Accurate analytic expressions for gain in a Pr3+: ZBLAN fiber amplifier using modified Gaussian field functions

Pr³⁺: ZBLAN fiber amplifiers are likely to be important components for 1.3 μm fiber systems. Efficient amplifiers require high Δn small-core fibers. Expressions for the gain of such amplifiers have been derived. To obtain useful analytic expressions, it is necessary to approximate the mode field distribution with a simple function. For this type of fiber, the usual Gaussian is not a good approximation, resulting in poor predictions of amplifier performance. This paper describes the use of a modified Gaussian function which better approximates the mode field distribution. It is shown by comparison to a full numerical solution that the analytic expressions based on this modified Gaussian are significantly more accurate