A lot of things are harder to do backwards – solving photonics problems is a case in point. “Where the forward calculations are well understood with Maxwell’s equations, solving one instance of an inverse design problem can often be a substantial research project,” explain John Peurifoy and Yichen Shen and their co-authors in a recent report. They then go on to show how their artificial neural network – (ANN) a brain-mimicking algorithm – can solve photonics problems far faster than conventional methods and solve them inversely too.
MIT senior Peurifoy and research affiliate Shen worked with graduate student Li Jing, professor of physics Marin Soljacic, and colleagues at MIT and Army Edgewood Chemical Biological Center in the US. They first used the ANN to calculate the spectra of light that would scatter from different nanoparticle structures. Their nanoparticle samples were spheres comprising several alternating concentric layers of titanium and silicon oxides. There are various numerical and analytic approaches for determining how a particular nanostructure will scatter light but the ANN was able to cut the simulation time for complex structures by up to an order of magnitude.
“Visually, we can see that the neural network is able to find a much closer minimum than the numerical nonlinear optimization method,” say the researchers in their report. “This result is consistent across many different spectra, as well as for particles with different materials and numbers of shells.”
In addition, they were able to run the problem in reverse to find the nanoparticle structures that would give rise to specific spectra, and here conventional approaches really struggle. Solving this kind of inverse photonic problem could help tailor bespoke nanophotonic structures for specific applications.
How it works
The researchers developed the neural network with four layers, and 250 “neurons” per layer. They “trained” it by feeding it tens of thousands of data points describing the structure of different nanoparticles and points from the scattering spectra output data that would result from illuminating them.
Various functions between the layers allow the ANN to map to output data, and different connections are weighted. By training the ANN with input and output data sets they showed it could “learn” a kind of intuition as to what scattering spectra different structures will give rise to.
They list a number of fields that have similar inverse problems, including quantum scattering theory, photonic devices, and thin film photovoltaic materials.
Full details are reported in Science Advances.