Carrier-envelope phase dependence in single-cycle laser pulse propagation with the inclusion of counter-rotating terms

TL;DR

This study investigates how including counter-rotating terms in the Maxwell-Bloch equations affects the propagation of single-cycle laser pulses, revealing phase-dependent soliton delays useful for phase measurement.

Contribution

It introduces a modified model incorporating counter-rotating terms, showing their significant impact on pulse broadening, group velocity, and phase-dependent soliton timing.

Findings

Counter-rotating terms suppress pulse broadening.

Carrier-envelope phase influences soliton delay.

Modified equations alter pulse propagation dynamics.

Abstract

We focus on the propagation properties of a single-cycle laser pulse through a two-level medium by numerically solving the full-wave Maxwell-Bloch equations. The counter-rotating terms in the spontaneous emission damping are included such that the equations of motion are slightly different from the conventional Bloch equations. The counter-rotating terms can considerably suppress the broadening of the pulse envelope and the decrease of the group velocity rooted from dispersion. Furthermore, for incident single-cycle pulses with envelope area 4$\pi$, the time-delay of the generated soliton pulse from the main pulse depends crucially on the carrier-envelope phase of the incident pulse. This can be utilized to determine the carrier-envelope phase of the single-cycle laser pulse.