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https://github.com/lxvm/deltarcwa.jl

An nanophotonics solver for inverse design of metamaterials
https://github.com/lxvm/deltarcwa.jl

electromagnetism julia maxwell-equations metamaterials nanophotonics physics plane-wave-expansion rcwa scattering

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An nanophotonics solver for inverse design of metamaterials

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README 

        
# DeltaRCWA.jl



## About



`DeltaRCWA.jl` is a frequency-domain solver for the scattering of

electromagnetic fields through stacks of periodic, variable-impedance sheets

suspended in vacuum that employs sheet-transition conditions with

[RCWA](https://en.wikipedia.org/wiki/Rigorous_coupled-wave_analysis).



This project was started by Luke Qi [in this

repository](https://github.com/Mastercheese77/deltaRCWA) and has been conducted

under the supervision of Professor Steven G. Johnson and Dr. Raphaël Pestourie.



## Device geometries



A geometry for `DeltaRCWA` represents a device composed of a stack of periodic,

variable-impedance sheets suspended in vacuum.

This can be viewed as a coarse proxy of a device composed of layered

[metasurfaces](https://en.wikipedia.org/wiki/Electromagnetic_metasurface).

An example of a valid geometry for `DeltaRCWA` is illustrated below:



![](images/stack_figure.png)



The illustration shows a single unit cell, though the actual device would repeat

the unit cell infinitely in the plane of the sheet.

The colorings of the layers in the sheet represent the metasurface impedance

parameters, described below.



## Sheet transition conditions



For a sheet given by its normal vector



that separates region



from region

,

the jump in the tangential electromagnetic fields at the

surface of the sheet in each region is modeled by [1]:









where



is the electrical impedance matrix and



is the magnetic conductance matrix defined at each point in the sheet.

These equations and Maxwell's equations are used to derive a scattering matrix

for the sheet in the planewave basis.



## Redheffer star product



[Redheffer's star product](https://en.wikipedia.org/wiki/Redheffer_star_product)

is used to combine the scattering matrices generated for each layer of the device into one describing the whole device.

Then the scattering matrix multiplies the incident mode amplitudes to obtain the

scattered mode amplitudes.



## Contents



- `notebooks`: interactive Pluto and Jupyter notebooks showcasing the uses of

`DeltaRCWA` as well as doing exploratory tests/debugging which will hopefully

be ready to include in `DeltaRCWA`

- `src`: the source code of `DeltaRCWA`

- `scripts`: contains Julia scripts to do convergence and validation tests

for different solution methods

- `test`: contains unit tests of `DeltaRCWA`'s star product methods



The root folder and `notebooks`, `scripts`, and `test` each contain a separate

Julia environment. See `notebooks/README.md` for an example on how to set one up.



## Documentation



Currently the documentation is informal at its best.

An attempt has been made to provide docstrings for most types and functions.

To see an example usage, open the Pluto notebook in `notebooks/interface.jl`.



## Tests



This is todo and not to be done until more of the package is working.



## References



- [1] [E. Kuester, M. Mohamed, M. Piket-May, and C. Holloway,

    “Averaged transition conditions for electromagnetic fields at a metafilm,”

    _IEEE Trans. Antennas Propag._, vol. 51, no. 10, pp. 2641–2651, Oct. 2003.](

    https://doi.org/10.1109/TAP.2003.817560)