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FIMMPROP

Bi-directional optical propagation tool

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FIMMPROP

Comparing EME and FDTD

Choose the right method, save hours on simulations.

EME and FDTD are the industry’s go-to waveguide simulation methods; both as rigorous solutions to Maxwell’s equations. When both methods are applicable and configured correctly there is no reason their result should differ. 

So how to pick which method to use?
This page shows pros and cons of each method through their application in common photonic devices.

Finite Difference Time Domain - FDTD
The FDTD method divides photonic devices with a very fine mesh. Maxwell’s equations are then solved along small steps in space and steps in time to evolve fields through the device.

The more fine the mesh, the more accurately the physics of light propagation is modelled.

Runtime is increased the more mesh points there are (larger bounding volume, finer mesh resolution) or if the designer simulates a larger amount of time.

 

EigenMode Expansion - EME
EME splits photonic devices into multiple cross sections and calculates a set of modes at each cross section; enough modes to act as a basis set to describe the field in that cross section. 

To connect the neighbouring mode lists, a scattering matrix is calculated and the full result is a scattering matrix for the entire device.

EME simulations increase in compute time the more modes that are required to form a basis set, the more cross sections needed to be calculated, and for larger cross sectional areas.

1. Tapers

FDTD

- Tapers can have a large length and FDTD simulation time increases with the bounding volume (and the time it takes for light to propagate through the device).

EME

+ Simulation time scales with the number of cross sections required not with the length; a 10 um length taper simulates in the same time as a 1000 um length taper.

+ Tapers are often designed to be adiabatic (coupling fundamental mode to fundamental mode) therefore require very few modes in their basis set to describe the field.

Taper showing dynamic discretisation - each line shows where a modelist is calculated
Taper showing dynamic discretisation - each line shows where a modelist is calculated

+ Photon Design Tip: To speed up iterative design, FIMMPROP EME will recycle calculations from a previous simulation (mode lists, scattering matrices) for any sections that are unchanged. 
When only a device’s length is changed, all calculations are recycled. This allows for a near instant ‘parameter sweep’, showing a taper’s behaviour at different lengths; quickly finding the adiabatic length.
The same scan in FDTD would require full re-simulation for each length.
[Click here to read application of this for MMI optimisation]

+ Photon Design Tip: FIMMPROP EME discretises ‘Z-varying’ devices like tapers non-uniformly, dynamically adjusting step size depending on variations in the eigenmodes for convergent results faster than uniform steps.   

2. Ring Resonators

FDTD

+ An FDTD simulation will provide a full spectral response with each simulation.

+ The FDTD method has no restrictions to the directions of propagation so the full ring could be simulated.

- Unless the mesh is edited, the full bounding volume of the device is simulated including ‘uninteresting’ space like the center of a ring leading to long simulation times. This makes FDTD mainly applicable for very small rings.

- Resonant frequency simulations may have light confined to the ring for many cycles (high q factor rings) leading to long simulation times.

EME

+ EME is a frequency domain tool so simulates a single wavelength. This allows a fast simulation of important resonant frequencies. 
+ Photon Design Tip: FIMMPROP can use built in scanner to investigate the full spectral response.

- EME must simulate ring coupler region in isolation (as perpendicular propagation directions are prohibitively difficult in EME). 

+ Photon Design Tip: Photon Design’s MT-FIMMPROP allows ring coupler simulations to be natively stitched together to connecting waveguides to also allow full ring resonator simulations.

  • Coupling region simulations can be re-used when repeated [Read More],
  • This allows for symmetrical coupling regions to be simulated twice as quickly.
  • Constant curvature bends and straight sections require just one mode list so are comparatively instant to simulate.
  • Only the computational regions are simulated so bulk regions (like the center of rings) are not simulated.

3. Gratings

EME

- Surface grating couplers require simulation of light propagating in free space which is prohibitively challenging to model with a basis set of bound mounds.

+ Periodic gratings for reflections are efficient in EME as the scattering matrix of a single period can be calculated and re-used for periodic structures.

+ Photon Design Tip: a scanner in FIMMPROP’s EME could near instantly show how many grating periods are needed to find a chosen. 

FDTD

+ No issues simulating surface grating couplers

+ Photon Design Tip: Use our ready made Python script to fully guide the design of a surface grating coupler. [Read More]

- No advantages between simulating periodic and non-period structures

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The many benefits of EME such its fast simulations (and the iterative designing this enables) make it Photon Design’s go-to choice for waveguide devices. Where EME is not applicable and on the occasion where it’s preferable, FDTD can fill in the gaps. These occasions include:

  • When light cannot be described as a basis set of bound modes (surface grating coupler)
  • Where time evolution must be considered (non-linear materials, photonic crystal lasers)