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Analysis of the data of FM SR lineshapes using a fitting method that simultaneously accounts for the dispersive and the dissipative effects of the resonant coupling. In the theoretical model, two dimensionless parameters A and B describe the overall z-3 coupling. A=2k3C3/γ0 represents the strength of the vW attraction (γ0, homogeneous linewidth) and B = k3Γ (k = ω0/c with ω0 the frequency of the probed transition in the free space) is for the modified decay rate, with the resonantly-enhanced transition width defined by:γ(z) = γ0(1+Γ/z3). The experiments are performed on Cs (6D32/) interacting with a sapphire surface with its c-axis parallel to the surface. Fits are carried out for the two hyperfine components (F = 3 and F = 4) of the probed transition 6P12/ → 6D32/, and for different values of the Cs temperature. In comparison, present report deals with a situation when the two parameters A and B are comparable, as due to the detuning of the sapphire polariton resonance with the birefringence orientation axis: indeed, for a c-axis parallel to the sapphire window, the atomic de-excitation channel is close to the center of the surface resonance, and this tends to maximize the dissipative effects, while the associated dispersive effect is no longer the dominant one.