential equations in the time domain, including noise. Spa-tial effects of the multimode VCSEL and of the MMF behaviorhave been calculated for the first time by integrating the fieldsand then taking them into account implicitly in the equationsthrough fixed coefficients, thus avoiding the time-consumingresolution of spatial partial differential equations (PDE). Thismethod results in fast calculations. Models can, thus, be directlyimplemented in commercial CAD languages, which do not sup-port PDE, as recommended by the SHAMAN project [3].
In Section II-A, the VCSEL spatiotemporal and temperaturemodel is introduced. The noise model is described in SectionII-B. Section III-A describes the calculation method of theVCSEL intensity profile at the MMF input. Section III-Bdescribes the MMF coupling model. Section III-C describes theMMF propagation. Section III-D describes the receiver output.Section IV covers simulation of the complete system also takinginto account driver and receiver electronics. Section V-A coversthe calculated and measured eye diagrams and in Section V-B,system BER is calculated. In Section VI, we present a summaryand conclusion.
II. VCSEL SPATIOTEMPORAL AND THERMAL MODEL
A. Spatiotemporal and Thermal Model Description
We consider VCSEL cylindrical oxide-confined structuressupporting linearly polarized (LP) modes. The inhom*ogeneouscarrier profile N(r, t) is expanded under the following Bessel or-thogonal series with the time-dependent expansion coefficientsNi(t) [4]:
N(r, t) = N0(t) −∞∑
i=1
Ni(t)J0
(σir
W
)(1)
1077-260X/$20.00 © 2006 IEEE
768 IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, VOL. 12, NO. 4, JULY/AUGUST 2006
TABLE ITYPICAL GIGABIT VCSEL MODULE PARAMETERS
where N0 is the average carrier number, W is the effectiveactive-layer radius, and σi is the ith root of the first-order Besselfunction J1(x).
Rate equations in carrier and photon number are commonlyused in order to calculate time domain behavior. Here, we con-sider VCSEL spatial multimode operation. We use a set of spa-tially independent differential equations providing an implicitdescription of a device’s spatial model dependence [4]. This pro-vides a good compromise between accuracy and computationalspeed. We completed these multimode VCSEL rate equationsby including specific temperature dependence and photon-noisesources. The rate equations for the transverse modes k are
dN0
dt=
ηiI(t)q
− N0
τn− Il(N0, T )
q
−N∑
k=0
G(T )Sk
(γk0N0−
∑N +1i=1 γkiNi−γk0Nt(T )
)1+
∑Ni=0 εikSi
(2)
dNj
dt=−Nj
τn(1+hj )
−N∑
k=0
G(T )Sk
[φkj0N0−
∑N +1i=1 φkjiNi−φkj0Nt(T )
]1+
∑Ni=0 εikSi
(3)
Fig. 1. Measured and calculated characteristics. (a) VCSEL total power fordifferent temperatures versus drive current. (b) Threshold current I th versustemperature.
dSk
dt= − Sk
τpk+
βk
τnN0 + nk (t)Sk
+G(T )Sk
[γk0N0 −
∑N +1i=1 γkiNi − γk0Nt(T )
]1 +
∑Ni=0 εikSi
(4)
dT
dt=
1Cth
[I(t)[Vj (T, I)+RsI(t)]−T−Tamb
Rth−
N∑k=0
Sk
τpk
]
(5)
where I(t) is the injection current, Il, the thermal leakage cur-rent, Sk is the total photon number for the mode k,N is thenumber of transverse modes and T is the device temperature.
Typical parameters are shown in Table I. Diffusive effects dueto the carrier density are modeled through the hj terms in (3).The overlap of the gain and mode profiles is taken into accountby the integrals γki and φkji . Equation (6) shows the overlapintegral for γki and φkji
γki =2
W 2
∫ W
J0
(σir
W
)ψk (r) rdr
φkji =2
W 2J20 (σj )
∫ W
J0
(σir
W
)ψk (r) dr. (6)
Equation (5) relates cavity temperature to thermal power dis-sipation, injection current I(t), and mode photon number Sk .The cavity temperature is determined by the equivalent thermalresistance Rth from the laser to the substrate heat sink and bythe thermal capacitance Cth.
