Trace formulation for photonic inverse design with incoherent sources

Abstract

Spatially incoherent light sources, such as spontaneously emitting atoms, naively require Maxwell’s equations to be solved many times to obtain the total emission, which becomes computationally intractable in conjunction with large-scale optimization (inverse design). We present a trace formulation of incoherent emission that can be efficiently combined with inverse design, even for topology optimization over thousands of design degrees of freedom. Our formulation includes previous reciprocity-based approaches, limited to a few output channels (e.g., normal emission), as special cases but generalizes to a continuum of emission directions by exploiting the low-rank structure of emission problems. We present several examples of incoherent-emission topology optimization, including tailoring the geometry of fluorescent particles, a periodically emitting surface, and a structure emitting into a waveguide mode, as well as discussing future applications to problems such as Raman sensing and cathodoluminescence.

Fast multi-source nanophotonic simulations using augmented partial factorization

“…With a suitable formulation, APF can consolidate the 2M simulations into a single or a few computations. Computing the thermal emission into a continuum 49 requires many simulations and can also be accelerated using APF. One may use APF to design classical and quantum photonic circuits with elements that couple numerous channels.…”

Efficient Inverse Design of Large-Area Metasurfaces for Incoherent Light

“…(For broadband devices such as solar cells, there is still a need for a frequency integral, but this integral can be computed efficiently using a weighted quadrature scheme designed for the solar spectrum . One can also apply the same reciprocal technique in the time domain to compute many frequencies simultaneously. , ) The concentrator and collimator designs in this paper were for a single output spot or a single output mode, but we have developed more general trace-optimization techniques for efficient averages over many spots or modes …”

“…In contrast to ref , which primarily involved spatially uncorrelated random sources, the random currents here are correlated in space. In our examples below, we assume that the amplitudes are uncorrelated for different angles (corresponding to spatially broad and translation-invariant illumination), as described above.…”

“…Similar to ref , we rewrite eq using the cyclic property of the trace function and the linearity of the ensemble average: where ⟨ bb † ⟩ is the current–current correlation operator (the correlation “matrix”). In contrast to eq , this new formulation requires only a single solve of Maxwell’s equations for a “reciprocal” simulation v = A –† w , where the output w is treated as a “source”.…”

Neural Operator-Based Surrogate Solver for Free-Form Electromagnetic Inverse Design

“…However, even the most data-efficient models can not offset the cost of data generation if the problem at hand requires only a handful of simulations in the first place. Therefore, we identify inverse design, − specifically gradient-based, as a discipline that is well-suited to benefit from the speed of surrogate models and suffers little from their drawbacks. , In gradient-based inverse design, a functional element is optimized by incrementally maximizing some figure of merit. Gradients of this figure of merit with respect to incremental changes in the geometry are then used to refine the device until an optimum is found iteratively.…”