Probe response of photonic cavity with graphene sheet: slow light and fast light

Abstract

We analyze the probe response at strong and weak coupling regimes and group delay of a probe field in a cavity optomechanical system. In present system is coupled with a graphene sheet. A strong THz pulse is generated by exploiting the nonlinearity of graphene. The interaction between optical and mechanical modes gives induced transparency under different detuning conditions, during the optical propagation of a signal. Due to the nonlinearity of graphene, the intensity of the four-wave mixing (FWM) dynamically changes under a driving laser source, more surprisingly. We can adjust the FWM intensity by controlling the power of the probe laser. In this report, we have studied the real and imaginary parts of the relative amplitude of the output field to the input field, the phase of the probe field, the transmission rate, and group delay. The phase of the transmitted field shows both anomalous and normal dispersion. In the presence of the graphene, the group velocity is more prominent both in positive and negative regimes which is unique with respect to other models. This study may be useful for ultrafast optical signal processing, and optical storage to design many device applications in quantum communication.

Appendices

Appendix A

Let ${{a}_{1}}^{*}{a}_{1}=<{{a}_{1}}^{*}{a}_{1}>+\delta ({{a}_{1}}^{*}{a}_{1})$

$$\begin{aligned} a_{1}^{*} a_{1} a_{1}^{*} a_{1} & = \left\{ {\left\langle {a_{1}^{*} a_{1} } \right\rangle + \delta \left( {a_{1}^{*} a_{1} } \right)} \right\}\left\{ {\left\langle {a_{1}^{*} a_{1} } \right\rangle + \delta \left( {a_{1}^{*} a_{1} } \right)} \right\} \\ & = \left\langle {a_{1}^{*} a_{1} } \right\rangle^{2} + \left\langle {a_{1}^{*} a_{1} } \right\rangle \delta \left( {a_{1}^{*} a_{1} } \right) + \delta \left( {a_{1}^{*} a_{1} } \right)\left\langle {a_{1}^{*} a_{1} } \right\rangle + \left\{ {\delta \left( {a_{1}^{*} a_{1} } \right)} \right\}^{2} \\ \end{aligned}$$

Now neglecting the square of the fluctuation part, the value of ${{a}_{1}}^{*}{a}_{1}{{a}_{1}}^{*}{a}_{1}$ is given

$$\begin{aligned} a_{1}^{*} a_{1} a_{1}^{*} a_{1} & = \left\langle {a_{1}^{*} a_{1} } \right\rangle^{2} + 2\left\langle {a_{1}^{*} a_{1} } \right\rangle \delta \left( {a_{1}^{*} a_{1} } \right) \\ & = \left\langle {a_{1}^{*} a_{1} } \right\rangle^{2} + 2\left\langle {a_{1}^{*} a_{1} } \right\rangle \left( {a_{1}^{*} a_{1} - \left\langle {a_{1}^{*} a_{1} } \right\rangle } \right) \\ & = \left\langle {a_{1}^{*} a_{1} } \right\rangle^{2} + 2\left\langle {a_{1}^{*} a_{1} } \right\rangle (a_{1}^{*} a_{1} ) - 2\left\langle {a_{1}^{*} a_{1} } \right\rangle^{2} ) \\ & = - \left\langle {a_{1}^{*} a_{1} } \right\rangle^{2} + 2\left\langle {a_{1}^{*} a_{1} } \right\rangle (a_{1}^{*} a_{1} ) \\ \end{aligned}$$

Appendix B

We determine the ${A}_{+}$, ${B}_{+}$, ${C}_{+}$ by using the following relation $X=Y{M}^{-1}.$