Temperature variations affect VCSELs through the thresholdcurrent Ith(T ) and in a lesser way through the slope efficiencyηLI(T ) leading to the optical power temperature dependenceshown in Fig. 1. Slope efficiency variations are principally due tothe Joule effect because of self heating induced by an increase incurrent. The calculated and measured total power versus currentfor different temperatures is shown in Fig. 1(a).
The threshold current in a VCSEL as a function of temper-ature is expected to reach a minimum as shown in Fig. 1(b),corresponding to the temperature for which there is a coinci-dence between the cavity mode and the gain peak. The change
GHOLAMI et al.: OPTIMIZATION OF VCSEL SPATIOTEMPORAL OPERATION IN MMF LINKS 769
Fig. 2. VCSEL output power for different modes and total as a function ofdrive current at 25◦C.
of Ith at lower temperatures is mostly due to the variations of thegain positions and at higher temperatures to leakage current in-crease [5]. Threshold current temperature behavior [Fig. 1(b)],showing a minimum value in the threshold current tempera-ture variation Ith(T ), corresponds to modern 850-nm VCSEL.This leads globally to less temperature-sensitive devices and isa common VCSEL design rule [5].
As a result of spatial hole burning (SHB) and of increasingtemperature, the leak age current can become significant becausethe active layer can not adequately confine the carriers.
The wavelength λ(T ) and gain spectrum temperature depen-dence have also been considered and included in the differentialgain rate GN (T ). Transparency density Nt(T ) increases withtemperature contributing an increase of Ith. VCSEL voltageV (T, I) dependence on temperature is considered for higherprecision.
B. Static, Dynamic, and Noise VCSEL Behavior
As shown in Fig. 2, the total emitted power is linear and doesnot depend on spatial-mode structure. Emission at the thresholdbegins in the LP01 mode then, with increasing current, the modesLP11 and then LP21 start to emit. When a new mode starts theslope of the previous dominant mode decreases, this is shownin Fig. 2.
Fig. 3 shows the VCSEL dynamic response to a square-shapedinput current. The total optical intensity profile correspondingto three different instants is shown. The intensity profile shapedepends on the relative mode intensities, which has an influ-ence on fiber coupling and also on modal dispersion, as will bedescribed later.
Carrier diffusion and SHB have a severe impact on VCSELperformance. In particular, these phenomena can producemode competition, secondary pulses, bumps, and optical tails inthe VCSEL turnoff transient and relaxation oscillations, as canbe seen in Fig. 3. This can limit both the system bit rate andthe bit error rate (BER) [6], [7]. Mode turnon delays depend onmode number and on injection current. These effects contributeto jitter.
Fig. 3. VCSEL dynamic response to a square-shaped input current for threedifferent modes and corresponding dynamic intensity profiles.
Fig. 4. RIN spectrum for total VCSEL output and for three different modes.
VCSEL relative intensity noise (RIN) levels are generallyhigher than those of edge emitting lasers. For short-distancefiber optic transmissions, power levels at the receiver can berelatively high, meaning that RIN contributes significantly tothe total receiver noise.
Mode-partition noise (MPN) has been experimentally ob-served in both VCSELs and edge-emitting lasers. [8], [9]. Thisis calculated numerically in our model by the spontaneous emis-sion fluctuations represented by the Langevin noise sourcesnk (t)sk (t) in the rate equations (4) [10].
In Fig. 4, the calculated RIN spectrum for different modesis shown. Peaks at lower frequencies in the noise spectrum aredue to mode competition. Noise power fluctuations in individualtransverse modes can become larger than those of the total noisepower for frequencies below the relaxation frequency fr [11].However, as in the case of the total power, the relaxation fre-quency depends only on the total photon number [6] and MPNdisappears for frequencies higher than fr.
Spatial filtering of VCSEL output, due, for example to fibercoupling and propagation can lead to an increase in, the to-tal noise level because of the change of correlation conditionsbetween modes [6].
770 IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, VOL. 12, NO. 4, JULY/AUGUST 2006
Fig. 5. VCSEL far-field to MMF coupling representation.
