Gradient-Based Inverse Electromagnetic Design Using Continuously-Smoothed Boundaries

There are many passive electromagnetic components whose behavior can be controlled by modifying the shape of the device's material boundaries. In this paper, we take advantage of continuous smoothing of material boundaries on a rectangular grid in order to accurately calculate the gradient of a figure of merit with respect to perturbations to the boundary of a dielectric structure. Grid smoothing is achieved by representing the geometry of the system in terms of continuously-defined boundaries and then mapping these boundaries onto a static rectangular grid. The gradients, computed using an adjoint method, can then be used in conjunction with existing efficient minimization algorithms to optimize the device. Unlike existing methods in topology optimization, this method of shape optimization gives us the freedom to efficiently optimize structures both with and without a constrained shape using an arbitrary parameterization of the underlying material boundaries. In order to demonstrate this method, we optimize a short non-adiabatic taper from a 0.5 $\mu$m wide input waveguide to an 9.0 $\mu$m wide output waveguide with constrained minimum feature sizes, achieving less than -0.05 dB insertion loss at the design wavelength of 1550 nm.