Modeling Free Space Optical Systems

Modeling Free Space Optical Systems
• Steven P. Levitan
• Timothy P. Kurzweg
• Jose A. Martinez
• Donald M. Chiarulli
University of Pittsburgh
• Philippe J. Marchand
• Lee Hendrick
• Xuezhe Zheng
University of California San
Diego
Funding DARPA: F30602-97-2-0122 / NSF: ECS 96-16879
Chatoyant - Goals & Methods
Chatoyant Design Environment
Electronics
Devices and
Circuits
Optics Packaging Mechanical
Tolerancing
Functional level
(VHDL)
Logic level
(GateSim)
Gate level
(Spice)
Optoelectronic System level O/E CAD tool to:
Analytical
Models
Physical Models
(Experimental
Data fitting)
Image Formation
Gaussian Beam
Propagation
Ray Tracing
(CodeV,Zemax)
Diffraction Analysis
(Diffract)
Area, Volume
Weight, Cost
Auto-CAD
Light Tools
• Develop 1st order analytical,
empirical, and lumpedparameter
models for
optoelectronic components
• Develop a hierarchical &
modular software environment
using Ptolemy engine
Misalignment
1st order
thermal
Finite
Element
Analysis
VCSEL Output - 300M Hz
Y
14.0
12.0
10.0
8.0
6.0
4.0
2.0
X x 10-9
0.0 10.0 20.0 30.0 40.0
• Predict performance
• Analyze technology vs.
architecture trade-offs
- Without costly prototyping
Y
5.0
4.0
3.0
2.0
Detector Output - 300M Hz
1.0
X x 10-9
0.0 10.0 20.0 30.0 40.0
Eye Diagram - 300MHz
Y
5.0
4.0
3.0
2.0
1.0
X x 10-9
0.0 0.5 1.0 1.5 2.0 2.5 3.0

Models of Optical/Electronic
Signals
• Messages are arrays of O/E signals
• Piece-wise linear Intensity or Voltage
• Gaussian shape, angle, position, wavelength,
polarization
• Source impedance
• Variable time step (Δt)
– discrete, continuous, PWL
Lumped parameter models
Quantum Optics
Electromagnetic Optics
Wave Optics
Gaussian Beams
Ray Optics
B.E.A. Saleh and M. Teich, Fundamentals of Photonics, Wiley, 1991
• Analytic models
– Physics based
• Empirical models
– Experimental data
fitting
• Derived models
Models of Components
Driver
ΔP
– Parametric models
extracted from or verified
by lower level tools
⎡ 2
⎡ W ⎤ 2 ⎤
( , ) = 0
r
I
r z I0
⎢ ⎥ exp⎢−
⎥
⎣W
( z)
2
⎦ ⎣ W ( z)
⎦
V
Pin
Pout
16
14
2.5V
12
10
8
4V
6
4
2
0
0 5 10 15 20 25 30 35 40 45 50
Input Power(mW)
Output Power(mW)
ηLI
/ V
P th
out =
( Pin
− IthVth
)
( 1−η
LI / Vth)
Vdd
2
Stage1
a b
R f
V0( s)
= ⋅ Poptic
( s)
⎛ R f C ⎞
1+
⎜ ⎟s
⎝ A ⎠

Piecewise Linear Model for Time
• Motivation:
– Modeling dynamic response
is necessary.
• Problem:
– Small signal model analysis
is invalid
• Solution:
– Use a mixture of analytic and
lumped-parameter models
– CMOS Large Signal Models
• Advantages:
– Dynamic time resolution
achieves high accuracy at
low computation cost
– Homogeneous simulation
environment
Input Stage 1 Output Stage 2 Output
High frequency response in Chatoyant
for a cascade driver configuration (f =
600 MHz & C ld = 1fF).
Electrical Drivers (Tests)
f= 10 MHz C=3.774ff f= 100 MHz C=3.774ff f= 1 GHz C=3.774ff
Spice Level 2 Model I Model II Spice Level 2 Model I Model II Spice Level 2 Model I Model II
Speed
Time 0.13 0.093 0.15 0.12 0.089 0.091 0.12 0.094 0.089
Iterations 307 100 200 313 100 100 300 100 100
Accuracy 0 9.1%/18.8 SD 1.8%/4.7 SD 0 3.4%/6.8 SD 3.3%/6.7 SD 0 10%/12.9SD 9.99%/13.8SD
6
5
4
3
2
1
f=10 MHz C=3.774 ff
0
0.00E+00
-1
5.00E-08 1.00E-07 1.50E-07 2.00E-07 2.50E-07 3.00E-07 3.50E-07 4.00E-07 4.50E-07
6
5
4
3
2
1
Time (secs)
f=1 GHz C=3.774 ff
0
0.0E+00 5.0E-10 1.0E-09 1.5E-09 2.0E-09 2.5E-09 3.0E-09 3.5E-09 4.0E-09 4.5E-09
-1
Time (secs)
Vout Model II
Vin
Vout Spice (Model II)
Vout Model II
Vin
Vout Spice (Model II)
6
5
4
3
2
1
-1
f=100 MHz C=3.774 ff
0
0.0E+00 5.0E-09 1.0E-08 1.5E-08 2.0E-08 2.5E-08 3.0E-08 3.5E-08 4.0E-08 4.5E-08
Time (secs)
Vout Model II
Vin
Vout Spice (Model II)
The times for the models include the
computational load of the whole system
(Chatoyant Implementation).

