# Simulation of Optical Fiber Amplifier Gain Using Equivalent Short Fibers

## TL;DR

This paper introduces an efficient modeling approach for optical fiber amplifiers using equivalent short fibers, enabling faster simulations while maintaining essential characteristics, validated through numerical studies on doped fibers.

## Contribution

The paper proposes a novel scale model called the equivalent short fiber that simplifies Maxwell-based simulations of optical amplifiers, improving computational efficiency.

## Key findings

- The equivalent short fiber model accelerates computations by a factor proportional to the length reduction.
- Numerical validation shows the model's effectiveness for specific fiber types.
- The model's applicability depends on fiber properties and desired accuracy.

## Abstract

Electromagnetic wave propagation in optical fiber amplifiers obeys Maxwell equations. Using coupled mode theory, the full Maxwell system within an optical fiber amplifier is reduced to a simpler model. The simpler model is made more efficient through a new scale model, referred to as an equivalent short fiber, which captures some of the essential characteristics of a longer fiber. The equivalent short fiber can be viewed as a fiber made using artificial (unphysical) material properties that in some sense compensates for its reduced length. The computations can be accelerated by a factor approximately equal to the ratio of the original length to the reduced length of the equivalent fiber. Computations using models of two commercially available fibers -- one doped with ytterbium, and the other with thulium -- show the practical utility of the concept. Extensive numerical studies are conducted to assess when the equivalent short fiber model is useful and when it is not.