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 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.
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.
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.
In the cases of one-photon resonance and complete non-resonance, the effects of the relative carrier-envelope phase(RCEP) φ on pulse form and spectra characteristics of two-color ultrashort laser pulses in a Ξ-type three-level atomic medium are investigated by using numerical simulation.The results show that in the single-photon resonance case the RCEP has evident control role of profile and spectral characteristic of the two-color pulses.The RCEP can decide the amplitude, propagating velocity,pulse splitting case and the number of sub-pulses.When φ=0,the pulse does not split, and the shape and intensity of the pulse keep basically unchanged during the process of propagation.In the case of complete non-resonance, the pulse splitting doesn′t arise again, and the supercontinuum with frequency range much larger than that in the one-photon case can be obtained.Although the effects of RCEP on pulse shape and spectral property are not as strong as those in the one-photon resonance case, varying φ can still make frequency range and intensity distribution at different frequencies vary obviously.When φ=0, the supercontinuum with wider spectral range, better continuity and stronger intensity of high frequency components can be obtained.
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.
By the numerical analyzing and simulation, we investigate effect of carrier envelope phase on propagation of femtosecond chirped Gaussian laser pulse in a dense three-level Λ-type atomic medium. It is shown that, when the small area 2π negative chirped pulses (or the 2π positive chirped pulses) with different value of initial carrier envelope phase φ0 propagate in the medium, splitting don’t occur and the chirped pulses evolve gradually to approximate normal Gaussian pulses with equal amplitude and group velocity, and the phase differences between them remain the same as the case of initial input pulses. When the 4π negative chirped pulses with different φ0 propagate in the medium, the pulses will split into at least two sub-pulses and the amplitude of the first sub-pulse is far more than the second sub-pulse; These first sub-pulses have equal amplitudes and propagating with equal group velocity in the medium, and the phase differences between these first sub-pulses remain the same as the case of initial input pulses; The amplitudes of these second sub-pulses are not equal and don’t change monotonously with linearly increasing of φ0 but take on a invert S-shaped pattern, and the phase differences between these second sub-pulses are different. The case of 4π positive chirped pulses is similar to the case of 4π negative chirped pulses, but the amplitudes of these second sub-pulses split off from the 4π positive chirped pulses have no obvious changes compared with the case of 4π negative chirped pulses.
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 .