Static Simulation of Gaussian
Beam Propagation
Gaussian Beam propagation
Dynamic Simulation:
Detector Response
Gaussian Beams On Detector Array
Detector Output Eye Diagram

BER
1.00E-04
1.00E-05
1.00E-06
1.00E-07
1.00E-08
BER = 10 -9 120ps
BER Modeling
1.00E-09
-400 -300 -200 -100 0 100 200 300 400
Offset from reference Decision Sample Time (ps)
BER
1.00E-03
1.00E-06
1.00E-09
1.00E-12
1.00E-15
1.00E-18
1.5 2.5 3.5 4.5 5.5 6.5
Recieved Photocurrent (uA)
Poptic
C
BER=10 -9
VDD
A
Rf
5.2μA
Vout
Krishnamoorthy, A.V., Woodward, T.K., Goossen, et. al
“Operation of a Single-Ended 550Mbit/s, 41fJ, Hybrid
CMOS/MQW Receiver-transmitter”, Electronic Letters,
April 1996.
System 1: 3D OESP / FFT Demo
Prototype
Digital Logic VCSEL / Detector Array
Sapphire Substrate
Lenslet Array
500μm
13mm
Silicon Microbench
7mm
Electrical Drivers / Amplifiers
7cm
20mm
7mm 13mm
Digital Logic
μBench Assembly
Function: FFT
512x512
32 bits complex
Throughput < 1 msec
Power < 340 W
Volume < 35 cm3 Function: FFT
512x512
32 bits complex
Throughput < 1 msec
Power < 340 W
Volume < 35 cm3

15 Degree Divergence
10 Degree Divergence
5 Degree Divergence
4 10 4
2 10 4
Gaussian Beam
Lenslet
0
6 10
4
4
4 10 4
2 10 4
•At Second Lenslet Plane
•Blue is off-axis clipped beam
•Red is on-axis clipping
•Approximately 40 μm offset
System Analysis with Different
VCSEL Beam Divergence
VCSEL 1 μm Mechanical
Tolerancing - Scalar Analysis
0 2 10 4
Clipped Beam
1
0.5
0
0.5
1 μm
508 μm
250 μm Lens
4 10 1
1
Uint
0.5 0 0.5 1
4
6 10 4
0.4
0.2
4 10
5
5
0
CAN NOT MODEL
NEED SCALAR MODELS…
20 mm
2 10 5
1 μm
40 μm
508 μm
0 2 10 5
4 10 5
Final Intensity Distribution on
the 80mm detector
Intensity Distribution Contour
At 2nd Lenslet Plane

VCSEL source
SDA Movement Decoder
Output Graph
System2: 1x2 Optical MEM
Switch in Chatoyant
Beam Splitter
Delay Element
1st Interferometer
Moveable Plate
2nd Interferometer
Scratch Drive Actuator
Static Result
Mirror
Beam Recombiner
Detector 1
Data Beam
Data Beam
Reference Beam
Detector 2
Switch Control Circuitry
Reference Beam
Reference Beam “Off” Data Beam
“On” Data Beam
Crosstalk
• 56% System Efficiency
• -15.5 dB Crosstalk between neighbors
• With 1.0 Degree Offset, Efficiency Drops to 53.5%,
Crosstalk Climbs to -11.42
Feedback
Circuitry

1200
1000
800
600
400
200
0
Mirror Tolerance = +1.0 Degrees
Monte Carlo Mechanical
Tolerancing
•Each mirror in interferometer has a tolerance range
•No mis-alignment produces a efficiency of 56% Crosstalk
Number of Sam ples
2.8
8.4
14
19.6
25.2
30.8
36.4
42
47.6
53.2
58.8
64.4
System Efficiency
Number of Samples
1000
800
600
400
200
0
One Beam Detected
Mirror Tolerance = +2.5 Degrees
2.8
8.4
14
19.6
25.2
30.8
36.4
42
47.6
53.2
58.8
64.4
Detected Power Efficiency (in %)
1x2 Switch Dynamic Outputs
Switch Selection Reference Beam
Feedback to SDA Mirror Position

1x2 Switch Output
Chatoyant Development
• New O/E Message Class
• Used New domain (DDF) for multi-rate systems
• Multi-platform (SunOS/Linux) support
• Use of TCL/TK Scripts for Monte Carlo Analysis
• VRML 3D Models
• Interfaces to/from low level electronic, optical, thermal &
mechanical tools
• Non-sequential surfaces, multiple time bases, & multiple
energy domains
• Ptolemy II???