Force-induced transparency and conversion between slow and fast light in optomechanics

The optomechanics can generate fantastic effects of optics due to appropriate mechanical control. Here we theoretically study effects of slow and fast lights in a single-sided optomechanical cavity with an external force. The force-induced transparency of slow and fast lights and the force-dependent conversion between the slow and fast lights result from effects of the rotating-wave approximation (RWA) and the anti-RWA, which can be controlled by properly modifying the effective cavity frequency due to the external force. These force-induced phenomena can be applied to control the light group velocity and to detect the force variation, which are feasible using current laboratory techniques.

Figure 1

Schematic diagram of the system. The COM consists of a fixed mirror and an oscillating mirror. The arrow with labels ${\varepsilon }_p,{\omega }_p$ is for a weak probe field and the arrow with labels ${\varepsilon }_d,{\omega }_d$ for a strong pump field. The output field is with the field amplitude ${\varepsilon }_{\mathrm{out}}$. An external force is applied on the oscillating mirror for producing the slow and fast light effects as discussed in the text.

Figure 2

(a) The steady state for the position $q_0$ vs the external force $f$ in the case of the pump field power $P_d=0.2$ mW. (b) The steady state for the position $q_0$ as a function of the pump field power in the case of the external force $f=-4\times {10}^{-6}$ N. Other parameters used are ${\omega }_d=2\pi c/\lambda$ with $\lambda =1064$ nm, ${\mathrm{\Delta }}_c=-10{\omega }_m,\kappa =2\pi \times 215$ kHz, $m=145$ ng, ${\omega }_m=2\pi \times 947$ kHz, and ${\gamma }_m=2\pi \times 141$ Hz.

Figure 3

(a) The real (solid line) and imaginary (dashed line) parts of ${\varepsilon }_T$ as functions of $\delta /{\omega }_m$ with $f_1=-4.74\times {10}^{-6}$ N. (b) The corresponding group velocity delay $\tau$ vs the normalized frequency $\delta /{\omega }_m$ for $f_1=-4.74\times {10}^{-6}$ N. (c) The real (solid line) and imaginary (dashed line) parts of ${\varepsilon }_T$ as functions of $\delta /{\omega }_m$ for $f_2=-3.88\times {10}^{-6}$ N. (d) The corresponding group delay $\tau$ vs the normalized frequency $\delta /{\omega }_m$ for $f_2=-3.88\times {10}^{-6}$ N. Other parameters are the same as in Fig. 2.

Figure 4

The real parts of ${\varepsilon }_T$ as functions of the force $f$ under the condition of the RWA, where we consider six typical values of $f/f_1$ from zero to values larger than 1.0. Other parameters are the same as in Fig. 3.

Figure 5

(a) The group velocity delay as a function of $f/f_1$ with $f_1=-4.74\times {10}^{-6}$ N and $\delta ={\omega }_m$. The blue (red) line is for an analytical (approximate) result by Eq. (6) [Eq. (7)]. (b) The group velocity delay as a function of $f/f_2$ with $f_2=-3.88\times {10}^{-6}$ N and $\delta =-{\omega }_m$. The blue (red) line is for an analytical (approximate) result by Eq. (6) [Eq. (8)]. Other parameters are the same as in Fig. 3.