ANSYS LUMERICAL / FDTD
Rigorous coupled-wave analysis returns the diffraction efficiency of periodic microstructures by wavelength, angle and polarisation. Because periodicity can be assumed, it is orders of magnitude faster than solving the same problem with FDTD.
Overview
The periodicity of the structure is used to expand the electromagnetic field into a Fourier series, and the coupled-wave equations are solved layer by layer. Because no time evolution is followed, a solution for a single wavelength and angle is obtained quickly.
Designing a metasurface requires sweeping the dimensions of the meta-atom to establish how phase and transmittance vary with them. Whether that sweep can be run in a realistic time is what determines how the design work proceeds.
Because periodic boundaries are assumed, finite-size effects and local defects cannot be treated. Verifying the structure as a whole requires another method alongside it.
Defining the periodic structure and the unit cell
Schematic: incident wave → periodic structure (unit cell) → diffraction orders
The advantages of RCWA
01
Sweeps of hundreds to thousands of conditions can be run in a realistic time.
02
The response can be obtained directly for each angle of incidence and polarisation.
03
Building a meta-atom library is one of the classic uses of RCWA.
Phase and transmittance obtained from a dimensional sweep
Where it fits
There are cases another method will solve faster and more accurately. The following is a guide to choosing.
Use RCWA
Consider another method
FDTD and RCWA compared on the same structure. Where the periodic approximation holds, the two agree.
Typical applications
Generating phase and transmittance libraries for meta-atoms
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How grating efficiency depends on angle and wavelength
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Evaluating the diffraction signal and the grating profile of overlay metrology targets
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Evaluating the reflection and transmission spectra of a periodic slab
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Inputs and outputs
For the incidence conditions and structure you set, the response is returned order by order.
INPUT
| Unit structure | The geometry and materials within the periodic cell |
| Period | Pitch in x and y |
| Incidence conditions | Wavelength, angle of incidence, azimuthal angle, polarisation |
| Expansion orders | The Fourier orders. Convergence needs to be checked |
RCWA
Rigorous coupled-wave analysis
OUTPUT
| Diffraction efficiency | Transmittance and reflectance for each order |
| Phase | Complex amplitude and phase for each order |
| Spectra | The response across a wavelength sweep |
| Library | A table of phase and transmittance against dimensions |
Frequently asked questions
The questions we are most often asked before adoption.
Should I use this or FDTD?
If the structure is periodic and you want diffraction efficiency, use RCWA. For finite-size structures, or arbitrary shapes with no periodicity, use FDTD. In metasurface design it is common to use both: build the library with RCWA, then verify locally with FDTD.
How do I choose the number of expansion orders?
Raise the order until the result stops changing. The higher the index contrast of the structure, the more orders are needed.
How do I build a meta-atom library?
Fix the material, wavelength, pitch and height, then sweep dimensional parameters such as the radius and record the phase and transmittance. In Photonica this can be handled as a connected RCWA workflow.
Can oblique incidence be handled?
Yes. You can specify the angle of incidence and the azimuthal angle and evaluate the angular dependence.
We can advise on everything from analysis setup to judging whether a result is sound. Hands-on training, where you work with the software yourself, is also available.
Support →
Training →
It is fine if there is information you cannot share — tell us only what you are comfortable with.
The demo is built around a structure close to your own. We can also give you an indication of the problem size and the run time on the spot.