\hat{\bf d}_{1\omega} \\ \hat{\bf c}_{2\omega} \\ \hat{\bf d}_{2\omega}
\end{pmatrix}.\end{aligned}$$ $\mathcal{S}_{\omega}$ characterizes the transformation from Unruh modes to Rindler modes $$\begin{aligned}
\mathcal{S}_{\omega} = \left({S_{\omega} \atop 0}{ 0 
\atop S_{\omega}}\right)\end{aligned}$$ and $\mathcal{U}_{\omega}$ characterizes the action of the object $$\begin{aligned}
\mathcal{U}_{\omega} = 
\begin{pmatrix}
U^{11}_{\omega} & 0 & U^{12}_{\omega}  & 0 \\ 
0 & I  & 0 & 0 \\ 
U^{21}_{\omega} & 0 & U^{22}_{\omega}  & 0\\ 
0 & 0 & 0 & I 
\end{pmatrix}\end{aligned}$$ where $$\begin{aligned}
U^{mn}_{\omega} = \left({\alpha^{mn}_{\omega \omega} \atop \beta^{mn*}_{\omega \omega}}{ \beta^{mn}_{\omega \omega}
\atop \alpha^{mn*}_{\omega \omega}}\right).\end{aligned}$$ We emphasize that the general formalism developed here is valid for a wide class of quantum optical devices (objects), such as beamsplitters, single-mode squeezers, two-mode squeezers, cavities, and even for devices with time-dependent parameters, for example, beamsplitters with time-dependent transmission coefficients. In this paper, we mainly apply the formalism to the simplest case, a beamsplitter.

Circuit model for a uniformly accelerated mirror
------------------------------------------------

The perfect moving mirror problem has been extensively studied for several decades. A perfect moving mirror provides a clear boundary for a quantum field, which vanishes along the mirror’s trajectory. The standard method for calculating the radiation from a perfect moving mirror is to find the Bogoliubov transformation between the input and 