Parity-time-symmetry–enhanced sideband generation in an optomechanical system

Optical high-order sideband generation, creating new frequencies with equal spectral separation, has developed potential applications in optical communication and metrology. Here, we investigate the generation of optomechanically induced high-order optical sideband spectra in an optical parity-time ($\mathcal{PT}$) -symmetric system. The system consists of an active optical mode, a passive optical mode, and a mechanical mode, where the mechanical mode is optomechanically coupled with the passive optical mode. Based on numerical analysis, the $\mathcal{PT}$-symmetric system enhances sideband spectra in both amplitude and number of sidebands. With certain parameters, forty sidebands head up on both sides of the control field near the exceptional point. The capability to generate optical high-order sidebands and control light propagation in micro- and nanomechanical systems may open up a promising perspective for complex integrated $\mathcal{PT}$ devices.

Figure 1

Schematic diagram of high-order sideband generation process in an active-passive COM structure. The left cavity mode is coherently pumped by a continuous-wave control field and a probe field. The mechanical mode is localized in the passive cavity and characterized by a resonant frequency ${\omega }_m$, damping rate ${\mathrm{\Gamma }}_m$, an effective mass $m$, and optomechanical coupling constant $g$. The other cavity with optical gain is active, while the optical nonlinearity is omitted. Two cavities are directly coupled by the coherent photon tunneling strength $J$. The optical excitation is achieved by a tapered fiber coupled to the passive cavity with the coupling rate ${\kappa }_e$. The cavity output can be monitored by using an optical spectrum analyzer. The inset shows the transmission characteristics of high-order optical sidebands.

Figure 2

(a) Efficiency rate $\eta$ of the probe light versus the optical detuning ${\mathrm{\Delta }}_p={\omega }_p-{\omega }_0$, for different values of the gain-to-loss ratio. The optical tunneling rate is fixed as $J/\gamma =1$. (b) Maximum transmission rate of the second-order sideband generation $\eta$ of the probe field versus the gain-to-loss ratio $\kappa /\gamma$ with ${\mathrm{\Delta }}_p={\omega }_m$. Other parameters are as in Table 1.

Figure 3

Calculation result of $\eta$ as a function of the detuning ${\mathrm{\Delta }}_p$ under two different values of the coupling strength $J$ for the passive-passive compound COM system (i.e., $\kappa /\gamma =-1$) and the active-passive compound COM system (i.e., $\kappa /\gamma =1$). We use the coupling strength $J/\gamma =0.2$ and $J/\gamma =2$.

Figure 4

Maximum value of $\eta$ in logarithmic scale changes with the photon-tunneling rate $J$ for (a) the passive-passive and (b) the active-passive compound COM system with ${\mathrm{\Delta }}_p={\omega }_m$.

Figure 5

(a) Transmitted output (in logarithmic scale) of the generated higher-order sidebands as a function of the gain-to-loss ration $\kappa /\gamma$ and sideband number $N$. Panels (b) and (c) are the the passive-passive (i.e., $\kappa /\gamma =-8$) and active-passive compound COM system (i.e., $\kappa /\gamma =0.8$), respectively. The other system parameters are in Table 1.

Figure 6

Spectra and real-time interferogram intensity of transmitted output in (a),(b) the broken $\mathcal{PT}$ symmetric phase, (c),(d) EP, (e),(f) the $\mathcal{PT}$ symmetric phase, and (g),(h) the passive-passive regime. At EP, $J=(\gamma +{\kappa }_e+\kappa )/4$. The parameters are $J=2\gamma ,{\kappa }_e=\kappa$, and $\mathrm{\Delta }T=1/{\omega }_m=1.93e^{-8}\text{s}$.