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Topology optimization of photonics devices: fluctuation-trend analysis concept; random initial conditions with Gaussian and Durden–Vesecky power density bandlimited spectra

We present a topology optimization method for a 1D dielectric metasurface, based on a new concept: fluctuation and trend analysis for initial random conditions. The key point of the proposed optimization method is that the procedure initially generates a couple of device distributions termed fluctuation/mother and trend/father, with specific spectra that efficiently sample not the local minimum of the objective function but basins of optimal solutions in the design space. Studying a 1D dielectric metagrating deflecting a normal polarized incident wave onto a range of angles, we show that a suitable choice of a specific power density spectrum for this initial couple highly increases the probability of reaching a basin of high-performance devices. We guess initial geometries holding the physical properties of the desired final device, allowing accurate targeting of these high-performance device basins in the design space. To include desired physical properties in the initial geometry model, we introduce a formalism allowing generation of a random process with a particular power density or correlation function. By means of a suitable definition of the trend function, we identify an ultimate power density bandlimited spectrum for the fluctuation functions allowing a very high probability and leading to a rapid descent to favorable basins of optimal solutions, consequently reaching high-performance final structure in the design space.