Electromagnetic Simulation Tools + Automatic Differentiation. Code for paper Forward-Mode Differentiation of Maxwell's Equations.

ceviche provides two core electromagnetic simulation tools for solving Maxwell's equations:

• finite-difference frequency-domain (FDFD)

• finite-difference time-domain (FDTD)

Both are written in numpy / scipy and are compatible with the HIPS autograd package, supporting forward-mode and reverse-mode automatic differentiation.

This allows you to write code to solve your E&M problem, and then use automatic differentiation on your results.

As a result, you can do gradient-based optimization, sensitivity analysis, or plug your E&M solver into a machine learning model without having to go through the tedious process of deriving your derivatives by hand.

There is a comprehensive ceviche tutorial available at this link with several ipython notebook examples:

1. Running FDFD simulations in ceviche.
2. Performing inverse design of a mode converter.
3. Adding fabrication constraints and device parameterizations.
4. Inverse design of a wavelength-division multiplexer and advanced topics.

There are also a few examples in the examples/* directory.

There are many ways to install ceviche.

The easiest is by

pip install ceviche

But to install from a local copy, one can instead do

git clone https://github.com/twhughes/ceviche.git
pip install -e ceviche
pip install -r ceviche/requirements.txt

from the main directory.

Alternatively, just download it:

git clone https://github.com/twhughes/ceviche.git

and then import the package from within your python script

import sys
sys.path.append('path/to/ceviche')

The ceviche directory contains everything needed.

To get the FDFD and FDTD simulators, import directly from ceviche import fdtd, fdfd_ez, fdfd_hz

To get the differentiation, import from ceviche import jacobian.

constants.py contains some constants EPSILON_0, C_0, ETA_0, Q_E, which are needed throughout the package

utils.py contains a few useful functions for plotting, autogradding, and various other things.

optimizers.py contains optimizer functions for doing inverse design.

viz.py are functions that help with plotting fields and sructures.

modes.py contains a mode sorter (WIP) that can be used to create waveguide mode profiles for the simulation, for example.

There are many demos in the examples directory, which will give you a good sense of how to use the package.

Tests are located in tests. To run, cd into tests and

python -m unittest

to run all or

python specific_test.py

to run a specific one. Some of these tests involve visual inspection of the field plots rather than error checking on values.

To run all of the gradient checking functions, run

chmod +x test/test_all_gradients.sh
tests/test_all_gradients.sh

If you use this for your research or work, please cite

@article{hughes2019forward,
  title={Forward-Mode Differentiation of Maxwell’s Equations},
  author={Hughes, Tyler W and Williamson, Ian AD and Minkov, Momchil and Fan, Shanhui},
  journal={ACS Photonics},
  volume={6},
  number={11},
  pages={3010--3016},
  year={2019},
  publisher={ACS Publications}
}

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