Derivation of analytical expressions for optical gain coefficient in bulk semiconductors

TL;DR

This paper introduces new analytical expressions for calculating the optical gain coefficient in bulk semiconductors using special functions, offering a precise alternative to numerical methods for semiconductor laser analysis.

Contribution

The paper develops novel analytical formulae involving polylogarithm and incomplete gamma functions for optical gain, improving accuracy over standard numerical approaches.

Findings

Provides accurate analytical expressions for optical gain

Validates formulae with different parameter values

Confirms results with existing literature data

Abstract

An analytical model is proposed to determine the expressions of the semiconductor optical gain coefficient by using the special functions. These expressions differ from the standard numerical calculations approaches and they involve sums of the polylogarithm and incomplete gamma functions. One of the calculation results presented here reproduces formulae developed in the study. The new formulae obtained here provide a sufficient way to calculate the semiconductor optical gain on the total carrier density and temperature in the semiconductor lasers. The obtained analytical expression gives an accurate and precise evaluation of the semiconductor gain function. The performance of the proposed formula is confirmed by its implementation of the different values of the parameter. The sufficiency obtained results of this approach was confirmed by the other literature data.