Abstract
We study the impact of a spatially homogeneous yet non-stationary dielectric permittivity on the dynamical and spectral properties of light. Our choice of potential is motivated by the interest in -symmetric systems as an extension of quantum mechanics. Because we consider a homogeneous and non-stationary medium, symmetry reduces to time-reversal symmetry in the presence of balanced gain and loss. We construct the instantaneous amplitude and angular frequency of waves within the framework of Maxwell’s equations and demonstrate the modulation of light amplification and attenuation associated with the well-defined temporal domains of gain and loss, respectively. Moreover, we predict the splitting of extrema of the angular frequency modulation and demonstrate the associated shrinkage of the modulation period. Our theory can be extended for investigating similar time-dependent effects with matter and acoustic waves in -symmetric structures.
Highlights
During the past years, a new class of Hamiltonians has been widely investigated, which extends quantum mechanics from the Hermitian into the non-Hermitian domain [1]
In 2010, Rüter et al were the first to realize a -optical coupled system that involves well-defined regions with gain and loss regimes, inherent to the complex-valued refractive index [17]. Such an extension of the concept of spacetime reflection into the classical domain stems from the works of El-Ganainy et al [18] and Makris et al [19, 20], who have employed the similarity between the Schrödinger and a scalar approximation of Maxwell’s equations to describe the dynamics of light beams in -symmetric optical lattices
-symmetric structures have mainly been investigated in the spatial domain and little attention has been paid to the study of the non-stationary regime
Summary
We study the impact of a spatially homogeneous yet non-stationary dielectric permittivity on the dynamical and spectral properties of light. Because we consider a homogeneous and non-stationary medium, symmetry reduces to time-reversal symmetry in the presence of balanced gain and loss. We construct the instantaneous amplitude and angular frequency of waves within the framework of Maxwell’s equations and demonstrate the modulation of light amplification and attenuation associated with the well-defined temporal domains of gain and loss, respectively. Our theory can be extended for investigating similar time-dependent effects with matter and acoustic waves in -symmetric structures
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