III. VCSEL COUPLING AND FIBER PROPAGATION MODEL
A. Intensity Profile at the Fiber Input
VCSEL-to-fiber coupling is of critical importance in thesesystems because it affects bandwidth, signal-to-noise ratio, andjitter. Fiber coupling depends on the VCSEL characteristicssuch as the active laser diameter, index guiding, and intensityprofiles, and also on the geometry and index profile of the MMF.Coupling schemes without additional optics is a key feature inlow-cost optoelectronic transceiver modules.
The ray tracing method has been used in order to calculatethe VCSEL to MMF coupling [12]. VCSEL transverse modeintensity profiles are calculated at distance z (VCSEL to MMFdistance).
A Hermite–Gaussian (HG) expansion of the LP modes hasbeen performed, in order to obtain the transformed intensityprofiles
ψ(r, z) =∑
n
cnGn (r, z) cn =∫ w0
−w0
ψ(r)Gn (r, 0) dr. (7)
The orthogonal HG functions Gn (r, z) are scaled, in orderto represent the fractional power. Coefficients cn are obtainedby integrating the mode profiles ψ(r) over the HG functionson the VCSEL origin axis (z = 0). The transformed field andtherefore the light intensity profile can then be calculated at anyVCSEL fiber distance.
B. MMF Specification and VCSEL Coupling
The coupling configuration between the VCSEL output pro-file at distance z and the MMF core with variable offsets isshown in Fig. 5. M is the light ray injection point on the fibersurface, r is the distance to the VCSEL center axis o′, and Lof
corresponds to the axial misalignment between the fiber centero and the VCSEL center axis o′, θof is the angular offset and φis the angle between two lines on the fiber surface, which con-nect o′ to M and o. rc is the distance between M and the fibercenter o.
The VCSEL to MMF distance, the fiber profile index, thecore diameter and the numerical aperture are the most criticalparameters.
Equation (8) shows the index profile function, called theα-profile, of the multimode graded index fiber, a is the coreradius, nf the center refractive index and ∆ is the relative indexdifference
n(rc) =
nf
√(1 − ∆
(rc
a
)a)For rc ≤ a
nf
√1 − ∆ For rc > a
. (8)
The maximum acceptance angle for entering a ray to the coreθM (rc) can be expressed by
θM (rc) =
sin−1
(nf
√∆
√2 − r2
c
a2
)For rc ≤ a
0 For rc > a
. (9)
We have used the ray tracing method, in order to calculate theVCSEL to MMF coupling [7]. Using the transformed far-fieldintensity profiles, we found the coupling efficiency and also thepower distribution in the different fiber core modes in differentcoupling conditions, finally leading to the MMF intermodaldispersion. rc can be related to r, Lof, and φ by
rc(r, Lof, φ) =√
r2 + L2of − 2rLof cos (φ). (10)
The total injected power in the fiber core is then calculatedby
ψtotal =∫ 2π
∫ R
ψ(r, z) cos φs rd rdθ (11)
ψ is the power profile at the distance z from the VCSEL, andφs is the angle between the ray and the vector normal to thesurface.
For each injected ray we can define an equivalent ray an-gle entering at the center of the MMF core with an equivalententering angle given by (12).
Equivalent entering angles are specified for each ray, thereforewhen using the intensity profile we can calculate the powerdistribution for all the angles
θc(r, z, φof, Lof) = sin−1
(2n2
f ∆r2c (r, Lof, φ)
a2
+
√1 − (r cos φ sin θof + z cos θof)2
z2 + r2
). (12)
Higher order modes tend to show more losses than lowerorder modes [12], in order to take into account this effect, weintroduce the following weight function:
Wai(r, z, φ, θof, Lof) = 1 −(
θc(r, z, φ, θof, Lof)θM 0
)4
(13)
where θM 0 is the maximum acceptance angle at the core centerand θc is the equivalent entering angle.
Losses due to the reflection from the air–fiber interfacehave been considered with a Fresnel transmission factorTpwr (r, φ, θM ) depending on angle and distance.
