Derivation of Impulse Response and Transfer Function of an Optical Fiber under Chromatic Dispersion and Application to a Linear Fiber-optic Communication System

Treating the frequency-dependent time delay caused by the presence of chromatic dispersion in a fiber-optical channel of length L as a random variable, it is possible to obtain a simple expression for the impulse response of the channel. This idea is used to derive the impulse response in terms of parameters such as the zero-dispersion wavelength, the second derivative of the refractive index, and the linewidth of the source. The result indicates an asymmetrical impulse response, and the corresponding transfer function has a low-pass characteristic with a first-order pole which may be readily determined from the fiber parameters.The derived impulse response is applied to the case of a simple fiber-optic communication system configured as a phase diversity receiver, to illustrate how a linear systems approach, under certain approximations, may be used to predict and analyze the behavior of such a system. The analysis includes calculations involving the field amplitudes in (n×n) hybrid couplers, and how such couplers must be connected in order to obtain the desired optical components in the phase diversity scheme is described.