In the framework of the input-output formulation for optical cavities, the evolution of the photon operator a for the field in an empty two-sided cavity is governed by the equation [34] ˙ a = − iω$_{c}$a − κ 2 a + √ κ/ 2 a$_{in}$ + √ κ/ 2 b$_{in}$. (9) Here a$_{in}$ and b$_{in}$ are the input photon operators for the left and right sides of the cavity, respectively, and κ is the cavity damping coefficient, which is assumed to be the same for the two sides. When the input field a$_{in}$ is an external coherent monochromatic probe field, with the frequency ω$_{p}$ and the power P$_{in}$ = ¯ hω$_{p}$ 〈 a † $_{in}$a$_{in}$ 〉 , and the input field b$_{in}$ is in the vacuum state, the mean number ¯ n = 〈 a $^{†}$a 〉 of photons in the cavity is given by [34] Here Δ$_{c}$ = ω$_{p}$ − ω$_{c}$ is the detuning of the probe field from the cavity resonance and is the cavity pumping rate. It is clear that the interaction of the quantum cavity field with the external classical probe field can be described by the Hamiltonian Note that the power of the transmitted field is related to the mean intracavity photon number ¯ n via the formula [34] When we insert Eq. (10) into Eq. (13) and compare the result with Eq. (8), we find and The external probe field excites the guided cavity mode µ$_{c}$ = ( ω$_{c}$, f$_{c}$, l$_{c}$ ), where f$_{c}$ = f$_{p}$ and l$_{c}$ = l$_{p}$ . In the single-mode regime, the electric positive-frequency component of the 6 P$_{out}$ = 1 2 ¯ hω$_{p}$κ ¯ n. (13) κ = (1 − | R | $^{2}$) v$_{g}$ | R | L (14) η = √ (1 − | R | $^{2}$) v$_{g}$P$_{in}$ 2 | R | L ¯ hω$_{p}$ . (15) H$_{P}$ = − i ¯ h ( ηe iω$_{p}$$^{t}$a − H . c . ) . (12) η = √ κ 2 P$_{in}$ ¯ hω$_{p}$ (11) ¯ n = η 2 κ $^{2}$/ 4 + Δ 2 c . (10)