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https://github.com/weiliangjinca/grcwa

Python implementation of rigorous coupled wave analysis, autograd supported for optimization purpose
https://github.com/weiliangjinca/grcwa

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Python implementation of rigorous coupled wave analysis, autograd supported for optimization purpose

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README 

        
=====

grcwa

=====

.. image:: https://img.shields.io/pypi/v/grcwa.svg

        :target: https://pypi.python.org/pypi/grcwa



..

   .. image:: https://img.shields.io/travis/weiliangjinca/grcwa.svg

	   :target: https://travis-ci.org/weiliangjinca/grcwa



.. image:: https://readthedocs.org/projects/grcwa/badge/?version=latest

        :target: https://grcwa.readthedocs.io/en/latest/?badge=latest

        :alt: Documentation Status



grcwa (autoGradable RCWA) is a python implementation of rigorous

coupled wave analysis (RCWA) for arbitrarily shaped photonic crystal

slabs, supporting automatic differentation with autograd



* Free software: GPL license

* Documentation: https://grcwa.readthedocs.io.



Citing

-------



If you find **grcwa** useful for your research, please cite the

following paper:

::



   @article{Jin2020,

     title = {Inverse design of lightweight broadband reflector for relativistic lightsail propulsion},

     author ={Jin, Weiliang and Li, Wei and Orenstein, Meir and Fan, Shanhui},

     year = {2020},

     journal = {ACS Photonics},

     volume = {7},

     number = {9},

     pages = {2350--2355},

     year = {2020},

     publisher = {ACS Publications}

   }

  



Features

---------

.. image:: imag/scheme.png



RCWA solves EM-scattering problems of stacked photonic crystal

slabs. As illustrated in the above figure, the photonic structure can

have *N* layers of different thicknesses and independent spatial

dielectric profiles. All layers are periodic in the two lateral

directions, and invariant along the vertical direction.



* Each photonic crystal layer can have arbitrary dielectric profile on

  the *2D* grids.

* **autograd** is integrated into the package, allowing for automated

  and fast gradient evaluations for the sake of large-scale

  optimizations. Autogradable parameters include dielectric constant on

  every grid, frequency, angles, thickness of each layer, and

  periodicity (however the ratio of periodicity along the two lateral

  directions must be fixed).



Quick Start

-----------

* Installation:



  .. code-block:: console

		  

		  $ pip install grcwa



  Or,



  .. code-block:: console



		  $ git clone git://github.com/weiliangjinca/grcwa

		  $ pip install .



* Example 1: transmission and reflection (sum or by order) of a square lattice of a hole: `ex1.py <./example/ex1.py>`_



* Example 2: Transmission and reflection of two patterned layers: `ex2.py <./example/ex2.py>`_, as illustrated in the figure below (only a **unit cell** is plotted)



  .. image:: imag/ex.png

	     

  * *Periodicity* in the lateral direction is  *L*\ :sub:`x` = *L*\ :sub:`y` = 0.2, and *frequency* is 1.0.



  * The incident light has an angel *pi*/10.



    .. code-block:: python

		  

		    import grcwa

		    import numpy as np

		    grcwa.set_backend('autograd') # if autograd needed

		    

		     # lattice constants

		     L1 = [0.2,0]

		     L2 = [0,0.2]

		     # Truncation order (actual number might be smaller)

		     nG = 101

		     # frequency

		     freq = 1.

		     # angle

		     theta = np.pi/10

		     phi = 0.



		     # setup RCWA

		     obj = grcwa.obj(nG,L1,L2,freq,theta,phi,verbose=1)		    



  * Geometry: the thicknesses of the four layers are 0.1,0.2,0.3, and 0.4. For patterned layers, we consider total grid points *N*\ :sub:`x` \* *N*\ :sub:`y` = 100\*100 within the unit cell.

    

  * Dielectric constant: 2.0 for the 0-th layer; 4.0 (1.0) for the 1st layer in the orange (void) region; 6.0 (1.0) for the 2nd layer in the bule (void) region; and 3.0 for the last layer.



    .. code-block:: python



		    Np = 2 # number of patterned layers

		    Nx = 100

		    Ny = 100

		    

		    thick0 = 0.1

		    pthick = [0.2,0.3]

		    thickN = 0.4



		    ep0 = 2.

		    epN = 3.

		    

		    obj.Add_LayerUniform(thick0,ep0)

		    for i in range(Np):

		        obj.Add_LayerGrid(pthick[i],Nx,Ny)

		    obj.Add_LayerUniform(thickN,epN)



		    obj.Init_Setup()



  * Patterned layer: the 1-th layer a circular hole of radius 0.5 *L*\ :sub:`x`, and the 2-nd layer has a square hole of 0.5 *L*\ :sub:`x`

  

    .. code-block:: python



		    radius = 0.5

		    a = 0.5



		    ep1 = 4.

		    ep2 = 6.

		    epbkg = 1.



		    # coordinate

		    x0 = np.linspace(0,1.,Nx)

		    y0 = np.linspace(0,1.,Ny)

		    x, y = np.meshgrid(x0,y0,indexing='ij')



		    # layer 1

		    epgrid1 = np.ones((Nx,Ny))*ep1

		    ind = (x-.5)**2+(y-.5)**2`_



* Example 4: transmission and reflection (sum or by order) of a hexagonal lattice of a hole: `ex4.py <./example/ex4.py>`_

  

Note on conventions

-------------------



* The vacuum permittivity, permeability, and speed of light are *1*.

* The time harmonic convention is *exp(-i omega t)*.



Acknowledgements

----------------



My implementation of RCWA received helpful discussions from `Dr. Zin

Lin

`_. Many

details of implementations were referred to a RCWA package implemented

in c called `S4 `_. The idea of

integrating **Autograd** into RCWA package rather than deriving

adjoint-variable gradient by hand was inspired by a discussion with

Dr. Ian Williamson and Dr. Momchil Minkov. The backend and many other

styles follow their implementation in `legume

`_. Haiwen Wang and Cheng Guo

provided useful feedback. Lastly, the template was credited to

Cookiecutter_ and the `audreyr/cookiecutter-pypackage`_.



.. _Cookiecutter: https://github.com/audreyr/cookiecutter

.. _`audreyr/cookiecutter-pypackage`: https://github.com/audreyr/cookiecutter-pypackage