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Chinese Physics Letters

Propagation of Few-Cycle Pulse Laser in Two-Level Atom Medium

Xiao Jian, Zhongyang Wang, Zhizhan Xu

Published Jul 1, 2001• 3 citations
Publisher

Abstract

By comparing the numerical solutions of Maxwell-Bloch equations beyond and within the slowly-varying envelope approximation and the rotating-wave approximation for the propagation of a few-cycle pulse laser in a resonant two-level atom medium, we found that both the Rabi flopping and the refractive index, and subsequently the carrier and the propagation velocity of the few-cycle pulse, are closely connected with the time-derivative behaviour of the electric field. This is because the Rabi flopping is such that the soliton pulse splits during propagation and that a shorter pulse propagates faster than a broader one.

DOI
10.1088/0256-307x/18/7/322

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By comparing the numerical solutions of Maxwell-Bloch equations beyond and within the slowly-varying envelope approximation and the rotating-wave approximation for the propagation of a few-cycle pulse laser in a resonant two-level atom medium, we found that both the Rabi flopping and the refractive index, and subsequently the carrier and the propagation velocity of the few-cycle pulse, are closely connected with the time-derivative behaviour of the electric field. This is because the Rabi flopping is such that the soliton pulse splits during propagation and that a shorter pulse propagates faster than a broader one.
The phase-dependent feature of few-cycle pulsed laser propagation in a resonant two-level atom medium is demonstrated by solving the full Maxwell-Bloch equations. Even in the perturbative region, the propagating carrier field and the corresponding spectra of the few-cycle pulsed laser are sensitive to the initial phase due to self-phase modulation. For the larger pulse area, the fact that the carrier-wave reshaping comes from the carrier-wave Rabi flopping is also responsible for this sensitivity, and the phase-dependent feature is more evident.
We have studied the spectral behaviour of few-cycle soliton pulses in a non-resonant two-level atom medium by solving the full Maxwell-Bloch equations. It is demonstrated further that the carrier effects play an important role in the propagation of the few-cycle pulse laser. When the frequency detuning is not very large, both the population distribution and the refractive index of the medium follow the oscillatory carrier field instantaneously; in this case, carrier-wave compression or carrier shock occurs and a supercontinuum broader than that in the resonant medium may be generated. When the frequency detuning is large, the carrier shock is weak and the spectrum is not continuous, only showing an odd harmonic radiation.
By solving the Maxwell-Bloch equations, we study the area evolution of a few-cycle pulse laser propagating in a resonant two-level-atom medium. We find that in short propagation distance, the pulse envelope, obtained within the slowly varying envelope approximation and the rotating-wave approximation, agrees nicely with the carrier field. In this case, the area theorem can still predict the profile of the area evolution of a few-cycle optical pulse. However, contrary to the long-pulse case, the variation of the few-cycle pulse area is caused by the pulse splitting but not by the pulse broadening or the pulse compression. Furthermore, the negative area occurs when the pulse area decreases. As a result, a pulse with area less than $\ensuremath{\pi}$ is not absorbed rapidly according to the usual Beer's law of absorption but evolves to nonvanishing zero $\ensuremath{\pi}$ pulse.
We have studied the spectral behaviour of few-cycle soliton pulses in a non-resonant two-level atom medium by solving the full Maxwell-Bloch equations. It is demonstrated further that the carrier effects play an important role in the propagation of the few-cycle pulse laser. When the frequency detuning is not very large, both the population distribution and the refractive index of the medium follow the oscillatory carrier field instantaneously; in this case, carrier-wave compression or carrier shock occurs and a supercontinuum broader than that in the resonant medium may be generated. When the frequency detuning is large, the carrier shock is weak and the spectrum is not continuous, only showing an odd harmonic radiation.
Propagation of a few-cycle laser pulse in a dense V-type three-level atomic medium is investigated by the numerical solution of the full Maxwell–Bloch equations without the rotating wave and slowly varying envelope approximations, and the numerical solution is obtained by using the predictor–corrector method and the finite-difference time-domain method. It is shown that, due to the strength of the electric field induced by the macroscopic polarization in a dense medium being stronger than that in a dilute medium and the influence of the near dipole–dipole (NDD) interaction, the time evolution of a few-cycle pulse in the dense medium is remarkably different from that in the corresponding dilute medium. In the dilute medium, oscillation arises at the trailing edge of the pulse; while in the dense medium, it appears at both the leading and trailing edges of the pulse; moreover, the oscillation at the leading edge is more obvious with the pulse area decreasing. The carrier-envelope phase has an obvious difference in the two cases with and without NDD interaction. The ratio, γ, of the transition dipole moments has strong influence on the time evolution and split of the pulse. In the dense medium, when γ = 1, NDD interaction delays propagation and split of the pulse; while when γ > 1, NDD interaction accelerates propagation and split of the pulse, moreover, the phenomenon is more obvious with the input pulse area decreasing. In the dilute medium, the larger area pulse doesn't split when γ = 1 while it splits when γ > 1.