GHOLAMI et al.: OPTIMIZATION OF VCSEL SPATIOTEMPORAL OPERATION IN MMF LINKS 771
Last, considering that rays with an angle greater than θM donot enter the fiber, the total entering energy can be calculated by
ψcoupl(Lof, θof, z)
=∫ π
∫ R
2ψ(r, z)Wai(r, z, φ, θof, )
· Tpwr (r, φ, θM )
√(r cos φ sin θof + z cos θof)2
z2 + r2rd rdφ.
(14)
C. MMF Propagation Modeling
The index profile shape has a considerable effect on the dis-tribution and the characteristics of the propagated light [2]. Foran optimum prabolic profile (α ≈ 2), the modal dispersion is ata minimum. In practice, α varies between 1.8 and 2.2 [2], [13].In addition, defects in the core and at the core-cladding interfacecan also affect the profile.
Material dispersion is also considered through the spectraldistribution of the VCSEL transverse modes and its effectivespectral width ∆λ. According to our measurements, the typicalspacing between transverse modes is typically 0.2 nm [3]. Inthe 850-nm fiber transmission window, a material dispersioncoefficient D = +80 ps/(nm · km) is assumed and taking intoconsideration no more than ten oscillating transverse modes,material dispersion is much smaller than intermodal dispersionin our application.
Average ray velocities for different equivalent entering an-gles are then calculated by the ray-tracing method, in order toevaluate correctly the modal dispersion.
We subdivided the graded index MMF in different index nl
cylindrical layers. The trajectory of each ray in the differentlayers was determined by using Snell’s law. By using ray trajec-tories and ray velocities in each layer the average ray velocitieswere determined. With the distributed power and the averagevelocities for different equivalent entering angles, the outputdynamic optical signal was reconstructed as a function of thefiber length. The fiber transfer function was then computed bythe fast Fourier transform (FFT) of the calculated temporal re-sponses.
Intermodal dispersion affects lower modes more significantlythan higher modes. Higher transverse modes inject most of theirpower in the higher fiber modes and, have less dispersion incomparison with lower modes. This does not vary with changesin the fiber index profile parameter α. This case is obtained witha “donut”-shaped radiation pattern [14] (see Fig. 3).
The fiber transfer function for different transverse modes isshown in Fig. 6(a). For a fiber length of L = 300 m and α = 1.9the launched VCSEL LP21 and LP11 modes have respectively120% and 65% superior bandwidth compared to LP01. Thefiber bandwidth of LP21 is about 4 GHz, whereas for LP01 it is1.8 GHz.
In Fig. 6(b), the fiber transfer function for three differentlateral offsets is shown. With lateral offset increasing from 0 to30 µm, the total bandwidth increases from 2 to 2.5 GHz, then itincreases sharply up to 6 GHz for 45-µm offset. Nevertheless,
Fig. 6. MMF transfer functions for a 300-m fiber length. (a) For three differentmodes. (b) For different lateral offsets.
Fig. 7. MMF bandwidth and coupling efficiency versus VCSEL-fiber distancez for a 300-m fiber length.
we have a decrease to 15% in the coupling efficiency. Increasingthe lateral offset makes the lower modes in the fiber disappearand most of the power is injected in the higher fiber modes and,therefore, the bandwidth increases.
Also, on increasing the angular offset to 10◦, the bandwidthdecreases from 2 to 1.8 GHz, increasing slightly for higheroffsets.
The relation between fiber bandwidth and VCSEL fiber dis-tance is shown in Fig. 7. For lower distances, the rays enteringthe fiber have lower waists, causing less intermodal dispersionthrough MMF propagation. On increasing distance, the disper-sion is increased because of an increase in the angle betweenrays and beam waists. However, the coupling efficiency de-creases with increasing distance.
As discussed earlier, RIN is also affected by the MMF trans-mission; this point has rarely been investigated in these applica-tions. Fig. 8 compares the RIN noise spectrum at the input andoutput of a 300-m length MMF. At higher frequencies, becauseof the limited bandwidth, RIN is attenuated. On the other hand,for lower frequencies, there is an increase and modification ofthe RIN spectrum due to MMF on mode correlation.
D. Receiver
Receivers integrated in the optoelectronic modules consist ofPIN photodiode arrays and transimpedance amplifiers followedby limiting amplifiers for signal reshaping.
