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Modelling of active photonic integrated circuits using PicWave

Modelling of active photonic integrated circuits using PicWave. Dominic F.G. Gallagher. Outline. Requirements for a PIC simulator Dividing the problem Modelling passive components using EME The circuit simulator Examples. PIC Elements. passive elements. Fibre I/O. SOA / EAM. TFF.

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Modelling of active photonic integrated circuits using PicWave

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  1. Modelling of active photonic integrated circuits using PicWave Dominic F.G. Gallagher

  2. Outline • Requirements for a PIC simulator • Dividing the problem • Modelling passive components using EME • The circuit simulator • Examples

  3. PIC Elements passive elements Fibre I/O SOA / EAM TFF Feedback loop Bragg reflector

  4. 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

  5. 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!

  6. Modelling Strategy Active PIC Quantum Well Gain Maxwell Solver for Model for active passive element elements analysis Gain FIR Filter Fitting Generator TDTW Algorithm (PICWave) Post-processing – spectral analysis etc

  7. TDTW: Travelling Wave Time Domain Method Segmentation of a Device dz=vg.dt Z-element dz section section Interface losses distributed feedback lateral segmentation into “cells” external injection

  8. TDTW: Advection Equations A Consider forward and backward fields. B Remove fast term exp(jw0t +/- jb0z) , giving: grating feedback gain detuning spontaneous emission

  9. A TDTW path network representing a PIC scattering matrix defines coupling at junctions Propagate just mode amplitudes

  10. Two distinct types of section... TE00-mode TM00-mode Straight waveguide transmitting TE00 and TM00 modes TE00-mode Cross-coupling between Y-junction coupling two TE00 modes – waveguides one from each arm, into a TE00 and TE01 mode modes

  11. 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

  12. TE00-mode TE00-mode TM00-mode TM00-mode Multi-mode Model Directional Coupler supporting both TE00 and TM00 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

  13. Example - Polarisation-dependent MZI 150um length TE in TM in 100um length

  14. re-write advection equations in matrix form: detuning from Bragg frequency grating feedback noise sources (spontaneous emission) gain/loss term

  15. Matrix coefficients: Index, gain and loss grating effects determined by relationship between KAB and KBA.:

  16. Spontaneous emission Random number with inverse normal distribution Spontaneous coupling factor (geometric only - i.e. due to N.A of waveguide) carrier density spontaneous recombination lifetime • in - uncorrolated in time -> white noise source • in - uncorrolated in space - assume sampling interval dz is much longer than diffusion length.

  17. IIR Gain Filter A(t) B(t) IIR Filter Lorentzian wavelength response: Pseudo-Lorentzian response:

  18. Lorenzian approximation of actual gain spectrum

  19. Harold/PICWave Interaction increase Ne gain spectra gpk(N) g2 (N) lpk (N) tspon ... Harold Curve Fitting solve heterostructure problem • solve heterostructure just a few times at start of simulation. • maintain speed of PicWave • out-of-bound detectors ensure simulation stays within fit range. PICWave

  20. Multi-Lorentzian Model

  21. Multi-Lorentzian Model – Original vs Fitted Spectra increasing Ne fitted spectra free spectral range original spectra

  22. Carrier Rate Equation For one z-element we have: photon number for z-element carrier density current density noise term carrier volume photon generation rate (measure this from inspection of gain filter output) assume quantum conservation DN=-DP

  23. 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.

  24. 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

  25. EME (FIMMPROP)/PICWave Interaction S-parameter spectra FIMMPROP FIR filter generation Compute lambda-dependent scattering matrix using rigorous Maxwell solver • Rigorous analysis of waveguide components - tapers, y-junction, MMI etc done in FIMMPROP. • PICWave generates an FIR (time domain) filter corresponding to the s-parameter spectra. PICWave

  26. + 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) FIR Filter b(t) a2(t) FIR Filter

  27. 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

  28. FIR Filter Response - Bragg Reflector FIR response original response Simple FIR filter works poorly - s(Df) is not periodic in FSR of TDTW

  29. FIR Filter Response - Bragg Reflector Force s(Df) to be periodic between -1/2dt to +1/2dt FIR response original response

  30. Modelling a 60um diameter ring resonator

  31. Resonator - response

  32. 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

  33. Optical 2R Regenerator Both passive and active elements - highly non-linear

  34. Optical 2R Regenerator 2GB/s NRZ bit pattern - optical input Input: 5:1 on/off Output: 25:1 on/off Gain: 25x But: noise

  35. The Sampled Grating DBR Laser

  36. 4 Section SG-DBR - vary current in Grating A & B together

  37. 4 Section SG-DBR - vary Grating A & B current and tuning current

  38. Optical 2R Regenerator Transverse Carrier Density Start of SOA 3900 A/cm2 End of SOA 4900 A/cm2 => Can take account of lots of physics if designed carefully

  39. 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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