Large permittivity increments for efficient predictive photonic devices optimization

In In this paper, we show two novel approaches for photonic device optimization. Both approaches exploit the Lippmann- Schwinger equation, and can be applied with significant gains in computational efficiency when used with adjoint variable method. The first method optimizes a binarized device by greedily proposing and evaluating the effect of changing different pixels in the design region. Using the update of the Green’s function of the system with Dyson’s equation, one can guarantee the improvement of the figure of merit even for a large discrete binary change. The final structure is binary and guarantees fabricability with varying minimum feature sizes. In the second approach, we develop a fast algorithm to perform a line search for continuous optimization with gradient descent. The algorithm enables the line search to be executed faster than evaluating a new gradient, making such a line search extremely valuable. This line search is based on a Shanks transformation of the series expansion of the Lippmann-Schwinger equation, which enables us to determine the optimal learning rate in the search direction and minimize the number of separate iterations needed to achieve an optimal device.