Computing eigenfrequency sensitivities near exceptional points
arXiv:2402.17648 · doi:10.1103/PhysRevResearch.6.023148
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 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.
References in corpus (21)
- Loss-induced suppression and revival of lasing
- Light interaction with photonic and plasmonic resonances
- Enhanced sensitivity operation of an optical gyroscope near an exceptional point
- Non-Hermitian Ring Laser Gyroscopes with Enhanced Sagnac Sensitivity
- Electromagnetically induced transparency at a chiral exceptional point
- Sensing with exceptional surfaces: combining sensitivity with robustness
- Petermann-factor limited sensing near an exceptional point
- Adaptive Finite Element Method for Simulation of Optical Nano Structures
- Perfectly absorbing exceptional points and chiral absorbers
- Chiral Coherent Perfect Absorption on Exceptional Surfaces
- Quantum chaos in optical systems: The annular billiard
- Quasinormal mode solvers for resonators with dispersive materials
- Shape deformation of nanoresonator: a quasinormal-mode perturbation theory
- Modal analysis of electromagnetic resonators: user guide for the MAN program
- Exceptional points-based optical amplifiers
- Petermann factors and phase rigidities near exceptional points
- Poles and zeros in non-Hermitian systems: Application to photonics
- Non-linear eigenvalue problems with GetDP and SLEPc: Eigenmode computations of frequency-dispersive photonic open structures
- Revisiting the hierarchical construction of higher-order exceptional points
- Computation of eigenfrequency sensitivities using Riesz projections for efficient optimization of nanophotonic resonators
- Fast simulation method for parameter reconstruction in optical metrology