Comparing EME and FDTD: Tapers
Examine the benefits of EME for taper 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 for creating tapers such as elevator couplers, fiber to chip couplers, and more.
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.
EME
Small Number of Modes
EME simulations scale with the number of modes needed to accuratly describe the field within a waveguide. Since tapers are often designed to be adiabatic (coupling fundamental mode to fundamental mode) they require very few modes in their basis set to describe the field.
Length Invariant Simulation Speed
EME is length invariant in its simulations. A 10 um taper simulates in the same amount of time as a 20um taper which simulates in the same time as a 100um taper. In fact, once EME software FIMMPROP has simulated a taper once, it can reuse modes that it has calculated to provide results for that taper at any length.
Tip: FIMMPROP uses this to produce fast parameter sweeps of taper length that reveal the adiabatic limit of a taper. The same scan in FDTD would require full re-simulation for each length.
[Click here to read application of this for MMI optimisation]
Mode Properties Instantly
EME evaluates the modes at multiple positions along the length of a taper to calculate the device’s scattering matrix. This allows FIMMPROP to provide the evolution of all the mode’s properties varying with length easily.
Graphing the mode powers and eigenvalues as a function of taper length shows the skilled engineer areas where tapering must be more gradual and where tapering can be more rapid. Extracting such a result from FDTD would be cumbersome at best.
Left: Mode power of first 5 modes along taper length.
Right: Eigenvalues of first 5 modes along taper length.
Both for an initial 6um design.
- Mode power stays in mode 1 (blue) at the start of the taper - tapering could be done more rapidly here.
- Mode anticrossings are key areas where cross coupling occurs - more gradual tapering required just after the midpoint of the taper length.
+ 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 much faster than uniform steps.
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). This means FDTD simulations scale quadratically with length. Changing the length of a simulation in FDTD requires complete re-simulation.
FDTD simulation results show how the field evolves over time through the taper; the end result is the output field (as a spectral response). Unless non-linearity is involved, the dynamics offer no immediate benefit though a spectral response could prove beneficial if multi-wavelength characteristics are of importance.