The PIN photodiode response has been modeled consideringtypical device parameters in the intrinsic region using the spe-cific electron and hole profiles. The total PIN current is the resultof the collected carriers in the corresponding doped regions with
772 IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, VOL. 12, NO. 4, JULY/AUGUST 2006
Fig. 8. VCSEL RIN noise spectra and their modification after propagationthrough a 300-m MMF.
Fig. 9. Block diagram of the complete model.
respective velocities [15]. This results in a specific PIN responsefunction with delay and rise and fall time.
The noise at the detector level is the sum of RIN, quantumnoise, dark noise, and thermal noise due to detector electronics.Temperature effects in the receiver are principally due to the re-sponsivity Rd through wavelength λ(T ) variation, and to darkcurrent ID(T ) through the gap energy variation [3], [16]. Re-sistor thermal Johnson noise is temperature-dependent throughthe Boltzman factor kBT .
IV. COMPLETE SYSTEM SIMULATION
Fig. 9 shows the complete block diagram of the model. Thesimulation procedure supports various system configurationsunder different operating conditions such as extinction ratio,
Fig. 10. Calculated (left) and measured (right) eye diagrams at 2.5 Gb/s, fordifferent temperature for a 250-m MMF fiber length.
average power, and temperature. VCSEL parameters can alsobe easily changed.
The first block simulates the driving circuit that modulatesthe signal, here we can add reshaping circuits in order to opti-mize the eye diagram. The second block represents the VCSELspatiotemporal model and calculates the rate equations in thetime domain, the output gives the intensity of the different LPmodes. Here, we can change the laser parameters and specifythe temperature. Then the near-field to far-field VCSEL modedistribution is calculated at the specified fiber distance, enablingthe calculation of the coupling between laser and fiber. Here, weintroduce coupling parameters. Subsequently, the light propa-gation through the graded-index MMF is calculated by the ray-tracing method. The receiver is modeled in the next block wheredifferent receiver parameters can be changed.
The output is displayed in the temporal domain. Opti-mization can be undertaken by eye diagram analysis and bycomparison with experiments. Frequency domain transferfunctions can also be calculated, which is useful for noise andbandwidth characterization.
V. DISCUSSION: EYE DIAGRAMS AND BER
A. Eye Diagram Simulations
Digital modulation characteristics are commonly evaluatedby studying eye diagrams and BERs for various modulationconditions [17]. Eye diagram results are presented in Fig. 10and compared to experimental results on actual commercialD-Lightsys packages.
Undershoot and overshoot in the temporal response can crossthe standard eye mask [1], yielding errors in the transmission.These effects are shown in Fig. 10. Under certain conditions,
GHOLAMI et al.: OPTIMIZATION OF VCSEL SPATIOTEMPORAL OPERATION IN MMF LINKS 773
Fig. 11. Eye diagrams at 10 Gb/s for an extinction ratio of 7.2 dB for 1- and300-m fiber length, with input signal reshaping and coupling offset.
we also observe a doubling of the rising edge of the signal,leading to an increase in jitter. The signal rising depends on thepreceding bit pattern, this is the case for example when a “0”precedes a “1.” Rising instants depend on their relative positionin the relaxation oscillations. This is affected by drive current,temperature and bit rate. For example the sequence “0101”behaves differently from the sequence “1001,” and the corre-sponding jitter can increase from 10 to 40 ps. Reshaping drivecurrent using specifically designed drive electronics can reducerelaxation oscillations and thus reduce jitter.
Mode competition is another source of jitter. Because of SHBand carrier diffusion in the active region, transverse mode inten-sities depend on bit patterns. For an alternating “101” sequence,the third mode is dominant. However, in the case of a differentsequence after many successive “0” the mode rank is completelychanged. Jitter is also due to the propagation through the MMFbecause of intermodal dispersion, as was discussed earlier.
Simulations at 10-Gb/s modulation are shown in Fig. 11.We compare transmission over a very short fiber length of 1 m(dispersion is irrelevant) with a transmission over 300 m ofMMF. Jitter results in 26 ps (for a 100-ps period) for 300 m.Jitter can be reduced by reshaping the drive current with anoptimized RL filter. The result is shown in Fig. 11(a) where jitteris 12 ps, compared to 18 ps without filter for a 1-m transmission.Overshoots and undershoots are also reduced by reshaping.
