Steady-State Losses of Optical Fibers and Fiber Resonators

We consider a multimode optical fiber with random imperfections. It is well-known that any type of imperfection built into a fiber causes coupling among its guided modes. 1-3 In a long fiber, the distribution of average power versus mode label approaches a steady state t h a t 1445 can be described by a steady-state loss coefficient and a unique distribution function. 3 Now assume t h a t we take a section of this fiber, place reflectors at either end, and observe the steady-state power distribution of this cavity. Without giving the matter much thought, we might expect the steady-state power distribution of the resonator to be identical to the steady-state power distribution of the long fiber. However, this is not the case. Mode coupling in a resonator has a very different effect on the steady-state power distribution and its loss coefficient than coupling in a long fiber. The reason for this difference in behavior is the fact t h a t the wave traveling back and forth in the resonator experiences a periodic structure whose Fourier transform has a line spectrum. In a resonator of length L/2, two modes with propagation constants and /32 are effectively coupled only if they satisfy the condition (3i -- = 2vn/L, where n is an integer. The losses and steady-state power distribution of the long fiber and the corresponding fiber resonator are very different. It is the purpose of this paper to clarify these differences. We dramatize the difference of the fiber and the resonator by considering a fiber supporting only two guided modes.