Transcript No Slide Title

Dominic F.G. Gallagher
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Outline
• Requirements for a PIC simulator
• Dividing the problem
• Modelling passive components using EME
• The circuit simulator
• Examples
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PIC Elements
passive
elements
Fibre I/O
SOA / EAM
TFF
Feedback
loop
Bragg reflector
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Laser Geometries
Fabry Perot laser
Ring cavity laser
f
DFB Laser
Tuneable DFB
External Cavity laser with FBG
Sampled Grating Tuneable Laser
Branched Tuneable Laser
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Requirements for a PIC Simulator
• Must be able to model passive elements correctly tapers, y-junctions, MMIs, AWGs
• Capable of modelling active elements correctly - SOAs,
modulators, laser diodes
• Hybrids
• Capable of modelling reflections - bidirectional
• Capable of retaining any physical processes that
interact - e.g. effect of diffusion on dynamics
• Capable of computing time response
• Capable of multi-wavelength modelling
• All of this must be able to scale to large circuits!
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Modelling Strategy
Active PIC
Quantum Well Gain
Model for active
elements
Maxwell Solver for
passive element
analysis
Gain
Fitting
FIR Filter
Generator
TDTW Algorithm
(PICWave)
Post-processing –
spectral analysis etc
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TDTW: Travelling Wave Time Domain Method
Segmentation of a Device
Z-element
dz=vg.dt
dz
section
section
Interface losses
distributed feedback
lateral segmentation into “cells”
external injection
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TDTW: Advection Equations
A
Consider forward and
backward fields.
B
Remove fast term exp(jw0t +/- jb0z) , giving:
1 A A

 j. .B  ( g  j. ) A  FA ( N e )
v g t z
1 B B

 j. . A  ( g  j. ) B  FB ( N e )
v g t z
grating feedback
gain
detuning
spontaneous
emission
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A TDTW path network
representing a PIC
scattering matrix defines coupling at junctions
Propagate just mode amplitudes
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Two distinct types of section...
TE00-mode
TM00-mode
Straight waveguide transmitting TE00
and TM00 modes
TE00-mode
Y-junction coupling two TE00 modes –
one from each arm, into a TE00 and
TE01 mode modes
Cross-coupling
between
waveguides
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Multi-mode Model
mode1
mode2
mode3
mode4
Mode5
• The TDTW engine can now propagate multiple modes, eg of different
polarisation.
• Independent phase index and mode loss for each mode
• For now, group index is same for each mode - changing group index
requires different segmentation since vg = dz / dt
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Multi-mode Model
TE00-mode
TM00-mode
Directional Coupler
supporting both TE00 and TM00
TE00-mode
TM00-mode
TDTW Model of coupler
• Polarisation-dependent directional coupler model implemented
• Independent phase index, group index and mode loss for each
polarisation
• Coupling defined as dAtm/dz = kappa.Ate - constant along length
• Coupling between polarisations ignored in this version
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Example - Polarisationdependent MZI
150um length
TE in
TM in
100um length
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re-write advection equations in matrix form:
 m11 m12   A( z, t )   FP ,a 
 A( z  z, t  t )




 B( z, t  t )   expg  j. .z  m

F
m
B
(
z


z
,
t
)


  P ,b 
22  
 21
detuning from
Bragg frequency
gain/loss
term
grating feedback
noise sources
(spontaneous
emission)
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Matrix coefficients:
m12   BA  z
m21   AB  z
m11  1  m12 m12*
m22  1  m21m
*
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Index, gain and loss grating effects
determined by relationship between KAB
and KBA.:
 AB   r   l   g*
 BA   r*   l*   g
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Spontaneous emission
N e b NA
FP  h 

 t  in (t , z )
r 2
Random number with inverse
normal distribution
spontaneous recombination
lifetime
carrier density
Spontaneous coupling factor
(geometric only - i.e. due to N.A
of waveguide)
• in - uncorrolated in time -> white noise source
• in - uncorrolated in space - assume sampling
interval dz is much longer than diffusion length.
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IIR Gain Filter
A(t)
B(t)
IIR Filter
Lorentzian wavelength
response:
Pseudo-Lorentzian response:
g (w )  g (w0 ) / 1   2 w  w0 
1

