Kavli Affiliate: Feng Wang
| First 5 Authors: Aditya Bahulikar, Feng Wang, Mustafa Cenk Gursoy, Rodrick Kuate Defo,
| Summary:
We present a symmetry-agnostic topology optimization framework for
photonic-crystal structures based on computation of the photonic density of
states in a manner analogous to $Gamma$-point integration. We provide a
generalization of the approach that allows for computations at different scales
with the additional scales being analogous to integration over the full
Brillouin zone and to regimes between the two limiting cases of full
Brillouin-zone integration and $Gamma$-point integration, though these other
scales do not preserve the symmetry-agnostic nature of the $Gamma$-point
framework. We also demonstrate how our approach can be generalized to the
problem of inverting photonic or phononic bandstructures. Finally, we show that
at the symmetry-agnostic scale analogous to $Gamma$-point integration, we can
recover a known two-dimensional photonic crystal for the TM polarization. A key
insight of our work is the determination of the minimum supercell size and the
minimum precision to which the frequencies within the photonic bandgap must be
sampled in order to observe photonic-crystal structures.
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