Fano resonance and amplification in a quadratically coupled optomechanical system with a Kerr medium

We discuss the Fano resonance and amplification in a quadratically coupled optomechanical system with a nonlinear Kerr medium. We find that effective cavity detuning and the strength of the Kerr nonlinearity lead to the appearance of the Fano resonance in the output probe field at room temperature, respectively. We show that the Kerr nonlinearity causes the asymmetric line shape to appear in the intensities of the output Stokes field and the second-order upper sideband generation. We also show that the Kerr nonlinearity can amplify the intensities of the output Stokes field and the second-order upper sideband generation, and the amplification factor is related to the strength of the Kerr nonlinearity. The findings of this study have potential applications in optical switching and frequency conversion.

Figure 1

Sketch of the membrane-in-the-middle optomechanical system with a nonlinear Kerr medium. The arrows represent the directions of the input and output lights. The membrane acts as a mechanical oscillator.

Figure 2

The real part $\mathrm{Re}\left[t_p\right]$ of the output probe field as a function of the normalized probe-coupling detuning $\delta /{\omega }_m$ for different values of the effective cavity detuning $\mathrm{\Delta }=2{\omega }_m-\kappa ,2{\omega }_m-0.5\kappa ,2{\omega }_m,2{\omega }_m+0.5\kappa ,2{\omega }_m+\kappa$ in the absence of the Kerr nonlinearity ($u=0$).

Figure 3

The real part $\mathrm{Re}\left[t_p\right]$ of the output probe field as a function of the normalized probe-coupling detuning $\delta /{\omega }_m$ for different values of the strength of the Kerr nonlinearity $u=0$, 0.002 ${\mathrm{s}}^{-1}$, 0.005 ${\mathrm{s}}^{-1}$, 0.01 ${\mathrm{s}}^{-1}$ when the effective cavity detuning $\mathrm{\Delta }=2{\omega }_m$. The lower figure zooms the narrow dip near $\delta =2{\omega }_m$ in the upper figure for $u=0$ (green solid), 0.002 ${\mathrm{s}}^{-1}$ (red dashed).

Figure 4

The intensity $|t_s{|}^2$ of the output Stokes field as a function of the normalized probe-coupling detuning $\delta /{\omega }_m$ for different values of the strength of the Kerr nonlinearity $u=0$, 0.005 ${\mathrm{s}}^{-1}$, 0.01 ${\mathrm{s}}^{-1}$. The other parameters are the same as those in Fig. 3. The insets zoom the regions near $\delta /{\omega }_m=2$.

Figure 5

The intensity ${\left|\eta \right|}^2$ of the second-order upper sideband generation in the output field as a function of the normalized probe-coupling detuning $\delta /{\omega }_m$ for different values of the strength of the Kerr nonlinearity $u=0$, 0.005 ${\mathrm{s}}^{-1}$, 0.01 ${\mathrm{s}}^{-1}$ when ${\wp }_p=0.01{\wp }_c$. The other parameters are the same as those in Fig. 3. The insets zoom the regions near $\delta /{\omega }_m=2$.