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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] 

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] 

<img src='content_image/331226.jpg'>

<img src='content_image/331241.jpg'>

Here Δ$_{c}$ = ω$_{p}$ − ω$_{c}$ is the detuning of the probe field from the cavity resonance and 

is the cavity pumping rate. 

<img src='content_image/331240.jpg'>

It is clear that the interaction of the quantum cavity field with the external classical probe field can be described by the Hamiltonian 

<img src='content_image/331239.jpg'>

Note that the power of the transmitted field is related to the mean intracavity photon number ¯ n via the formula [34] 

<img src='content_image/331236.jpg'>

When we insert Eq. (10) into Eq. (13) and compare the result with Eq. (8), we find 

and 

<img src='content_image/331237.jpg'>

<img src='content_image/331238.jpg'>

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 

