output modes by taking into account the Dirichlet boundary condition.

However a realistic mirror is not perfect but usually partially transparent, for which the Dirichlet boundary condition is not satisfied. In this paper, we are interested in a uniformly accelerated imperfect mirror whose motion looks nontrivial for an inertial observer. Rather than use the standard method (which is still valid if appropriate boundary conditions are considered), we shall employ the circuit model developed in the previous section, leading to a much simpler way to attack this problem.

The idea is to work in the accelerated frame, in which the mirror is static and can be considered as a beamsplitter. Without loss of generality, we assume that the mirror uniformly accelerates in the $R$ wedge. The beamsplitter transforms the right Rindler modes as $$\begin{aligned}
\label{beamsplitter}
\hat{b}^{\prime R}_{1\omega} &=&\text{cos}\,\theta_{\omega} \hat{b}^R_{1\omega}- i e^{i \phi_{\omega}} \text{sin}\,\theta_{\omega} \hat{b}^R_{2\omega}, \nonumber\\
\hat{b}^{\prime R}_{2\omega} &=&\text{cos} \,\theta_{\omega}  \hat{b}^R_{2\omega}- i e^{-i \phi_{\omega}} \text{sin}\,\theta_{\omega} \hat{b}^R_{1\omega},\end{aligned}$$ where $\theta_{\omega}$ an $\phi_{\omega}$ are frequency dependent. The relative phase shift $i e^{\pm i \phi_{\omega}} $ ensures that the transformation is unitary. The intensity reflection and transmission coefficients of the beamsplitter are $$\begin{aligned}
R_{\omega} = \text{sin}^2\,\theta_{\omega}, \,\,\,\,\,\,\,\, T_{\omega} =  \text{cos}^2\,\theta_{\omega}. \end{aligned}$$ By comparing Eqs. (\[beamsplitter\]) and 