Kerr-Controlled Light Drag Switching in Optomechanical Cavity

We present a comprehensive theoretical study of light drag effect in an optomechanical system incorporating Kerr non-linearity. The ability to dynamically control the speed and direction of light propagation is a well-established goal in optics, with applications ranging from all-optical routing to quantum information processing. We determine that an intensity-dependent refractive index, resulting from the Kerr limit [Formula: see text], provides exceptional control over the optomechanically induced transparency (OMIT) response. Our study shows that Kerr non-linearity changes the transparency condition of the OMIT to [Formula: see text], allowing for power-tunable control of the transparency frequency. Remarkably, we found that when the Kerr shift exceeds the critical value [Formula: see text], the dispersion slope reverses from normal to anomalous, resulting in a reversal of the light-dragging effect signal. This Kerr shift reversal enables complete optical switching between superluminal propagation (fast light) and subluminal propagation (slow light) exclusively by changing the power of the control laser. We systematically investigate the dependence of the light-drag on the probe detuning, laser detuning, mechanical damping rate, angular velocity and cavity decay rate. Our results show that the drag signal exhibits a linear dependence on the angular velocity, is maximal under the OMIT transparency condition and is significantly enhanced at low mechanical damping rates due to increased mechanical coherence and stronger optomechanical interaction. The drag signal enhancement factor is inversely proportional to the mechanical damping rate, demonstrating that high-quality mechanical resonators are essential for achieving strong optical drag effects.We demonstrate that the drag magnitude reaches [Formula: see text] [Formula: see text] for [Formula: see text] versus [Formula: see text] [Formula: see text] for [Formula: see text] when plotted versus probe detuning [Formula: see text] and laser detuning [Formula: see text], with linewidth broadening from FWHM [Formula: see text] to [Formula: see text] with increasing [Formula: see text]. Versus angular velocity [Formula: see text], the drag is antisymmetric [Formula: see text], zero at [Formula: see text], and saturates to [Formula: see text] versus [Formula: see text] for [Formula: see text], with low damping requiring smaller [Formula: see text] for saturation. Most importantly, Kerr non-linearity provides an all-optical knob to switch drag sign: below critical power [Formula: see text] OMIT dominates with positive drag up to [Formula: see text] [Formula: see text], at [Formula: see text] rad/s drag vanishes ([Formula: see text]) rad, and above critical power Kerr dominates giving negative drag down to [Formula: see text] [Formula: see text], with subsequent switching to [Formula: see text] [Formula: see text] at high [Formula: see text]. This demonstrates controllable fast-to-slow light switching and positive-to-negative rotary drag switching via pump intensity, crucial for non-reciprocal light propagation and rotational sensing. For experimentally achievable coefficients in silicon nitride cavities of [Formula: see text] radian/s and [Formula: see text], the required switching power is on the order of milliwatts, which is within current experimental possibilities. This work opens new avenues for fully optical control of light propagation in on-chip mechanical optoelectronic devices, with potential applications in quantum information processing, micro-sensing and optical buffering.