The effect of pulse width on propagation characteristics of the femtosecond ultrashort laser pulse in V-type three-level atomic media with different densities is investigated by using the numerical solution,which is obtained by PC-FDTD method for the full Maxwell-Bloch equation.It is shown that the effect of the pulse width on propagation characteristics of the pulse is different for different atomic density cases.When the ultrashort pulse propagates in the dilute medium with smaller atomic density,the pulse is not easy to split.When the pulse doesn't split,the pulse amplitude will decrease obviously with the pulse width increasing.When the ultrashort pulse propagates in the medium with very large atomic density,the pulse is easy to split,and the number of sub-pulses increases with the pulse width increasing Moreover the increase of the pulse width accelerates the pulse splitting.
The effect of pulse width on propagation characteristics of the femtosecond ultrashort laser pulse in V-type three-level atomic media with different densities is investigated by using the numerical solution,which is obtained by PC-FDTD method for the full Maxwell-Bloch equation.It is shown that the effect of the pulse width on propagation characteristics of the pulse is different for different atomic density cases.When the ultrashort pulse propagates in the dilute medium with smaller atomic density,the pulse is not easy to split.When the pulse doesn't split,the pulse amplitude will decrease obviously with the pulse width increasing.When the ultrashort pulse propagates in the medium with very large atomic density,the pulse is easy to split,and the number of sub-pulses increases with the pulse width increasing Moreover the increase of the pulse width accelerates the pulse splitting.
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 propagation of femtosecond chirped Gaussian laser pulse in a dense 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 the sign and size of the chirp coefficient has considerable effect on pulse propagation property, and the effect is closely relative to size of the pulse area. When the area of chirped pulse is smaller than 4π, splitting doesn’t occur and the chirped pulse evolves gradually to an approximate normal Gaussian pulse (C=0), and this characteristic doesn’t vary with the chirp coefficient varying. However, variation of the chirp coefficient will changed the amplitude and group velocity of the pulse. For the positive chirp(C>0), amplitude and group velocity of the pulse decrease with chirp coefficient increasing, for the negative chirp(CC increasing. Both the chirped pulses with area equal to larger than 4π will split into sub-pulses of different numbers and shapes, the time and number of the pulse splitting will be determined by the sign and size of the chirp coefficient. But in the two cases, the pulse splitting patterns are much different, and the effects of the coefficient are also different. When the pulse area equals 4π, larger chirp coefficient will lead to increased sub-pulse number, but when the pulse area is larger than 4π, larger chirp coefficient will lead to decreased sub-pulse number. In addition, regardless of pulse area being larger or smaller, changing sign and size of the chirp coefficient always produces obvious effect on the atomic population.
Effects of pulse width on ultrashort laser pulse and spectrum and their carrier-envelope phase(CEP) dependence in a dense V-type three-level atomic medium are investigated with numerical solutions of a full Maxwell-Bloch equation without slowly varying envelope and rotating wave approximations.It is shown that: As pulse width is small,pulse splitting number is less,spectrum is wide,high-frequency part of the spectrum is significant,CEP has great effect on pulse and spectrum,particularly effect on time interval between sub-pulses and strength of high-frequency part is more obvious;As pulse width increasing,pulse splitting number increases,width of spectrum narrows and high-frequency part of the spectrum decreases gradually,effect of CEP on pulse and spectrum weakens gradually.
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.
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 theoretically investigate the effect of the atomic densities N on propagation and spectral property of femtosecond chirped Gaussian pulse in a three-level Λ-type atomic medium by using the numerical solution of the full Maxwell- Bloch equations. It is shown that, when the positive chirped pulse with area 3π, propagate in the medium with smaller N, pulse splitting doesn’t occur and many small oscillations at the trailing edge of the pulse appear, in addition, the level |2< population ρ22 of the pulse exhibits an oscillation feature with time evolution, moreover, the spectral component near the central frequency of the pulse shows an oscillation characteristic too, and the propagation and spectral property of the negative chirped 3π pulse is very similar to that of the positive chirped 3π pulse. For the positive chirped 3π pulse pulses, propagate in the medium with larger N, pulse splitting also doesn’t occur but many small oscillations both at leading edge and the trailing edge of the pulse appear, and the population ρ22 of the pulse only exhibits an scarcely oscillation feature with time evolution, at the same time many oscillations both in blue shift and red shift components of the pulse appear but the spectral component near the central frequency of the pulse oscillate more severely, and the propagation and spectral property of the negative chirped 3π pulse is very similar to that of the positive chirped 3π pulse, but comparing with the case of the negative chirped 3π pulse, the propagation of the positive chirped 3π pulse is delayed at the same distance and the delayed time becomes longer with the distance increasing.