Sensitive dependence of the linewidth enhancement factor on electronic quantum effects in quantum cascade lasers

TL;DR

This paper presents a comprehensive method to calculate the linewidth enhancement factor in quantum cascade lasers, accounting for quantum effects and electronic interactions, crucial for laser frequency stability and comb formation.

Contribution

It introduces a general scheme using non-equilibrium Green's functions to systematically include all relevant electronic effects in LEF modeling.

Findings

LEF in quantum cascade lasers ranges from 0.1 to 1 depending on bias and frequency.

Quantum many-body effects significantly influence the LEF.

The method accurately predicts the impact of various electronic effects on laser linewidth.

Abstract

The linewidth enhancement factor (LEF) describes the coupling between amplitude and phase fluctuations in a semiconductor laser, and has recently been shown to be a crucial component for frequency comb formation in addition to linewidth broadening. It necessarily arises from causality, as famously formulated by the Kramers-Kronig relation, in media with non-trivial dependence of the susceptibility on intensity variations. While thermal contributions are typically slow, and thus can often be excluded by suitably designing the dynamics of an experiment, the many quantum contributions are harder to separate. In order to understand and, ultimately, design the LEF to suitable values for frequency comb formation, soliton generation, or narrow laser linewidth, it is therefore important to systematically model all these effects. In this comprehensive work, we introduce a general scheme for computing the LEF, which we employ with a non-equilibrium Green's function model. This direct method, based on simulating the system response under varying optical intensity, and extracting the dependence of the susceptibility to intensity fluctuations, can include all relevant electronic effects and predicts the LEF of an operating quantum cascade laser to be in the range of 0.1 - 1, depending on laser bias and frequency. We also confirm that many-body effects, off-resonant transitions, dispersive (Bloch) gain, counter-rotating terms, intensity-dependent transition energy, and precise subband distributions all significantly contribute and are important for accurate simulations of the LEF.