Q-Factor Optimization of Modes in Ordered and Disordered Photonic Systems Using Non-Hermitian Perturbation Theory

The quality factor, Q, of photonic resonatorspermeates most figures of merit in applications that rely on cavity-enhancedlight-matter interaction such as all-optical information processing,high-resolution sensing, or ultralow-threshold lasing. As a consequence,large-scale efforts have been devoted to understanding and efficientlycomputing and optimizing the Q of optical resonatorsin the design stage. This has generated large know-how on the relationbetween physical quantities of the cavity, e.g., Q, and controllable parameters, e.g., hole positions, for engineeredcavities in gaped photonic crystals. However, such a correspondenceis much less intuitive in the case of modes in disordered photonicmedia, e.g., Anderson-localized modes. Here, we demonstrate that thetheoretical framework of quasinormal modes (QNMs), a non-Hermitianperturbation theory for shifting material boundaries, and a finite-elementcomplex eigensolver provide an ideal toolbox for the automated shapeoptimization of Q of a single photonic mode in bothordered and disordered environments. We benchmark the non-Hermitianperturbation formula and employ it to optimize the Q-factor of a photonicmode relative to the position of vertically etched holes in a dielectricslab for two different settings: first, for the fundamental mode ofL3 cavities with various footprints, demonstrating that the approachsimultaneously takes in-plane and out-of-plane losses into accountand leads to minor modal structure modifications; and second, foran Anderson-localized mode with an initial Q of 200,which evolves into a completely different mode, displaying a threefoldreduction in the mode volume, a different overall spatial location,and, notably, a 3 order of magnitude increase in Q.