a,b
b
a
b a
b
ABSTRACT
Optical communication systems have been widely preferred for network communications, especially for
Datacoms Local Area Network links. The optical technology is an excellent candidate for on-board systems due to the potential weight saving and EMC immunity. According to the short length of the link and a cost saving, Vertical Cavity Surface Emitting Laser (VCSEL) and multimode fiber are the best solution for gigabit systems. In this context, we propose a modeling of 850nm VCSEL based on the rate equations analysis to predict the optical interconnect performances (jitter, bit error rate). Our aim is to define the operation conditions of VCSEL under large signal modulation in order to maximize the Extinction Ratio (current I
OFF below threshold) without affecting link performances. The VCSEL model is developed to provide large signal modulation response. Biasing below threshold causes stochastic turn-on delay. Fluctuations of this delay occur, due to the spontaneous emission. This leads to additional turn-on jitter. These stochastic effects are included in the model by adding the Langevin photon and electron noise sources.
The VCSEL behavior under high-speed modulation is studied to observe the transient response and extract the resonance frequency, overshoot and turn-on delay. The associated jitter is evaluated with the standard deviation of the turn-on delay probability density function.
Simulations of stochastic and deterministic jitters are realized under different conditions of modulation (OFF current levels). Comparing simulations with measurement results carried out on VCSEL and a short haul gigabit link validates the approach.
Keywords: Avionics, Gigabit Ethernet, VCSEL, turn-on delay, jitter, bit-pattern effect, spontaneous emission.
Copyright 2008 Society of Photo-Optical Instrumentation Engineers. This paper was published in
Semiconductor Lasers and Laser Dynamics III, edited by Krassimir P. Panajotov, Marc Sciamanna,
Angel A. Valle, Rainer Michalzik, Proc. of SPIE Vol. 6997 , and is made available as an electronic reprint with permission of SPIE. One print or electronic copy may be made for personal use only.
Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper are prohibited
1.
INTRODUCTION
Avionic systems remain mostly based on electric equipment and are modulated at low data rates (10 and 100Mb/s). The increasing demand of data rates greater than 1Gb/s as much as the weight saving has led to optical solutions for short distance link data-communications. However, since the design of communication links for Local Area Network (LAN) differs from long haul telecommunication links, the primary factor affecting the design will be the cost of the components of the link. All these factors have led to the choice of multimode fibers, which will allow important cost savings on transmitter and receiver. Moreover, 850nmVertical Cavity Surface Emitting Lasers (VCSELs) provide attractive performances at reasonable costs, in comparison to edge-emitting lasers.

At high data rate modulation, our aim in this paper is to investigate nearly single-mode VCSEL dynamics under subthreshold biasing, to discuss the impact of the turn-on delay, and turn-on jitter on the overall performances. This paper is divided into four sections.
In section 2, the avionic system of application is presented. In section 3, theoretical model of the large signal modulation of 850 nm VCSEL is presented, based on single-mode rate equations with the Langevin forces added in order to evaluate the statistical performances in terms of delay and jitter. In section 4, simulations of turn-on delay and jitter are shown. In section 5, measurements are presented, for both VCSEL and complete link, and results are compared to the characteristics of the studied link that must be achieved in regard to the IEEE standards criteria.
2.
AVIONIC LINK CHARACTERISTICS
The Avionic Data Communication Network (ADCN) is the new aircraft system in charge of interconnecting avionic equipment. It’s a Local Area Network (LAN) based on Avionics Full DupleX (AFDX) technology. The AFDX has been developed by Airbus to replace ARINC 429 due to the increasing of data-communications. This technology uses the
Ethernet concept and Internet protocols namely the IEEE 802.3 [1], and has been standardized by ARINC 664, part 7 [2].
Also, the media of communications uses the twisted pair technology for all cables. Frames are switched and the topology is a network star built around switches. For avionics constraints, a special cable ( Star Quad cable) has been developed, and transmissions are at 10 or 100Mbps. The link is full duplex, which means that the systems in the AFDX network can transmit and receive at the same time on the same link. This is possible because a link is made up of two pairs of wires, one pair for transmitting and the other for receiving.
For future aircraft programs, due to the increasing data communications to gigabit Ethernet and weight saving, aircraft manufacturers begin to prefer optical fiber physical layer rather than copper wires. Developing an optical solution at gigabit Ethernet is hence more and more investigated. The 1Gbps AFDX optical physical layer shall comply with IEEE
802.3 Standard Gigabit Ethernet 1000BASE-SX Physical Medium Dependant (PMD) requirements [1] and also with
ARINC 804 requirements [3].
The aim of this work is to study timing performances on a short distance link (100m) based on 850 nm VCSEL for application to an optical AFDX gigabit link. The worst case-scenario corresponds to the link between the equipments located in the main avionic bay at the cockpit and those at the rear part of the aircraft (cf. Fig. 1). The total link loss is evaluated by considering this case link, including production breaks (representative of a real aircraft-type application).
Production breaks
Electronic Equipment connector Equipment
Under test link
Equipment
Fig. 1 System of application: Avionic Data Network Communications (ADCN) over 100m link

