Giant enhancement of optical high-order sideband generation and their control in a dimer of two cavities with gain and loss

Abstract

Parity-time ($\mathcal{PT}$) symmetric systems, which rely on the balanced gain-loss condition and render the Hamiltonian non-Hermitian, have provided a new platform to engineer effective light-matter interactions in recent years. Here we explore the high-order sideband features of the output fields obtained from a $\mathcal{PT}$-symmetric optical system consisting of a passive nonlinear cavity coupled to an active linear cavity. By employing a perturbation technique, we derive analytic formulas used to determine the nonlinear transmission coefficient of optical second-order sideband in this structure. Using experimentally achievable parameters, it is clearly shown that the efficiency of the second-order sideband generation can be greatly enhanced in the $\mathcal{PT}$-symmetric dimer, extremely in the vicinity of the transition point from unbroken- to broken-$\mathcal{PT}$ regimes. Moreover, we further analyzed the influences of the system parameters, including the photon-tunneling rate between two cavities, Kerr nonlinearity strength, and optical detuning, on the second-order sideband generation. Subsequently we investigate the higher-order sideband output spectrum by numerical simulations, where the sideband amplitude also is largely enhanced in the $\mathcal{PT}$-symmetric arrangement, compared with the passive-passive double-cavity system. Our obtained results provide a new avenue for acquiring optical high-order sidebands and operating light, which may inspire further applications in chip-scale optical communications and optical frequency combs.