Global optimization of photonic structures with PyMoosh and Nevergrad

Tutorial python notebooks, accompanying the paper An illustrated tutorial on global optimization in nanophotonics by P. Bennet et al. (arXiv:2309.09760).

We demonstrate how to do global optimization of the geometry of multi-layered photonic structures, 2D gratings and plasmonic nanostructures. Multi-layer simulations are done with PyMoosh, 2D gratings with a home-made RCWA code and plasmonic nanostructures with pyGDM. As optimization toolkit we use Nevergrad. For more information about PyMoosh, our Python-based simulation library designed to provide a comprehensive set of numerical tools allowing to compute essentially all optical characteristics of multilayered structures, please consult our recent 'PyMoosh tutorial'.

Goal of the example problems

The tutorials have two main goals:

1. Providing a simple introduction and a starting point for global optimization of multi-layer structures.

2. Describing how to apply global optimization to different problems in nano-photonics

Five specific applications are treated:

1. Optimization of a Bragg mirror.

2. Solving of an ellipsometry inverse problem.

3. Design of a sophisticated antireflection coating to optimize solar absorption in a photovoltaic solar cell.

4. Optimization of a 2D grating for minimum specular reflectance at a given wavelength.

5. Design of a plasmonic nanostructure for directional emission from a local emitter.

List of all notebooks

You can run the Notebook directly on your own computer, or you can connect to the Colab platform to use external server if you want more computational resources. We advise you to use Colab to run the 3D case to save time resources.

• 01_simple_Bragg_optimization_with_pymoosh.ipynb: Very simple tutorial on how to use PyMoosh's internal DE optimizer (link to google colab version)

• 02_simple_optimization_with_nevergrad.ipynb: Very simple tutorial on how to use Nevergrad optimizers for photonics (link to google colab version)

• 03_benchmark_optimization_with_nevergrad.ipynb: Tutorial on how to benchmark several algorithms, demonstrated on a small Bragg mirror problem (link to google colab version)

• 04_simple_Ellipso_optimization.ipynb : Tutorial on setting up the ellipsometry problem (link to google colab version)

• 05_simple_Photovoltaics_optimization.ipynb : Tutorial on setting up the photovoltaics problem (link to google colab version)

• 06_simple_2Dgrating_optimization_with_Nevergrad.ipynb: Tutorial on setting up the 2D grating problem (link to google colab version). In this example we reproduce the optimization of a 2D grating to minimize its specular blue reflection (450 nm). Each layer of the structure is composed of one block of dielectric in air. Each block is characterized by its width, thickness and position in a period of 600 nm. The width, thickness and position of each blocks are subject to the optimizer. The optical properties are computed with a RCWA method. For more information about this optimization, please consult the work described in Barry et al. Sci Rep 10, 12024 (2020).

• 07_simple_3D_plasmonic_nanostructure_directional.ipynb: Tutorial on setting up the 3D nanoantenna problem (link to google colab version). In this example we reproduce the optimization of a directional plasmonic nanoantenna that couples with a local quantum emitter, and steers the light towards a defined solid angle as described in Wiecha et al. Opt. Express 27, pp. 29069, (2019). The optimization target is to maximize the ratio of emission towards a specific target solid angle and emission towards the rest of the sphere surface. The emitting system is a local oscillating dipole at fixed wavelength (800 nm), representing for example a quantum dot, coupled to a gold nanostructure, for simplicity of the tutorial, in vacuum. The optimization acts on the geometry of the gold nanostructure, which is constituted of 40 small gold cubes, each of 40x40x40 nm^3. Their X, Y positions are discretized in steps of these blocks, and subject to the optimizer.

3D nanoantenna problem

This tutorial aims at reproducing the general trend in Wiecha et al. Opt. Express 27, pp. 29069, (2019). However, for runtime and readibility of the notebook, we keep the configuration simpler. The nanoantenna is made from smaller and fewer gold elements, the antenna is placed in a homogeneous environment (air) and the emitter is above the antenna, such that we do not need to add a forbidden zone constraint in the material positioning.

In the subfolder 3D_nanoantenna_benchmark you will find three files.

• 09_benchmark_3Dnanostructure_MPI.py : This program is used to optimize the same problem than the previous one, a 3D nanoantenna. This example is an MPI-parallelized version to accelerate the benchmarking of multiple algorithms. To start its execution, mpi and mpi4py need to be installed. Then, for example to run 8 parallel processes, launch via: "mpirun -n 8 python python_script.py" as shown with the bash file 08_3Dnanostructure_run_parallel_optimizations_MPI.sh, or directly run the bash file(please assure you to adapt the number of CPU used before to run the file).

• 10_benchmark_3Dnanostructure_optimization.ipynb : This tutorial aims at reproducing the trends in Wiecha et al. Opt. Express 27, pp. 29069, (2019). Here we reload the results calculated by the MPI-parallelized script (Python file 08_benchmark_3Dnanostructure_MPI.py). The multiple optimization runs need to be done via MPI first. PLEASE RUN THE '08' PROGRAM BEFORE TRYING TO RUN THIS NOTEBOOK.

Caution: pyGDM uses numba, as a result the MPI script uses pickle with some JIT-compiled numba objects to save the results. Reloading these objects requires to use the exactly same python installation as used for generation of the simulations, otherwise difficult to interpret errors can occur.

Benchmark results

The figures from our paper An illustrated tutorial on global optimization in nanophotonics by P. Bennet et al. (arXiv:2309.09760) are generated with the '11.1_Paper_results.py' program. We also provide a Jupyter Notebook version of this program 12_paper_results.ipynb.