3.
THEORETICAL APPROACH: DELAY, AND JITTER ESTIMATION
Mainly, the VCSEL is biased below the threshold in order to enhance the extinction ratio. However, when biased below threshold, the optical gain of the semiconductor laser is insufficient for stimulated emission and the output power provided by the spontaneous emission is small. The laser threshold needs to be reached, which gives rise to additional turn-on delay and consequently, turn-on jitter, causing degradation of the VCSEL response. In order to define the optimal performance operation, we have modeled the transient re
OFF currents (I
Indeed, when the laser is directly modulated by a current pulse train with I stimulated emission is reached. This delay comes with damped ringing at the relaxation resonance frequency f upper limit for the achievable modulation frequency. For discussing the modulation characteristics, we do not consider here the transverse mode competition of VCSEL, which means coupled rate equations of electrons an
OFF
) and for I
ON
far above the threshold level, via the rate equations. d photons. They are expressed as : dN dt
=
qN
I w
+
N
− G dP dt
=
BN + N w
G sponse in terms of delay, overshoot and jitter versus the the laser is nearly singlemode. Our study is based on the
P + F
N
P −
P
+ F
P
OFF
<I
TH
to I
) (1)
) (2) given by
The VCSEL intrinsic parameters used in (1) and (2) are defined and listed in Table 1. The electron lifetime
τ − 1 =
Table 1. VCSEL parameters
A + B N . F
B
Symbol
A
τ
β
Γ
N
I variable
N variable
P variable e
W
τ
G
η
N p th
N
(t) and F
Value
P
(t) are the Langevin forces for the electron and photon number resp.
3
0.049
10
3.03
× 10
1 × 10
88.42
9.52
× 10
6 × 10
0.6
-4
3.04
× 10
-12
-9
10
Dimension
A Drive current
. Carrier number
. Photon number
. Number of QW
. Optical Confinement factor
. Spontaneous emission factor
-1 s Electron lifetime
-1
-1
-1
.
.
Description
Modal gain
Photon lifetime
Non-radiative recombination factor
Spontaneous recombination factor
Quantum efficiency
Carrier number at threshold
ON
, there is a delay before clo6
U-
R
yielding
τ is also
OFF
=0 (without prebias) to I
02 04
TIIIIIIIII1
Time (ns)
06 08
ON
=12*I
TH
(far above threshold) for N (dashed curve) and P Fig. 2. Turn-on event from I

