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.
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.
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.
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.
Using numerical solution of the full Maxwell–Bloch equations, which is obtained by the finite-difference time-domain method and the iterative predictor–corrector method, we investigate the modulation effect of relative carrier–envelope phase (hereinafter referred to as the relative phase) on resonant propagation of two-colour femtosecond ultrashort laser pulses in a V-type three-level atomic medium. It is found that the pulse splitting occurs for a smaller value of relative phase; when the value of relative phase increases to a certain value, only the variation of pulse shape is present and the pulse splitting does not occur any more; moreover, when the value of relative phase is smaller, the pulse group velocity is larger. The relative phase also has an obvious effect on population and spectral property. Different population transfers can be realized by adjusting the value of relative phase. Generally speaking, for the pulses with smaller areas their spectral strengths and frequency ranges decrease obviously with the value of relative phase increasing; for the pulses with larger areas, with value of the relative phase increasing, their spectral strengths decrease remarkably but the relative strengths of the higher frequency components increase significantly, while the spectral frequency range is not varied evidently.
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 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.