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Technical Notes
varFDTD in Lumerical MODE treats a 3D waveguide structure as an efficient 2D model, which makes propagation analysis far faster. This article covers how it differs from FDTD, BPM and EME, benchmarks speed against accuracy, and shows where it fits in PIC design.
Lumerical MODE The 2.5D variational FDTD (varFDTD) solver simulates light propagation efficiently in a wide range of waveguide structures, from systems built on ridge waveguides to geometries as complex as photonic crystals. It predicts the performance of optically large components more accurately than the beam propagation method, and together with an optimised compute engine it makes for a robust waveguide design environment suited to virtual prototyping and optimisation of planar integrated optical components and circuits.
The finite-difference time-domain (FDTD) method is one of the most general and accurate ways to simulate light propagation in nanoscale components. Applied to three-dimensional structures, however, FDTD becomes extremely demanding computationally, which makes it hard to handle large integrated optical components efficiently. Several alternatives exist for simulating waves propagating over long distances. The well-known beam propagation method (BPM) is based on a slowly varying envelope assumption and can simulate large structures quickly, but its accuracy falls off for propagation at wide angles and for components with high index contrast. The more rigorous eigenmode expansion method (EME) is ideal for handling bidirectional propagation, but it is inefficient for simulating omnidirectional propagation because many modes are needed for sufficient accuracy. Unlike conventional propagation methods, varFDTD in Lumerical MODE can model linear and nonlinear phenomena in planar waveguide systems over a broad band without assuming anything about the optical axis, the device geometry or the materials used. For planar waveguide components, varFDTD needs only the simulation time and memory of a 2D FDTD calculation while delivering accuracy and generality comparable to 3D FDTD. Combined with the eigenmode solver and the bidirectional eigenmode expansion (EME) solver, Lumerical MODE becomes an excellent tool for virtual prototyping of large integrated optical components, reducing the need for expensive and time-consuming fabricated prototypes.
The varFDTD solver is ideal for simulating omnidirectional light propagation in optically large planar integrated optical components. As Figure 1 shows, the method reduces a three-dimensional problem to an effectively two-dimensional one by converting the vertical waveguide structure into an effective dispersive material that accounts for material dispersion and waveguide dispersion at the same time.
There are currently two approaches to collapsing a three-dimensional geometry in the varFDTD solver.
In both cases the key assumption is that coupling between the different slab modes supported by the vertical waveguide structure can be neglected. For many devices that support only two vertical modes of different polarisation, such as SOI-based slab waveguide structures, this is a very good assumption. In such cases varFDTD produces results equivalent to 3D FDTD with the simulation time and memory of a 2D FDTD simulation. That lets designers iterate efficiently over many design parameters, and makes it possible to simulate components too large for 3D FDTD to handle.
Here we use a simple ring resonator to demonstrate the varFDTD solver in Lumerical MODE.
Lumerical MODE collapses the 3D geometry into a 2D set of effective materials automatically. The effective materials produced are also dispersive. Note that the dispersion comes both from the properties of the original materials and from the geometry of the slab waveguide. The resulting materials are then fitted, using Ansys’s own Multi-Coefficient Materials model, into a form suitable for simulation by the FDTD algorithm.
Once the effectively 2D materials have been produced, the 2D FDTD simulation can proceed using Ansys’s optimised compute accelerator, which allows parallel computation on multi-core processors and multi-node high performance computing systems.
The built-in eigenmode expansion monitor gives high-resolution, accurate broadband transmission data for any waveguide mode from a single simulation. Figure 5 shows the signal transmitted into the fundamental mode at the through-port position. As Table 1 shows,
varFDTD agrees very closely with the 3D FDTD result and is 100 times faster. Figure 5 also compares 2D FDTD (where the index is simply the effective index of the vertical slab mode) against 3D FDTD, and the agreement there is poor. In particular, bandwidth and FSR (free spectral range), the key quantities usually extracted from such a simulation, are computed very accurately by varFDTD but not by standard 2D FDTD. To make varFDTD, 2D FDTD and 3D FDTD easier to compare, both plots in Figure 5 shift the central peak of the varFDTD and 2D FDTD transmission spectra to coincide with the 3D FDTD result. In practice this precise peak alignment can be achieved by thermal tuning.
| Simulation type | Memory | Run time on a 2010-model Intel Core i7 machine |
|---|---|---|
| 2D FDTD | 15MB | about 12 seconds |
| 2.5D FDTD | 18MB | about 15 seconds |
| 3D FDTD | 338MB | about 150 seconds |
Given the accuracy and speed the varFDTD solver delivers, Lumerical MODE can move ring resonator optimisation forward considerably. Because simulating ring resonators and other silicon photonic devices normally requires a larger simulation region and a longer simulation time, the varFDTD solver plays a very important part in optimising designs at this level of complexity.
The varFDTD solver makes it straightforward to determine accurately the broadband transmission into the several modes a wide taper supports. Collapsing the vertical structure into an effective slab works perfectly over a wide region such as a taper, so no approximation is made to light propagation within the waveguide slab and this variational FDTD treatment gives results very close to 3D FDTD
.
AWGs are essential devices for dense wavelength division multiplexing in optical networks. Their size and complexity, and their sensitivity to phase error, can make AWGs difficult for many propagation methods to compute. With the varFDTD solver in Lumerical MODE, accurate broadband results can be obtained from a single simulation.
Simulating nonlinear effects in a waveguide often requires long simulation times and long propagation distances. Combining the varFDTD solver with the flexible material plugins provided by Lumerical MODE makes it possible to simulate long-distance wave propagation efficiently while capturing the interaction between linear and nonlinear effects accurately.Flexible material plugins is built on an open framework, and end users can develop models tailored to their own needs as dynamic link library plugins written in native C, C++ or FORTRAN. Used together with the multi-coefficient material model, these plugins can simulate complex nonlinear materials such as the one in Figure 9.
The varFDTD solver in Lumerical MODE is a general-purpose solver for simulating broadband, omnidirectional light propagation in waveguide components. For planar geometries where coupling between different slab modes is negligible, varFDTD achieves results comparable to 3D FDTD with only the simulation time and memory of 2D FDTD. Combined with the eigenmode solver and the bidirectional eigenmode expansion (EME) solver, Lumerical MODE becomes an excellent tool for virtual prototyping of large integrated optical components, reducing the need for expensive and time-consuming fabricated prototypes.
[1] Manfred Hammer and Olena V. Ivanova, MESA Institute for Nanotechnology, University of Twente, Enschede, The Netherlands, “Effective index approximation of photonic crystal slabs: a 2-to-1-D assessment”, Optical and Quantum Electronics, Volume 41, Number 4, 267-283, DOI: 10.1007/s11082-009-9349-3.
[2] Allan W. Snyder and John D. Love, Optical Waveguide Theory. Chapman & Hall, London, England, 1983.
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