cos2  w M 
2

g (w )  g (w0 )
1

1

cos2  w M   K 2 sin 2  wM 
2

2

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Lorenzian approximation of actual gain spectrum
Lorenzian gain
filter response
Material gain
photon energy
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Harold/PICWave Interaction
increase Ne
gain spectra
Harold
Curve Fitting
solve
heterostructure
problem
• solve heterostructure just a few
times at start of simulation.
gpk(N)
g2 (N)
lpk (N)
spon
...
PICWave
• maintain speed of PicWave
• out-of-bound detectors ensure
simulation stays within fit range.
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Multi-Lorentzian Model
IIR-1
IIR-2
+
1000
gain (a.u)
(a.u.)
gain
800
800
IIR-3
z-element
Lorentzian-2
600
600
400
measured
Lorentzian-1
Lorentzian-3
-0.5
-0.4
-0.3
fitted
400
200
-0.2
0
200
-0.1
0
0.1
0.2
0.3
0.4
0.5
-0.1 -400 0
0.1
0.2
0.3
0.4
0.5
-200
0
-0.5
-0.4
-0.3
fitted
-0.2
-200
-600
Lorentzian-4
measured
Lorentzian-1
-800
-400
Frequency
offset/FSR
Frequency
offset/FSR
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Multi-Lorentzian Model – Original vs Fitted Spectra
increasing Ne
fitted spectra
free spectral range
original spectra
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Carrier Rate Equation
For one z-element we have:
photon number for z-element
carrier density
dNe
1 dP#

dt
VN dt
current density
Ne
J


 FN
 s ( N e ) qe .d
stim
noise term
carrier volume
assume quantum
conservation DN=-DP
photon generation rate
(measure this from inspection
of gain filter output)
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Extension to 3D
In TDTW method, extension to include lateral carrier profile Ne(x,y) is simple.
Instead of 1 carrier density in each z-element we have nx.ny discrete densities.
contacts
current flows
computation cells
lateral diffusion
Active layers
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Integration with Frequency Domain Models
TDTW cannot predict e.g. the scattering loss of a y-junction this must be computed with a more rigorous EM solver.
Two main choices:
•BPM - beam propagation method
•EME - eigenmode expansion
For circuit modelling EME is better:
• Bidirectional - takes account of all reflections
• Scattering matrix - integrates well with circuit model
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EME (FIMMPROP)/PICWave
Interaction
S-parameter
spectra
FIMMPROP
Compute
lambdadependent
scattering matrix
using rigorous
Maxwell solver
FIR filter
generation
• Rigorous analysis of waveguide
components - tapers, y-junction,
MMI etc done in FIMMPROP.
PICWave
• PICWave generates an FIR (time
domain) filter corresponding to the
s-parameter spectra.
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Importing EME Results into Circuit Model
EME is a frequency domain method
TDTW is time domain
- must convert
Use FIR filter (finite impulse response)
a1(t)
a2(t)
FIR Filter
+
FIR Filter
b(t)
N
b jp [it ]   ck ,ip, jp aip [it  k ]
ip k 1
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FIR Filter Response Bragg Reflector
1. Input s(w) from EME
2. Compute FIR filter coefficients
3. Launch impulse into filter
4. Measure impulse response function FFT -> spectrum
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FIR Filter Response Bragg Reflector
FIR response
original response
Simple FIR filter works poorly - s(Df)
is not periodic in FSR of TDTW
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FIR Filter Response Bragg Reflector
Force s(Df) to be periodic between
-1/2dt to +1/2dt
FIR response
original response
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Modelling a 60um diameter
ring resonator
Drop
Couplers
modelled by
EM solver.
Transmission
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Resonator - response
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Ring Resonator
FDTD time:
14 hrs on a 3GHz P4 - 2D only! (Using Q-calculator)
Circuit simulator:
modelling the coupler (EME): few mins
running circuit model (TDTW): few secs
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Optical 2R Regenerator
data l2
A
C
control l1
SOA
B
data out l2
D
SOA
Both passive and active elements - highly non-linear
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Optical 2R Regenerator
2GB/s NRZ bit pattern - optical input
Input: 5:1 on/off
Output: 25:1 on/off
Gain: 25x
But: noise
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The Sampled Grating DBR Laser
Grating A
Gain
Section
Phase
Section
Grating B
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4 Section SG-DBR - vary current in Grating A & B together
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4 Section SG-DBR - vary Grating A & B current and tuning current
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Optical 2R Regenerator
Transverse Carrier Density
Start of SOA 3900 A/cm2
3.5
carrier density ( x1e18/cm3)
3
2.5
End of SOA 4900 A/cm2
2
1.5
1
0.5
0
0
2
4
6
lateral position (um )
8
10
=> Can take account
of lots of physics if
designed carefully
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Conclusions
• presented strategies for modelling large circuits
including both active and passive elements
• TDTW can be easily coupled with Maxwell Solvers
using FIR filters
• Can create very high speed algorithm while maintaining
a lot of physics if system is designed carefully
• Have developed a product PICWave to implement this
circuit simulator
• EME ideal method for integration with circuit model
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