Analysis of pattern forming instabilities in an ensemble of two-level atoms optically excited by counter-propagating fields

TL;DR

This paper investigates pattern forming instabilities in cold two-level atomic clouds driven by counter-propagating laser fields with feedback, analyzing nonlinear propagation, gratings, and thresholds to match experimental observations.

Contribution

It introduces a comprehensive formalism for modeling pattern formation in a thick medium with feedback, including absorption effects and various grating interactions.

Findings

Feedback reduces the instability threshold by a factor of two.

Envelope curves effectively bound all threshold variations with mirror distance.

Results align well with experimental data on length scales and thresholds.

Abstract

We explore various models for the pattern forming instability in a laser-driven cloud of cold two-level atoms with a plane feedback mirror. Focus is on the combined treatment of nonlinear propagation in a diffractively thick medium and the boundary condition given by feedback. The combined presence of purely transverse transmission gratings and reflection gratings on wavelength scale is addressed. Different truncation levels of the Fourier expansion of the dielectric susceptibility in terms of these gratings are discussed and compared to literature. A formalism to calculate the exact solution for the homogenous state in presence of absorption is presented. The relationship between the counterpropagating beam instability and the feedback instability is discussed. Feedback reduces the threshold by a factor of two under optimal conditions. Envelope curves which bound all possible threshold curves for varying mirror distances are calculated. The results are comparing well to experimental results regarding the observed length scales and threshold conditions. It is clarified where the assumption of a diffractively thin medium is justified.