Generalisation of the Menegozzi & Lamb Maser Algorithm to the Transient Superradiance Regime

TL;DR

This paper extends the Menegozzi & Lamb maser algorithm to accurately simulate transient superradiance in the high field regime by deriving a convergent integral Fourier representation of the Maxwell-Bloch equations, enabling efficient and flexible modeling.

Contribution

We develop a generalized, convergent Fourier-based algorithm for transient superradiance, improving upon the original ML method's limitations in high field regimes.

Findings

The new algorithm accurately reproduces transient SR responses.

It is computationally efficient with $ ext{O}(N)$ complexity.

Fidelity can be adjusted for different velocity distributions.

Abstract

We investigate the application of the conventional quasi-steady state maser modelling algorithm of Menegozzi & Lamb (ML) to the high field transient regime of the one-dimensional Maxwell-Bloch (MB) equations for a velocity distribution of atoms or molecules. We quantify the performance of a first order perturbation approximation available within the ML framework when modelling regions of increasing electric field strength, and we show that the ML algorithm is unable to accurately describe the key transient features of R. H. Dicke's superradiance (SR). We extend the existing approximation to one of variable fidelity, and we derive a generalisation of the ML algorithm convergent in the transient SR regime by performing an integration on the MB equations prior to their Fourier representation. We obtain a manifestly unique integral Fourier representation of the MB equations which is $\mathcal{O}\left(N\right)$ complex in the number of velocity channels $N$ and which is capable of simulating transient SR processes at varying degrees of fidelity. As a proof of operation, we demonstrate our algorithm's accuracy against reference time domain simulations of the MB equations for transient SR responses to the sudden inversion of a sample possessing a velocity distribution of moderate width. We investigate the performance of our algorithm at varying degrees of approximation fidelity, and we prescribe fidelity requirements for future work simulating SR processes across wider velocity distributions.