Simultaneous vibrational resonance in the amplitude and phase quadratures of an optical field based on Kerr nonlinearity

Vibrational resonance (VR) is a nonlinear phenomenon in which the system response to a weak signal can be resonantly enhanced by applying a high-frequency modulation signal with an appropriate amplitude. The majority of VR research has focused on amplifying the amplitude or intensity of the system response to a weak signal, whereas the study of the phase information of system responses in VR remains limited. Here, we investigate the VR phenomena in both amplitude and phase quadratures of an optical field in a Kerr nonlinear cavity driven by a near-resonant weak signal and a far-detuned modulation signal. Analytical and numerical results demonstrated that the resonant enhancement in the amplitude and phase quadratures of the system response to a weak signal simultaneously occurs as the amplitude of the modulation signal is varied. There is a linear relation between the amplitude and frequency of the modulation signal for achieving an optimal VR effect. Furthermore, we generalized our study to investigate the quadrature at an arbitrary phase and determined that the VR enhancement sensitively depends on the phase. Our findings not only broaden the scope of VR research by incorporating phase information but also introduces an approach for amplifying an optical field by manipulating another optical field.