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.

Date Published: 26 February 2020
PDF: 13 pages
Proc. SPIE 11290, High Contrast Metastructures IX, 112900Q (26 February 2020); doi: 10.1117/12.2545703

Published in SPIE Proceedings Vol. 11290:
High Contrast Metastructures IX
Connie J. Chang-Hasnain; Andrei Faraon; Weimin Zhou, Editor(s)