Kavli Affiliate: Feng Wang
| First 5 Authors: Aditya Bahulikar, Feng Wang, Mustafa Cenk Gursoy, Rodrick Kuate Defo,
| Summary:
We present a structure-adaptive topology optimization framework for
engineering photonic band gaps with TM-polarized sources based on computation
of the photonic density of states with a uniform source substituting for the
standard Dirac delta function sources in formalisms analogous to $Gamma$-point
integration and to integration over a full Brillouin zone. We generalize the
limiting uniform and Dirac delta function sources to more general collections
of sources, such that the union of the sources in a given collection is
hyperuniform. The uniform-source approach necessarily leads to the fastest
computations. We also demonstrate how our approach can be generalized to the
treatment of the frequency-dependent optical response of materials. Finally, we
show that we can recover known two-dimensional photonic crystals for the TM
polarization. A key advantage of our work is its ability to optimize for a
specific midgap frequency and band gap in a structure-adaptive manner. Our work
leverages the insight that the determination of the minimum supercell size and
the minimum precision to which the frequencies within the photonic band gap
must be sampled will lead to the observation of photonic-crystal structures
when the $Gamma$-point formalism for the uniform-source approach is employed.
Additionally, our $Gamma$-point and full Brillouin zone formalisms for the
uniform-source approach inherently encourage binarized designs even in gradient
descent.
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