legume-gme 0.0.2

Differentiable plane-wave and guided-mode expansion for photonic crystals

legume

legume (le GUided Mode Expansion) is a python implementation of the GME method for photonic crystal slabs, including support for multi-layer structures. Plane-wave expansion for purely 2D structures is also included.

Install

Eventually this should be pip installable from PyPi, but for now hopefully this will work for you:

git clone https://github.com/fancompute/legume.git
pip install -e legume
pip install -r legume/requirements.txt

Alternatively just git clone it, make sure you have all the requirements installed, and add the path to the folder in your python path: export PYTHONPATH=$PYTHONPATH:/path/to/the/location/of/legume.

Autograd

One exciting feature is the autograd backend that can be used to automatically compute the gradient of the eigenmodes and eigenfrequencies with respect to any input parameters! When running GME, you can specify 'gradients' = 'exact' (default), or 'gradients' = 'approx' (faster). The latter discards the gradient due to the guided mode basis itself and only keeps the gradients from the diagonalization. Here are some rules of thumb on what to use:

• If you're optimizing hole positions (i.e. parameters that don't change the average permittivity), you're in luck! In this case, the approx gradients should actually be exact!
• If you're optimizing dispersion (real part of eigenfrequencies) w.r.t. parameters that do not include the layer thicknesses, you could still try using approx gradients, as they might be within just a few percent of the exact ones.
• If you're optimizing loss rates (imaginary part of eigenfrequencies) and/or if your parameters include the layer thicknesses, then the approx gradients could be significantly off, exact is recommended.

Guided-mode computation options

GuidedModeExp.run() takes a number of optional arguments. Below is a list of the most important ones, with a short explanation.

• gmode_compute: {'exact'}, 'interp' Define whether the guided modes are computed in the beginning and then interpolated, or whether they are computed exactly at every k-step.
• gmode_inds: {[0]}, list/numpy array List of indexes of the guided bands to be included in the expansion. These alternate between TE and TM defined with respect to the propagation direction.
• numeig: {10}, int Number of eigen-frequencies to be stored.
• eig_sigma: {0.}, float Target frequency, the closest numeig eigen-frequencies are stored.
• compute_im: {True}, bool Specifies if the imaginary parts of the frequencies should also be computed.
• gradients: {'exact'}, 'approx' Specifies whether to compute exact gradients, or approximate (faster)
• eps_eff: {'average'}, 'background' Using the 'average' or the 'background' permittivity of the layers in the guided mode computation.
• verbose: {True}, bool Print information at intermmediate steps.

Convergence

If you think the GME run might not be fully converged, I suggest changing the parameters in the following order:

• First, make sure you have a high enough gmax, which is defined upon initialization of GuidedModeExp.
• Then, include higher-order modes by increasing the number of indexes included in options['gmode_inds'].
  • Note that after including more modes in gmode_inds, you should test again the convergence w.r.t. gmax.

Note that GME is, in the end, only an approximate method, so even if it is converged with respect to the above parameters but produces strange results, it might be that it's not that well-suited for the structure you are simulating.