Computing eigenfrequency sensitivities near exceptional points
Physical Review Research(2024)
摘要
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 to an optical microdisk cavity and derive a
semi-analytical 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.
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