Under large signal modulation, the VCSEL response to a current step is not instantaneous as sketched in Fig. 2, where the laser is directly modulated from I number reaches N th strongly of I
OFF
OFF
, as will be shown below.
<I
TH
to I
ON
. The crossing time t c
is defined as the time at which the carrier
, the threshold carrier population in the active region. This crossing time is dependent of I
ON
and
In order to quantify the effects occurring during the turn-on event, the dynamics of the photon number P(t) is separated into a stochastic regime (t<t c
) and a deterministic regime (t>t c
) There is a delay time t d
between the applied bias and the pulse rise time to the ON level, equal to the sum of the carrier density rise time to the lasing threshold τ
D and the optical switch-on time to the optical ON level t on
: t d
= τ
D
+ t on
. Resolution of the two-coupled equations (1) and (2) under large signal direct modulation leads to these turn-on delay times τ
D and t on
in the stochastic and deterministic regimes respectively.
The turn-on delay τ
D is defined as the time between the application of an ideal step current and the lasing threshold [4] and can be determined from the carrier equation (Eq. 1). According to Joyce and Dixon [5], we can express the turn-on delay τ
D as follows (when the OFF state is slightly below the threshold) :
τ
D
= τ ' e
⋅
I
ON
I
ON
− I
OFF (3)
− I
TH where τ ' e
= ( A + 2 B ⋅ N )
− 1 is defined as the differential lifetime, assumed to be constant in the entire range of integration and equal to its threshold value: τ ' e
= ( A + 2 B ⋅ N th
)
− 1 . When the bias level is far below threshold, the expression of the turn-on delay in (3) becomes, without the approximation in [5]:
τ
D
= τ e
⋅
I
ON
I
ON
− I
OFF (4)
− I
TH
Modulating the laser under pseudorandom bit sequences leads to fluctuations of this delay τ
D due to bit-pattern effect, represented by the crossing time t c
. The statistics of the turn-on delay time τ
D
allow the derivation of the turn-on jitter.
Previous studies [6] have led to the expression of the probability density function (PDF) of the turn-on delay t c is the data rate:
where D p(t c
) = ln 2 ⋅ B ⋅
τ e
τ
D
⎛
⎜⎜
1 −
τ t c
D
⎞
⎟⎟ ln 2 ⋅ D ⋅ τ e
− 1
(5)
Considering the two orthogonal polarizations that both contribute to the emitted VCSEL light, the PDF of the rise time t on
= t d
− t c
can be derived from the photon rate equation (Eq. 2) [7-8]: p ( t on
) = 4 ⋅ ω 2
R
⋅
P
P
2 on
2 off
⋅ t on
⋅ exp[ − ( ω
R
⋅ t on
) 2 ] ⋅ exp
⎡
⎢ − 2 ⋅
P
P on off
⋅ exp
⎛
⎜⎜
− ( ω
R
2
⋅ t on
) 2 ⎞
⎟⎟
⎤
⎥
(6) where P off represents the mean value of the photon number at the turn-on delay t c
and f
R
the resonance frequency at the ON state. The jitter is defined as the standard deviation of the PDF. Since those two processes are not correlated, the
PDF accounting for both bit pattern effect and spontaneous emission is obtained by the convolution of expressions (5) and (6), leading to : p ( t d
) =
τ
D
0 p ( t c
) ⋅ p ( t on
) ⋅ dt c
(7)
The model described above was implemented in Matlab and is presented in the following section.

In order to study the VCSEL behavior investigate the impact of the spontaneous emission and the bit pattern, but also data rates. We implement the model to a
850nm VCSEL with current threshold I
Fig. 3(a) shows the turn-on delay bit-pattern effect in function of I further jitter; this contribution corresponds to the summati from I levels separating the OFF level to the threshold. off
smaller than I
4.
TURN-ON DELAY AND during the turn-on event, different co th
=0.85mA. off
τ
D as a function of the ON and OFF states. In Fig. 3(b) is depicted the jitter induced by
, showing a minimum slightly below threshold. The transit across threshold causes th
. Jitter is increased because of the pattern ge
JITTER SIMULATIONS on of the jitters for each current level during the transition nerator used for VCSEL
10
700
600 t? 500 a
' 400
0 aoo
2 200
100
2O
.
.
IS
0.2
• Without Joyce and Dixon Approx.
---- A With Joyce and Dixon Approx.
•
-
-
• -A-
A
A
[
•
0.8
0.4
'OFF"TH
0.6
(a)
.
.
.
-4nditions of modulation are applied to modulation from current
τ
D for I
ON
=12*I
0-S
'OFF"TH
TH
(b)
, (b) Jitter due to bit pattern effects for I
1.5
Fig. 3. (a) Turn-on delay
ON
=12*I
TH

