A typical single-mode silica glass fiber has a mode profile that is well approximated by a Gaussian beam. At λ = 1.55 μm, this Gaussian mode has a (1/e2 intensity) diameter of ∼10 μm. One method of launching light into a fiber calls for placing the polished end of the fiber in contact with (or close proximity to) the polished end of another, signal-carrying fiber that has a matching mode profile. Alternatively, a coherent beam of light may be focused directly onto the polished end of the fiber. If the focused spot is well aligned with the fiber's core and has the same amplitude and phase distribution as the fiber's mode profile, then the launched mode will carry the entire incident optical power into the fiber. In general, however, the focused spot is neither perfectly matched to the fiber's mode, nor is it completely aligned with the core. Under these circumstances, only a certain fraction of the incident optical power will be launched into the fiber. The numerical value of this fraction, commonly referred to as the coupling efficiency, will be denoted by η throughout this chapter.

It is well-known that the strength of the launched mode may be computed by evaluating the overlap integral between the mode profile and the (complex) light amplitude distribution that arrives at the polished facet of the fiber. The problem of computing the coupling efficiency η is thus reduced to determining the light amplitude distribution immediately in front of the fiber.