Parametric instability of non-Hermitian systems near the exceptional point

Abstract

In contrast to Hermitian systems, eigenstates of non-Hermitian ones are in general nonorthogonal. This feature is most pronounced at exceptional points where several eigenstates are linearly dependent. In this work we show that near this point a new effect takes place. It exhibits in energy increases in the system when its parameters change periodically. This effect resembles parametric resonance in a Hermitian system but there is a fundamental difference. It comes from the unique properties of the exceptional point that leads to parametric instability that occurs almost at any change in a parameter, while in the case of Hermitian systems it is necessary to fulfill resonance conditions. We illustrate this phenomenon by the case of two coupling waveguides with gain and loss. This phenomenon opens a wide range of applications in optics, plasmonics, and optoelectronics, where the loss is an inevitable problem and plays a crucial role.

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Cited by in corpus (15)

• $\mathcal{P}\mathcal{T}$ symmetry and anti-symmetry by anti-Hermitian wave coupling and nonlinear optical interactions
• PT-symmetry in nonlinear twisted multi-core fibers
• Tight-binding lattices with an oscillating imaginary gauge field
• Non-Hermitian dynamics of slowly-varying Hamiltonians
• Probing phase transitions in non-Hermitian systems with Multiple Quantum Coherences
• Complex Berry phase instability in PT-symmetric coupled waveguides
• Strong-coupling-assisted formation of coherent radiation below the lasing threshold
• Signature of exceptional point phase transition in Hermitian systems
• Subthreshold phonon generation in an optomechanical system with an exceptional point
• Static synthetic gauge field control of double optomechanically induced transparency in a closed-contour interaction scheme
• Overcoming the diffraction limit on the size of dielectric resonators using an amplifying medium
• Correlated Nonreciprocity around Conjugate Exceptional Points
• Mixedness timescale in non-Hermitian quantum systems
• Spatial transient behavior in waveguides with lossy impedance boundary conditions
• Dynamic manifestation of exception points in a non-Hermitian continuous model with an imaginary periodic potential