The standard deviation of the PDF expressed in (Eq. 5) gi seen in Fig. 4(a). Further studies of VCSEL’s behavior versus OFF levels have been realized in Fig. 4(b). Evaluation of the jitter performances allows prediction of their degradation.
Fig. 4. (a) Jitter due to spontaneous emission,
In order to verify the results of the turn-on delay estimation modelling, the same laser was examined, through a test setup presented in Fig. 5. The laser was modulated, via the
Random Bit Sequence) at 1.25Gb/s, from OFF levels und bias and modulation currents were adjust peak voltages.
Several testing of the VCSEL response were achieved at the three points: at the output, after 100m of an avionic standardized multimode fibre (MMF) and at the photodiode module. These three outputs were supplied to the oscilloscope.
60
+ t 40
U
S 30
+
+
+
+
+
(a)
'ON"TH
000
400
300
200
800
700
600
100
*
'ON"TH
(b) Total Jitter in function of ON level for I
(b) ves the turn-on jitter due to spontaneous emission as can be
5.
MEASUREMENT RESULTS ed. The SQA was also used to drive the
Anritsu SQA (Signal Quality Analyser) by a PRBS (Pseudo er the threshold to ON level set to be equal to I laser by setting the offset and peak-to-
OFF
=0.85*I
TH
ON
=10mA. The

Anritou QSA MPI010
setup and evaluate the turn-on delay,
AIOxVCSEL
X=S5Onm
10Dm 62.5/125pm MMF
Photodiode
Tektronix CIA 74044
Fig. 5. Test setup bias-free and biased optical pulses are
On Fig. 6, the turn-on delay measurements are displayed, determined by a comparative method [9-10]. In order to eliminate the delay time of the electrical compared. The optical sampling scope allows comparing bias-free modulation with biased modulation.
On Fig. 7-8 respectively, the eye diagra
(GbE) is made possible by displaying the eye mask for th operation, the requirement is met, even with zero bias VCSEL modulation.
• 100m link eye diagrams
Fig. 7. 100m-link optical eye diagram: VCSEL m
600
- 400
2 200
00
Fig. 6. VCSEL characteri m measurements are displayed, and comp
0.5
'OFF"Th zation: (a) Turn-on delay ese requirements [1]. One can
1.5
arison with the IEEE Gigabit Ethernet
note that for the system
— odulated (a) without bias flrU& rm nu
—
(b) above threshold

• Complete link performances
Fig. 8. 100m-link eye electrical diagram: VCSEL modulated (a) without bias (b) above threshold
6.
CONCLUSION AND PERSPECTIVES
On the basis of rate equations and with some approximations, the model of the dynamic response of VCSEL under subthreshold bias conditions was proposed. The model allows an estimation of the laser turn-on delay for different OFF current levels, below the threshold. This was possible with the intrinsic parameters available.
The link performances were also tested, by displaying the eye diagrams, and comparing them with the IEEE GbE standard mask. The presented model may be useful to the design process and evaluation of high speed performances of short haul MMF link, for avionic datacoms.
To complete the approach, a large signal equivalent circuit model of VCSEL can be determined and used to describe the laser dynamics [11]. Also, the reliability of the complete link over the temperature range and the under the vibrations strains will be tested. To be adequate with real conditions of operation, the impact of the production breaks will determine the validity of the solution for application to avionics system.
REFERENCES
1 IEEE 802.3 Standard, section Three, clause 38 (2002).
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6
Phys.
, vol. 50, no. 7, pp. 4591-4595 (1979).
D.M. Cutrer, K.Y. Lau, "Ultralow power optical interconnect with zero-biased, ultralow threshold laser-how low a threshold is low enough?" IEEE Photonics Technology Letters, vol. 7, pp. 4-6 (Jan 1995).
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9
R.S.Tucker, "High-speed modulation of semiconductor lasers", IEEE J. Lightwave Technol., 3, 1180-1192 (1985).
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10 D. Wiedenmann, R. King, C. Jung, R. Jager, R. Michalzik, “Design and Analysis of Single-Mode Oxidized
VCSEL’s for High-Speed Optical Interconnects”, IEEE J. of Selected Topics in Quantum Electronics, Vol. 5, no. 3, pp.
503-511 (May/June 1999)
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