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.
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.
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.
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 .
We investigate effect of atomic densities (N) on propagation and spectral property of large area femtosecond Gaussian pulse (the pulse area is larger than 2π) in a three-level Λ-type atomic medium by using the numerical solution of the full Maxwell-Bloch equations without the slowly varying envelope and the rotating-wave approximations, and the solution is obtained by PC-FDTD method. It is shown that, variation of value of the atomic density has considerable effect on propagation and spectral property and the effect is closely relative to size of the pulse area. For the pulse with area 4π, propagate in the dilute medium with smaller atomic density, clear pulse splitting doesn’t occur, slight pulse spectrum broadening appears, the strength of the spectral component with higher frequency increases with the distance increasing; when the pulse propagates in the dilute medium with larger atomic density and in the dense medium, the main pulse splits into two sub-pulses, and the spectrum broadening in the dilute medium with larger atomic density is much larger than that in the dense medium. For the pulse with larger area 8π, the case of the pulse propagates in the dilute medium with smaller atomic density is similar to that of the 4π pulse; but when the pulse propagates in the dilute medium with larger atomic density and in the dense medium, the case is considerably different from that for 4π pulse, the main pulse splits into three sub-pulses, and the spectrum broadening in the dilute medium with larger atomic density is much smaller than that in the dense medium.
We investigate effect of atomic densities( N) on propagation and spectral property of femtosecond Gaussian pulses in a three-level Λ- type atomic medium by using numerical solution of full Maxwell-Bloch equations. It is shown that,for pulses with smaller area 2π,propagate in mediums with different N,pulse splitting does not occur and strength of spectral component near central frequency decreases considerably as N increases. For pulses with area 4π,pulse splitting could occur when pulses propagate in dilute medium with greater atomic density and in dense medium,and pulse spectral bandwidth and strength of spectral component with higher frequency increase with increasing of N in dilute medium. Spectrum broadening in dense medium is much smaller than that in dilute medium with greater atomic density. For pulses with larger area 8π,pulse splitting is similar to that of 4π pulses. Pulse spectral bandwidth and strength of spectral component with higher frequency increase monotonously with increasing of N. And spectrum broadening in dense medium is much larger than that in dilute medium with smaller atomic density.
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 interference resonant propagation of two-color 4π-4π femtosecond Gaussian pulses in three-level Λ-type atomic medium with different values of the relative phase φ is investigated by using numerical solution, which is obtained by the finite-difference time domain (FDTD) method and the iterative predictor–corrector (PC) method for the full Maxwell-Bloch equations. It is found that, for a smaller value of the φ, the pulse splitting occurs, and when the value of the φ increases to a certain value, only the variation of pulse shape present but the pulse splitting no longer occurs; accordingly, their spectral strengths and frequency ranges of the two-color pulses decrease remarkably with the value of φ increasing; Moreover, the relative phase also has an obvious effect on population, different population evolutions can be achieved by adjusting the value of φ.