This example represents wavelength conversion based on a SOA integrated with a multi-ring
resonator , which is used as filter capable of efficiently separating unwanted four-wave mixing terms from pump
and probe signals. This hybrid photonic integrated circuit (PIC) comprises both active and passive subelements.
Due to small ring radii, time-domain modeling of the multi-ring resonator requires a huge simulation bandwidth, over
150 THz, which is incompatible with the efficient time-domain modeling of SOAs and other active devices. To solve
this problem, we use time-and-frequency-domain modeling (TFDM), an original approach that improves accuracy, memory requirement
and simulation speed in comparison with traditional pure time-domain methods. In TFDM, clusters
of connected linear PIC elements are modeled in frequency domain, while interconnections between such clusters and
nonpassive PIC elements are modeled in time domain.
The schematic shown in
, illustrates the combination
of time- and frequency-domain models. Probe and pump signals are coupled at a waveguide coupler, which is described by
an FIR filter. The three-ring filter is modeled also by an FIR filter constructed by assembling S-matrices of each ring
coupler. After this precalculation, a time-domain simulation is started. The spectrum after the SOA has several FWM
terms () which are efficiently
attenuated after the microring resonator
Using a pure time-domain modeling approach, to ensure accurate FIR filtering, we need a time step that is at least 16 times
smaller than the minimal group delay. For ring radii of 3 µm, a time step of 6 fs, or, expressed in the simulation bandwidth,
166 THz, is required and thus, an excessive amount of memory and simulation time is needed. Accurate simulations of
this setup with the TFDM approach, however, take less than one minute on an ordinary personal computer by using
a reasonable simulation bandwidth.
Keywords: SMATRIX, Time-and-frequency-domain, SOA, Microring, Four-wave Mixing, FWM, Photonic Integrated Circuits, PICs
Similar demonstrations are available in VPIComponentMaker Photonic Circuits and on the VPIphotonics Forum.
 M. Razaghi, M. Gandomkar, V. Ahmadi, N. Das, and M.J. Connelly, "Numerical analysis of wavelength conversion based on semiconductor optical amplifier integrated with microring resonator notch filter", NUSOD, paper TuA4 (2011).
 S.F. Mingaleev, E. Sokolov, C. Arellano, I. Koltchanov, and A. Richter, "Hybrid time-and-frequency-domain approach for modeling photonic integrated circuits", NUSOD, paper ThA4 (2011)