Exceptional Point Dynamics in Photonic Time Crystals for Enhanced Optical Sensing

TL;DR

This paper introduces the concept of exceptional points in photonic time crystals with gain-loss modulation, demonstrating enhanced optical sensing capabilities through temporal non-Hermiticity and non-Hermitian Floquet Hamiltonians.

Contribution

It extends exceptional point physics into the temporal domain using a photonic time crystal with gain-loss modulation, providing a new paradigm for reconfigurable and broadband exceptional-point photonics.

Findings

Identification of a temporal exceptional point supporting mode coalescence.

Analysis of Riemann-sheet topology, mode exchange, and Berry-phase effects.

Demonstration of enhanced sensing via $ oot{2} ext{epsilon}$ perturbation response and CRB calculations.

Abstract

Exceptional points (EPs) in non-Hermitian photonics offer singular sensitivity enhancements but have thus far been realized almost exclusively in spatially engineered platforms with fixed geometries and limited tunability. Here we extend EP physics into the temporal domain by introducing balanced gain--loss modulation in a photonic time crystal (PTC). A time-periodic refractive-index modulation $n(t)=n_{0}+\delta n\cos(\Omega t)$ generates an effective non-Hermitian Floquet Hamiltonian that supports coalescence of quasi-eigenmodes in frequency space, constituting a genuine \textit{temporal exceptional point}. Using a reduced two-mode model for the dominant frequency sidebands, we derive a non-Hermitian dimer Hamiltonian $H_{\mathrm{PT}}(\Delta,\gamma,\kappa)$ that is strictly $\mathcal{PT}$-symmetric for $\Delta=0$ and identify the exact EP condition. Numerical analysis reveals the associated Riemann-sheet topology, mode exchange and Berry-phase accumulation upon encirclement of the EP, and the characteristic $\sqrt{\varepsilon}$ perturbation response indicative of enhanced sensing. We further construct a non-Hermitian transmission model that is exact within the reduced two-mode description, compute the Cram\'er--Rao bound (CRB) for temperature estimation under an explicit noise model, and show that EP-enhanced sensitivity persists when compared to a linewidth-matched Hermitian reference under identical resource constraints. Monte Carlo simulations confirm that the CRB is saturable using spectral measurements. These results establish temporal non-Hermiticity as a new paradigm for dynamically reconfigurable, broadband, and geometry-independent exceptional-point photonics.