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Journal of Modern Optics

Time evolution of few-cycle pulse in a dense V-type three-level medium

Xia Tan, Xijun Fan, Yanling Yang, D. M. Tong

Published Jul 3, 2008• 19 citations
Publisher

Abstract

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.

DOI
10.1080/09500340802130670

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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.
Propagation of a few-cycle laser pulses in a dense V-type three-level atomic medium is investigated based on full-wave Maxwell-Bloch equations by taking the near dipole-dipole (NDD) interaction into account.We find that the ratio, γ, of the transition dipole moments has strong influence on the time evolution and split of the pulse: when γ ≤ 1, the NDD interaction delays propagation and split of the pulse, and this phenomenon is more obvious when the value of γ is smaller; when γ = √ 2, the NDD interaction accelerates propagation and split of the pulse.
Using the numerical solution of the full Maxwell-Bloch equations without the slowly varying envelope approximation and the rotating-wave approximation, propagation behavior of few-cycle laser pulse in a dense ladder-type three-level atomic medium is investigated and it is compared with the case in the corresponding dilute medium. It is found that, in the propagation process, time evolution of the pulse in the dense medium is obviously different from that in the dilute medium, and the difference will become more evident with increasing of the initial pulse area. When the initial pulse area is smaller, in the propagating process, the pulse shape in the dilute medium just have a small change; the pulse shape in the dense medium has considerable variation but the pulse splitting doesn't occur. When the initial pulse area is larger enough, for the dense medium case, the pulse splits into sub-pulses with different numbers and shapes at different propagation distances; while for the dilute medium case, variation of the pulse shape is still smaller in propagation process. The cause producing above difference is from two effects in the dense medium: the effect of the local-field correction (LFC) from the near dipole-dipole interaction and effect of stronger polarization field than that in the dilute medium. In which the effect of stronger polarization field plays a main role, but the role of LFC also cannot be neglected,and the stronger polarization field is due to the atomic density increasing .
Full Maxwell-Bloch equations are solved with PC-FDTD method to investigate population evolution of dense V-type three-level medium in few-cycle laser pulses.It is shown that the ratio of transition dipole moments(γ) has strong influence on appearing time and oscillation frequency of population inversion.As γ=1 population inversion with LFC appears later than that without LFC and near dipole-dipole(NDD) interaction delays population inversion.As γ1,appearing with LFC is earlier than that without LFC and NDD interaction accelerates the population inversion.The number of population inversion with unequal transition dipole moments is more than that with equal transition dipole moments.Moreover,evolution of populations in a dense medium is quite different from that in a dilute medium.At input surface,in a dilute medium,population inversion appears with time evolution.With increasing of medium density,populations show quasi-periodicity oscillation and oscillation frequencies of populations with LFC are less than that without LFC.
Full Maxwell-Bloch equations were solved by Predictor-Corrector method and finite-difference time-domain method to investigate spectrum of a sub-cycle laser pulse propagating in a dense Λ-type three-level atomic medium.It is found that both in a dilute medium and a dense medium,the spectrum is broaden due to the self-phase modulation(SPM);however,the width is much larger in the dense medium than that in a dilute medium because of NDD interaction.In the dense medium,the supercontinuum spectrum occurs due to SPM and NDD interaction,and the maximum frequency is 10 ωp.
We investigate numerically the propagation behaviors of an ultrashort laser pulse in a dense Λ-type three-level atomic medium by using the full Maxwell-Bloch equations without the slowly varying envelope approximation and the rotating-wave approximation. We find that with propagation distance and time increasing, variations of the Rabbi frequency and the population in a dense medium are quite different from those in a dilute medium even though Lorentz local field correction (LFC) is not considered. In a dilute medium, the populations occupied initially at the ground state are completely transferred into the lower excited-state with the increase of the propagation distance; however, in the dense medium, about a half is still kept on the ground state and the others are transferred into the lower excited-state. The population oscillation occurs at the input surface of a dense three-level medium due to carrier-wave Rabi oscillation, and the oscillating time with LFC is much longer than that without LFC; the time derivative of the electric field has stronger effects on the time evolution of the pulse in the dense medium than that in a dilute medium, which is clearly shown from the time evolution of the Rabi frequency; especially the oscillating amplitude with LFC in the trailing edge of the pulse is larger than that without LFC at the input surface of the three-level medium.
The propagation behaviors, which include the carrier-envelope phase, the area evolution and the solitary pulse number of few-cycle pulses in a dense two-level medium, are investigated based on full-wave Maxwell-Bloch equations by taking Lorentz local field correction (LFC) into account. Several novel features are found: the difference of the carrier-envelope phase between the cases with and without LFC can go up to pi at some location; although the area of ultrashort solitary pulses is lager than 2pi, the area of the effective Rabi frequency, which equals to that the Rabi frequency pluses the product of the strength of the near dipole-dipole (NDD) interaction and the polarization, is consistent with the standard area theorem and keeps 2pi; the large area pulse penetrating into the medium produces several solitary pulses as usual, but the number of solitary pulses changes at certain condition.