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Large optical ring resonators

Simulation with PICWave software based on a FIMMPROP component model

PICWave can easily and efficiently model ring resonators of 100's um diameter. The algorithm is many orders of magnitude more efficient than e.g. FDTD for this application, computing a triple 200um diameter ring resonator down to a wavelength resolution of 50MHz and spectral range of 50nm in just a couple of minutes.

The result shown in the picture below shows a case of a 60um diameter ring resonator; PICWave yielded a result in a few seconds, while OmniSim-FDTD needed 14 hours.

A large ring resonator simulated in PICWave

Simulation of a large ring resonator in PICWave:
circuit designed in the PICWave layout, geometric equivalent and resulting spectra

The difference is even bigger for larger ring resonators. The reason is that PICWave can use a large time step, and so can handle simulation durations in the range of several ns, yielding spectral resolutions finer than 1GHz. In fact, MHz resolutions are attainable. This kind of resolutions is important in the case of large ring resonators.

Even the accuracy obtained is better. As you can see from the graph, PICWave agreement with the theoretical solution is remarkable, and calculated in a few seconds.  

Modelling with FIMMPROP  

In this example we demonstrate how the FIMMPROP-PICWave link can be used when modelling a ring-resonator in PICWave.  

As illustrated below, the structure can be divided into the parts than can be modelled using built-in PICWave circuit elements – the ring (assuming no losses) and straight waveguides; and those which require detailed modelling with an EM solver i.e. FIMMPROP: the coupling regions. 

Schematic view of the structure

Schematic showing the circuit to be modelled by PICWave;
the coupling regions will be modelled using frequency-domain results imported from a rigorous FIMMPROP simulation

The majority of ring resonator circuit is therefore constructed from built-in PICWave elements, apart from the coupling regions which are modelled using FIR sections. Via the PICWave-FIMMPROP link interface, the FIR sections can store FIMMPROP models of the coupling regions internally, and their scattering matrix spectra (coupling vs. wavelength) can be computed automatically via a TCP/IP connection with FIMMPROP.  

Schematic view of the structure

Ring resonator circuit in PICWave: coupling regions are modelled with FIR sections,
each containing a FIMMPROP model from which a scattering matrix spectrum can be computed
via TCP/IP connection with FIMMPROP; PICWave waveguide sections are sufficient to model the rest of the circuit.

The FIR sections use the imported spectrum to generate an equivalent time-domain filter, which gives the time-domain response of the coupling regions. The figure below displays the imported scattering matrix spectrum and the corresponding FIR filter frequency-domain response, showing close agreement between the two. 

FIR Filter

FIR filter response: (left) imported scattering matrix spectrum for the coupling region showing
the amplitude (blue) and phase (green) of the transmission from port 1 to port 4;
(right) corresponding wavelength response (amplitude only) of one of the FIR sections
modelling a coupling region, showing close agreement with imported scattering matrix spectrum.

The circuit was then simulated in the time-domain, and optical impulse signal with a flat spectrum was injected into the ring resonator and the response was measured. The effects of the modelled wavelength response of the coupling regions can be seen in the spectral results yielded by a time-domain simulation of the ring resonator. 

Transmission spectrum

Transmission spectrum of ring resonator from PICWave simulation: height of transmission peaks varies with wavelength in accordance with the wavelength response of the coupling regions – modelled using results imported from FIMMPROP