Computing eigenfrequency sensitivities near exceptional points

Abstract

Exceptional points are spectral degeneracies of non-Hermitian systems where both eigenfrequencies and eigenmodes coalesce. The eigenfrequency sensitivities near an exceptional point are significantly enhanced, whereby they diverge directly at the exceptional point. Capturing this enhanced sensitivity is crucial for the investigation and optimization of exceptional-point-based applications, such as optical sensors. We present a numerical framework based on contour integration and algorithmic differentiation to accurately and efficiently compute eigenfrequency sensitivities near exceptional points. We demonstrate the framework for an optical microdisk cavity and derive a semianalytical solution to validate the numerical results. The computed eigenfrequency sensitivities are used to track the exceptional point along an exceptional surface in the parameter space. The presented framework can be applied to any kind of resonance problem, e.g., with arbitrary geometry or with exceptional points of arbitrary order. Published by the American Physical Society 2024