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.
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.
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 .
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.
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.
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.
By solving the full Maxwell-Bloch equations,the effects of the carrier-envelope phase(CEP)on pulse propagating and spectra characteristics of few-cycle ultra short laser pulses in a dense V type three-level atomic medium are investigated.The results show that the carrier propagation and spectrum evolution of the pulse are sensitive to its CEP and the phase sensitivity is more obvious for larger area pulse.The CEP can affect the amplitude,propagating velocity and pulse splitting case.Moreover,under the same condition,the pulse spectra are affected by the initial carrier-envelope phases due to the different coherence effect,which don't induce obvious changes of higher spectral components.When,the super continuum with wider spectral range and better continuity of high frequency components can be obtained.
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.