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Chinese Physics B

Relative carrier—envelope phase dependence of resonant propagation of two-colour femtosecond pulses in V-type atomic medium

Xia Tan, Zhendong Wang, Lei Wang, Fan Xi-jun

Published Jun 1, 2010• 1 citation
Publisher

Abstract

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.

DOI
10.1088/1674-1056/19/6/064211

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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.
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.
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.
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.
The interference resonant propagation and spectral properties of a superposition of two femtosecond chirped Gaussian pulses with equal pulse area and same size but opposite sign of the chirp coefficient (C) in a three-level Λ-type atomic medium is investigated by using the 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 the double pulses with smaller area, (2π, 2π) double pulses, the pulse splitting occurs when the value of the |C| is smaller, and only the variation of pulse shape is present but the pulse splitting no longer occur when the value of the |C| increases to a certain value; New high frequency component doesn’t basically appear and the strength of the spectral component near the central frequency decreases considerably but the strength of blue shift component is not varied obviously with the value of |C| increasing. For the double pulses with larger areas, the case of pulse splitting is similar to that of (2π, 2π) pulses, but the strength of the spectral component with higher frequency increase evidently comparing with the case of (2π, 2π) double pulses. Moreover, the value of the |C| also has an obvious effect on population, different population evolutions can be achieved by adjusting the value of |C|.
In one-photon resonance and detuning cases,effect of relative carrier-envelope phase(RCEP) on evolution of two-color sech-type femtosecond pulses and spectrum in a dense V-type three-level atomic medium is investigated with full Maxwell-Bloch equations.Modulation of RCEP on pulse shape and spectral property of two-color pulses in detuning case is more evident than that in single-photon resonance case.And in detuning case we get spectrum broadening much greater than that in resonance case.Supercontinuum with the highest frequency of 18 times of incident frequency appears.
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.