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Optical Ring Resonator

3D simulation with FIMMWAVE and FIMMPROP software

An optical ring resonator made in silicon on insulator waveguides (SOI) was entirely simulated with the Photon Design mode solver FIMMWAVE and its 3D propagation tool FIMMPROP. FIMMPROP was used to model the coupling region and the FIMMWAVE bend solvers were used to calculate the properties of the bend modes in the ring. The spectral response of the device was then calculated analytically.

Simulation of the optical ring coupler
Calculation of the bend modes in the ring
Calculation of the transmission spectrum
Further simulations: full ring and multiple ring modelling

Schematic view of the ring resonator
Schematic view of the ring resonator

1. Simulation of the optical ring coupler

FIMMPROP, our optical propagation tool based on Eigenmode Expansion (EME), can simulate the coupling regions of ring resonator filters very efficiently and with very good accuracy thanks to its taper algorithm, even for large ring diameters that cannot be solved with the FDTD method. EME allows to solve the structure in terms of local modes, which is a very efficient way to simulate optical coupling.

Intensity profile for the ring coupling
Intensity profile in the ring coupler when the fundamental TM-like mode is launched in the ring.

FIMMPROP is a very efficient method for modelling such structures:

  • The calculation is extremely fast: the coupling coefficients for a 3D 50um-radius SOI ring coupler were calculated in just a few minutes on a 4-core computer with an accuracy of the order of 0.01%.

  • FIMMPROP is able to take advantage of the symmetries of the structure:

    • symmetry with respect to the central XY plane along the z-axis: the second half of the coupler is calculated by "z-flipping" the results of the first half, which reduces calculation time by 50%

    • vertical symmetry within the waveguide cross-sections, which reduces the calculation time by a further 30%.

  • In FIMMPROP, all the inputs are simulated at once. This means that the problem will be solved simultaneously for both the TE-like and TM-like polarisations.

  • The input and output sections in FIMMPROP can be used to launch the input power and measure the output power in the bend mode of the ring in a fully automated way, thanks to the bend modes capabilities of FIMMWAVE.

 Taking advantage of symmetries


Design parameters:

  • Materials: silicon cores, silica cladding
  • Ring diameter: 100um
  • Width of waveguides: 0.5um, thickness of waveguides: 0.5um
  • Gap: 100nm

The design of a ring resonator in FIMMPROP can be performed easily with dedicated pre-defined components. The different parts of the device can be set to materials, allowing FIMMPROP to take dispersion effects into account when working at different wavelengths.

Ring Resonator Coupler shown in FIMMPROP

View of the ring resonator coupler in FIMMPROP, with a plot of the refractive index profile and a set of local modes for one of the cross-sections. In the main window you can see the input and output sections with the ports in yellow.


Simulation parameters:

  • Simulation wavelength: 1500nm
  • Size of the computational domain: width: 3um, height: 1.5um, length: 15um
  • Number of local modes: 20
  • Local modes solved with the FDM Solver, grid size for the cross-section: 25nm

Coupling coefficients

FIMMPROP calculated the scattering matrix of the structure using its taper algorithm. An estimated accuracy of 0.01% was obtained to calculate the coupling coefficient for the TE-like mode. The results are given below.

Coupling coefficient TE-like mode 7.51% +/- 0.01%
Coupling coefficient TM-like mode 37.5% +/- 0.4%

Mode coupling analysis

FIMMPROP can plot the evolution of the effective indices of the local modes along the device, as shown below for the first four modes of the structures. At the beginning of the device, when the ring is far from the straight waveguide, the modes are decoupled. The modes of the straight section have constant effective indices, as can be seen below (green and bright blue lines). When the waveguides get closer, the modes become coupled. The variations between z = 5um and 15um illustrate the effect of the coupling region on the effective indices.

Evolution of effective indices of local modes along coupling region
Effective indices of the local modes of the ring resonator plotted against z.
At z = 0, the blue lines correspond to modes in the ring (note: the bend modes are strictly speaking solutions of a different eigensystem), the yellow and orange lines to the modes in the straight waveguides.

Calculation of uncertainty and accuracy optimisation

FIMMPROP allows you to calculate how much power is lost from the simulation along the device, allowing to estimate the uncertainty on the results and to optimise the resolution needed to obtain convergent results.

Power loss along the device
Evolution of power loss with resolution of the FDM Solver
for the fundamental TE-like mode launched from the straight waveguide

2. Calculation of the bend modes in the ring

The bend modes in the ring were calculated using the FDM Solver in FIMMWAVE. The FDM Bend Solver allows you to calculate bend modes. In this case the bend modes had already been calculated in order to launch the correct bend mode in the FIMMPROP ring coupler simulation.

TM-like mode
Effective index at 1.5um 2.96478
Group index at 1.5um 4.0906
TE-like mode
Effective index at 1.5um 2.96468
Group index at 1.5um 4.0902

Thanks to the high confinement and the large radius, the losses in the ring were found to be negligible.

Bend mode in the ring
Fundamental TM-like bend mode in the ring

3. Calculation of the transmission spectrum

Using the results provided by FIMMWAVE and FIMMPROP, the transmission spectrum of the ring coupler was calculated analytically using:

where t is the transmission coefficient of the coupling region in amplitude, R is the radius of the ring, neff is the effective index, Ng is the group index, Φ is the phase shift in the loop and λ is the wavelength. The reference values were taken at 1.5um. 

The results are plotted below: 

Transmission spectrum for the ring resonator
Transmission spectrum of the ring coupler

You can very easily obtain a high resolution spectrum around a resonance peak:

Transmission spectrum for the ring resonator
Transmission spectrum of the ring coupler around a resonance

4. Further simulations: full ring and multiple ring modelling

FIMMPROP can also be used in conjunction with PICWave to calculate highly accurate transmission spectra for advanced geometries of ring resonators including multiple rings.

5. References

Examples of ring resonator modelling using FIMMPROP have been presented at the ECIO 2010 conference in Cambridge, UK.