A time-dependent analysis of an all-single-mode fiber-optic resonator is presented in which the input field is allowed to exhibit an arbitrary dependence on time. In particular, the transmissivity of the resonator is evaluated for an input field possessing an arbitrary temporal coherence, which allows one to consider the role of the source coherence time as compared with the fiber time delay.A passive-loop resonator can be constructed by means of a polarization-preserving monomode optical fiber and of a low-loss single-mode-fiber directional coupler, as illustrated in Fig. 1. An input field( 1) launched into the coupler at the input port 1 will partially emerge at port 3, from which it is guided along the fiber loop and reaches port 2 and will be partially coupled to the output port 4. The field at port 2 will couple partially to port 4 and partially to port 3, thus continuing to circulate in the loop.The characteristics of this all-fiber ring resonator have been investigated both theoretically and experimentally 1 ' 2 in a completely coherent case in which the coherence time t, of the field is implicitly assumed significantly to exceed -r = LIV, where L is the fiber loop length and V = (do3/dw)-l is the group velocity of the propagating mode. More recently, an analysis of the performance characteristics of the resonator in terms of the light-source coherence was carried out 3 in which the exciting source was assumed to be an amplitude-stabilized single-mode laser fieldwith a correlation time T* of the instantaneous frequency-correlation function (0(t)k(t')) much shorter than r.In this Letter we report on the case in which el (t) exhibits an arbitrary time dependence (as long as the bandwidth of the input field satisfies the relation bc&v/ << 1 and the fiber chromatic dispersion can be neglected) and derive a general expression for the resonator transmissivity T in terms of the autocorrelation functionof the input field. This analysis finds its practical justification in the fact that, as the length L of the loop increases, r can become comparable with t,.The behavior of the field inside the resonator can easily be obtained by relying on the pertinent geometry sketched in Fig. 1. More precisely, after indicating by 63(t) and E4(t) the complex amplitudes of the fields at ports 3 and 4, one immediately getswhere k is the (intensity) coupling coefficient, yo = (I e1l 2 + I E212 ) is the fractional coupler intensity loss, and we have used the relation, and b = (1 --yo)exp(-aoL + if3L). E 2 (t) = exp(-oL + iflL)E 3 (t -), ao being the amplitude-attenuation coefficient of the fiber. By eliminating E 3 from the set of Eqs. (4), one finds the following relation between E4 and E 1 :E 4 (t) -Xe 4 (t -r) = ae 1 (t) + bE 1 (t -