An offset in the coupling of the VCSEL to the MMF leadsto lower fiber dispersion because of mode filtering [18]. Thisresults in lower jitter, for example 14-ps jitter is obtained for40-µm offset.
B. BER Estimation
Studying the BER versus extinction ratio is a standard proce-dure for evaluating the transmission performance of an opticallink. Extinction ratio (ER) is here defined as 10 log(P1/P0)where P0 and P1 are the VCSEL output power levels corre-sponding to the low-state and high-state bit, respectively. In
order to quantify the influence of critical parameters such asfiber length, modulation speed, and coupling, we have devel-oped a method which enables us to estimate the BER from thesimulated and measured eye diagrams.
This is not an easy task because of the complex form of theresponse including noise, random and deterministic jitter, inter-symbol interference (ISI), and VCSEL relaxation oscillationsgiving overshoot and undershoot. All these effects are rarelytaken into account, generally only the Q-factor is consideredfor BER estimation.
We have extended the BER calculation method describedin [19] by including jitter.
The transmitted pattern is divided into eight possible combi-nations of three bits. Gaussian distributions are fitted for eachof these combinations. The BER is estimated for each pattern,including jitter, and then a weighted average is performed as afunction of the probability of occurrence of each combination
BERTot =8∑
p=1
P (p)[BERQpD + BERJpSI] (15)
BERQpD = erfc
(Qp√
2
)Qp =
|D − µp|σp
(16)
BERJpSI =12erfc
(|SI − 0.5DJp|√
2RJp
)
+12erfc
(|UI − SI − 0.5DJp|√
2RJp
). (17)
Equation (15) gives the expression of the total BER resultingfrom the eight different patterns. P (p) is the probability of oc-currence of the pattern p. Equation (16) gives the BER of patternp due to the Q-factor where D is the decision threshold and, µp
and σp are the mean and standard deviation. Equation (17) givesthe BER of pattern p caused by jitter. SI is the sampling instant,UI is the unit interval (bit period) DJp and RJp are the determin-istic and random jitter, respectively. For the patterns without astate transition, we have considered BER Jp = 0.
In Fig. 12, the estimated BER for different bit rates, fiberlength, and lateral offset are compared.
VI. SUMMARY AND CONCLUSION
We have performed a detailed study on the static and dy-namic behavior of VCSEL arrays associated with MMF for10-Gb E communications. In order to discuss performances toachieve the bit rate of 10 Gb/s per channel, the complete VC-SEL spatial multimode behavior was considered for differentinjection currents and temperatures. The multimode VCSEL ra-diation pattern injected in the MMF fiber is monitored throughthe fiber propagation using the ray tracing method. Temperaturedependence is obtained in the −40◦/ + 85◦C range. Modula-tion response, RIN, eye diagram, and BER were simulated andcompared to measurements on prototype modules.
Eye diagram simulation shows that the worst-case conditionsthat can be found as a function of input current signal and
774 IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, VOL. 12, NO. 4, JULY/AUGUST 2006
Fig. 12. Calculated BER versus extinction ratio for different operating condi-tions. (a) Bit rate. (b) Fiber length. (c) Coupling lateral offset.
temperature. The influence of fiber length on jitter due tointermodal dispersion is also determined.
We propose a new method for BER estimation based on eyediagram analysis including jitter, which considers eight differentbit patterns compared to the two generally used.
System parameter influence has to be considered at the max-imum BER of 10−12 specified for 10-Gb E. For example,Fig. 12(a) shows that a maximum bit rate of 10 Gb/s causespenalties from 1 to 2 dB in the extinction ratio when comparedto 5 Gb/s. The influence of fiber length is not as critical, asshown on Fig. 12(b), due to the positive effect of filtering forhigher fiber lengths, which leads to less noise and to smootheroscillations.
We also observe that injection lateral offset gives better per-formances mainly because of stronger mode filtering leading toless jitter, as shown in Fig. 12(c).
