Lumerical’s Rigorous Coupled-Wave Analysis (RCWA) solver can be used to analyze the optical response of a plane wave incident on a multilayer structure. Unlike the STACK solver, the RCWA solver can be used with structures that have periodic variations in the layer geometry, for example photonic crystals and diffraction gratings. With simulation times that are generally much shorter than FDTD, the RCWA solver is an ideal tool for the analysis of these types of periodic structures.

The RCWA solver can calculate the following results:

- The fraction of incident power that is transmitted and reflected.
- The power in each grating order of the structure.
- The electric and magnetic fields inside the multilayer structure.

All results are available for both S and P polarizations.

With release 2022 R1, the RCWA solver can be used through the rcwa script command. For details on how to use the RCWA solver, see the rcwa command documentation.

## RCWA Solver Physics

The RCWA method is a semi-analytical technique for solving Maxwell’s equations in one direction for multilayer structures. The method uses a discrete Fourier transformation to discretize the electric and magnetic fields.

The RCWA method involves the following steps:

- Solve Maxwell’s equations analytically in each layer to obtain a set of eigenvalue problems which can be resolved independently. The solutions are calculated in Fourier space, and the fields are expressed with a Fourier expansion. Due to the periodicity of the structure, only discrete k-vectors are allowed. Increasing the number of k-vectors increases the accuracy as well as the simulation time.
- The solution to each section is propagated bi-directionally to calculate the S-matrix of the entire device. The internal fields can also be reconstructed, if desired.

## RCWA vs. FDTD vs. STACK

The RCWA, FDTD, and STACK solvers can all be used to perform optical simulations of multilayer structures. Which solver is most suitable for a given simulation depends on the details of the geometry and the optical source.

In general, FDTD can be used for any simulation that can be done with RCWA or STACK. However, RCWA and STACK will be faster in most cases, unless very broadband results are required. FDTD is also a fully numerical method, while RCWA is semi-analytical and STACK is analytical, so the results from FDTD will generally be less accurate than RCWA or STACK results. RCWA and STACK simulations are also much simpler to set up than FDTD simulations, reducing the chances that the simulation is not properly set up.

For simulations with a plane wave source incident on a multi-layer structure, STACK can be used if the layers are uniform in the transverse direction. If the layers are non-uniform but periodic in the transverse direction the RCWA solver can be used. If the layers are not periodic in the transverse direction the FDTD solver must be used.

For simulations of emissive multi-layer structures like OLEDs, the STACK solver can be used if the layers are uniform (see Planar OLED Microcavities - Color Shift and Extraction Efficiency). If the layers are not uniform, for example with some sort of patterning, the FDTD solver must be used (see OLED (2D)). It is not currently possible to use the RCWA solver for emissive structures, as it doesn’t have a dipole source option available.

## Units and Normalization

Unless otherwise specified, all quantities are returned in SI units. Please see Units and Normalization for more information.