It is interesting to note that 〈 a $^{†}$a 〉 = 〈 a $^{†}$〉〈 a 〉 , 〈 σ $^{†}$σ 〉 = 〈 σ $^{†}$〉〈 σ 〉 , and 〈 a $^{†}$σ 〉 = 〈 a $^{†}$〉〈 σ 〉 . These relations are valid only in the case of a weakly driven cavity. The explicit expressions for the mean photon number N$_{cav}$ = 〈 a $^{†}$a 〉 and the atomic excited-state population P$_{e}$ = 〈 σ $^{†}$σ 〉 can be represented in the forms N$_{cav}$ = η $^{2}$(Δ2 a + γ $^{2}$/ 4) ( G 2 + κγ/ 4 − Δ$_{c}$Δ$_{a}$) 2 + (Δ$_{c}$ γ + Δ$_{a}$ κ ) $^{2}$/ 4 (33) and P$_{e}$ = η $^{2}$G2 ( G 2 + κγ/ 4 − Δ$_{c}$Δ$_{a}$) 2 + (Δ$_{c}$ γ + Δ$_{a}$ κ ) $^{2}$/ 4 , (34) respectively. Since the parameters G , γ , and Δ$_{a}$ vary in space, the intensity of the transmitted light depends on the position of the atom. We note from Eq. (33) that the atom can significantly affect the guided cavity field if the condition G 2 ≫ max( κγ/ 4 , | Δ$_{c}$ || Δ$_{a}$ | , | Δ$_{c}$ | γ/ 2 , | Δ$_{a}$ | κ/ 2) is satisfied. It has been shown that, in the case of a high-finesse microcavity driven by a weak probe field, under the condition of strong cou- pling, the position of the atom can be inferred from the intensity of the transmitted light [2–6]. IV. NUMERICAL RESULTS In this section, we present our numerical results. We use a truncated basis to solve numerically the density-matrix equations (26) in the steady-state regime. From the steady- state solution for the density matrix ρ , we calculate the mean number N$_{cav}$ = 〈 a $^{†}$a 〉 of photons in the guided cavity field and the population P$_{e}$ = 〈 σ $^{†}$σ 〉 of the atomic excited state. We also calculate the second-order photon correlation function g (2) cav = 〈 a $^{†}$a$^{†}$aa 〉 / 〈 a $^{†}$a 〉 $^{2}$, which characterizes the photon statistics [35]. It is known that the photon distribution of a coherent state is a Poisson distribution, which gives g (2) cav = 1. When g (2) cav > 1 or g (2) cav < 1, the photon statistics is said to be super- or sub-Poissonian, respectively. The occurrence of sub-Poissonian photon statistics, indicated by the inequality g (2) cav < 1, means that the state of the field is nonclassical [35]. We plot in Fig. 2 the mean number N$_{cav}$ of intracavity photons and the population P$_{e}$ of the atomic excited state as functions of the distance r − a from the atom to the fiber surface. The FBG mirror reflectivity is | R | 2 = 0 . 9, which corresponds to the finesse F = π | R | / (1 − | R | $^{2}$) ∼ = 30, a moderate value. The FBG cavity length is L = 10 cm. 12