Of course temperature will also affect these figures.Our study shows that simulation on a short range 10-Gb E
system has to be performed on the whole link (driver-VCSEL-coupling-MMF-receiver) and not only in a VCSEL back-to-backconfiguration.
Because the model does not explicitly depend on spatial pa-rameters, computation is fast and can thus be easily imple-mented using commercial computer Aided Design languagessuch as SPICE or VHDL-AMS as was defined in the SHAMANproject [20].
ACKNOWLEDGMENT
The authors would like to acknowledge the other ReseauMicro et Nano Technologies (RMNT) SHAMAN project part-ners, IPSIS, ENST, ENSAE, and PHASE in France. The exper-imental work has been done in the laboratory which is part ofthe Optics Valley PRISME Experimental Platform sponsoredby the programs ASTRE (Conseil General de l’Essonne) andSESAME (Region Ile-de-France) France.
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Asghar Gholami was born in Isfahan, Iran, in 1970. He received the B.S. andM.S. degree, from Isfahan University of Technology (I.U.T.), Isfahan, in 1993and 1996, respectively, both in electrical engineering. Currently he is workingtoward the Ph.D. degree at the Universite Paris-Sud, Orsay, France, in “highbit rate optical fiber communication for short distances” at the OptoelectronicLaboratory, Telecommunications Department, Ecole Superieure d’Electricite(Supelec), Gif, France.
From 1996 to 2002, he worked on circuit and system design in a researchlaboratory in Isfahan, Iran.
GHOLAMI et al.: OPTIMIZATION OF VCSEL SPATIOTEMPORAL OPERATION IN MMF LINKS 775
Zeno Toffano (M’90) received the postgraduate degree in electronics from theEcole Superieure d’Electricite (Supelec), Gif, France, and the Ph.D. degree insolid-state physics from the Universite Orsay, Orsay, France, in 1985.
Since 1987, he has been with the Optoelectronics Laboratory, Telecommu-nications Department, Supelec. He is currently working on models and charac-terizations of semiconductor lasers for optical communications and on quantumeffects in communications. He has also been engaged in giving lectures on op-toelectronics and quantum physics at Supelec.
Alain Destrez received the Master’s degree in physics from the Universite deReims, Rheims, France, in 1981, and the Diplome d’Ingenieur degree in engi-neering from the Ecole Superieure d’Electricite (Supelec), Gif, France, in 1983.
Since 1983, he has been with the Optoelectronics Laboratory, Telecommu-nications Department, Supelec. He is currently in charge of lectures regardingfiber-optic transmission.
Mr. Destrez is a member of the Societe Fraaise d’Optique (SFO).
Sebastien Pellevrault was born in Paris, France, in 1981. He received theMaster’s degree from the Ecole Superieure d’Electricite (Supelec), Gif, France,in 2005. Currently he is working toward the Ph.D. degree at Universite Paris-Sud,Orsay, France, in high-bit-rate optical communications at the OptoelectronicLaboratory, Telecommunications Department, Supelec.
Mathias Pez received the Diplome d’Ingenieur degree in telecommunica-tions engineering from the Ecole Superieure de Mecanique et d’Electricite(ESME/Sudria), Paris, France, in 1994, and a specialization Masters de-gree from the Ecole Nationale Superieure de l’Aeronautique et de l’Espace(SupAero/ENSAE), Toulouse, France, in 1995.
From 2001 to 2002, he researched optical interconnects at Thales Researchand Technology, Orsay, France. He founded the spin-off company D-LightsysS.A., Marcoussis, France, from previous laboratory activities in 2003.
Fracois Quentel received the graduate degree from the Ecole NationaleSuperieure de Physique de Strasbourg, Paris, France, in 1998, the M.Sc. de-gree in photonics in 1998, and the Ph.D degree in photonics on the integrationof micro-optical elements within parallel optical interconnect modules fromLouis Pasteur University, Strasbourg, France, in 2005.
In 1998, he joined Thales Research and Technology. He is one of the co-founders of the company D-Lightsys, S.A., Marcoussis, France, a spin-off ofthe Optical Interconnect Laboratory, Thales, France. Since January 2003, he hasbeen in charge of new product development within D-Lightsys.
