The preliminary study reported here investigates if unit-cell inclusion-symmetries may be broken in time-reversalinvariant topological insulator designs, while maintaining the desired global behaviour of pseudo-spin-dependent edge state based bi-directional, back-scattering robust, energy propagation. By allowing symmetries to be broken additional geometrical design freedom is attained, which may turn out to enable an improvement of various performance measures such as bandwidth and field confinement. The particular study considers a time-reversal-invariant acoustic topological insulator design, designed using a modified version of our recently proposed topology optimization based method for designing photonic and acoustic topological insulators.1 This method relies on a carefully constructed model system combined with the application of density based topology optimization to design two carefully interfaced crystal phases to maximize the flow of energy through the system. Through simple modifications of the method, we demonstrate that it is possible to design structures with different symmetry conditions from those that have previously been investigated using the method.
This study considers a recently proposed topology optimization based approach for designing photonic membrane cavities supporting a dipole cavity mode. Foremost, the study demonstrates that the approach is robust towards the choice of initial guess provided for the optimization problem, in the sense that near identical final designs are obtained for vastly different initial guesses. This finding suggests that the final designs are near-optimal under the given design constraints. Secondarily, by stopping the design procedure after the same fixed number of design iterations for all initial guesses, it shows that the designed photonic cavity is sensitive towards certain small perturbations of their geometry, stressing the need for utilizing robust optimization techniques and imposing fabrication conforming length-scales in the cavity geometries.
In this work, we perform numerical studies of two photonic crystal membrane microcavities, a short line-defect L5 cavity with relatively low quality (Q) factor and a longer L9 cavity with high Q. We compute the cavity Q factor and the resonance wavelength λ of the fundamental M1 mode in the two structures using five state-of- the-art computational methods. We study the convergence and the associated numerical uncertainty of Q and λ with respect to the relevant computational parameters for each method. Convergence is not obtained for all the methods, indicating that some are more suitable than others for analyzing photonic crystal line defect cavities.