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ACTA PHOTONICA SINICA

Inhomogeneous Broadening Effect on the Propagation Characteristics of Ultrashort Laser Pulse

张华荣 ZHANG Hua-rong, 李成 Li Cheng, 余向阳 Yu Xiangyang

Published Jan 1, 2010• 1 citation
Publisher

Abstract

An effective 'Forecast-correction fourth-order Runge-Kutta' numerical method is programmed to study the propagation characteristics of ultra-short laser pulse in inhomogeneous broadening two-level medium.The results show that the pulse propagation can be modulated by the inhomogeneous broadening line-width.While the inhomogeneous broadening line-width is greater than the pulse spectrum width,the evolution of pulse area consists with the area theorem,and the pulse propagation maintains stability.With decreasing line-width,the evolution of pulse area becomes complex,and pulse propagation no longer maintains stability and with atailoscillation.The pulse peak and pulse propagation velocity can also be modulated by the line-width.

DOI
10.3788/gzxb20103901.0006

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An effective 'Forecast-correction fourth-order Runge-Kutta' numerical method is programmed to study the propagation characteristics of ultra-short laser pulse in inhomogeneous broadening two-level medium.The results show that the pulse propagation can be modulated by the inhomogeneous broadening line-width.While the inhomogeneous broadening line-width is greater than the pulse spectrum width,the evolution of pulse area consists with the area theorem,and the pulse propagation maintains stability.With decreasing line-width,the evolution of pulse area becomes complex,and pulse propagation no longer maintains stability and with atailoscillation.The pulse peak and pulse propagation velocity can also be modulated by the line-width.
We present a numerical method for solving the Maxwell-Bloch equations describing pulse propagation for a two-level medium. The method is accurate, efficient, stable, and well suited for this type of simultaneous equations. By applying the numerical scheme we investigate the evolutions of pulse area, pulse propagation, pulse velocity, and spectral shapes under both homogeneous and inhomogeneous broadening conditions. The results show that the area evolution and pulse-reshaping procedure are significantly influenced by detuning and inhomogeneous line shape, which also impact the oscillation tail and pulse peak. In addition, the pulse-peak traces indicated the pulse velocity always increases with greater deviation in pulse-area value from the value 2\ensuremath{\pi}. We also demonstrate the pulse velocity increased for a larger detuning or a wider inhomogeneous line shape. Furthermore, the spectral feature shows that pulse spectra evolve into an oscillating shape.
An accurate and effective numerical method is presented to solve the Maxwell-Bloch equations that are used to describe the optical pulse propagation and interaction with inhomogeneously broadened two-level medium.The convergence and stability of this numerical method are proved by comparing with the analytic solutions and area theorem derived under special condition.The simulations of arbitrary conditions is discussed by employing this method and analyze the pulse evolution for different detunings,relaxation times and inhomogeneously broadened linewidthes.The established numerical method provides a good way to have further study about the coherent interaction of short optical pulses with resonant mediums,and can be used to solve the corrections of Maxwell-Bloch equations.
We consider the effect of a background dielectric on the steady-state propagation of a laser pulse through inhomogeneously broadened two-level atoms embedded in the dielectric. Because this problem apparently does not admit of analytic solutions, we have solved it numerically. A comparison of our results with the known analytic solutions for the homogeneously broadened atomic line shows that the two are similar. It seems that the new numerical solutions, unlike those for the homogeneous line, are not factorable, a fact to which we ascribe the difficulty in finding analytic solutions. We have found that as the atomic line broadens, the pulse widens and its height decreases, maintaining its area virtually constant.
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.
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.
Using numerical simulations, we study propagation of ultrashort light pulses in an inhomogeneously broadened two-level medium. There are two main issues in our study. The first one concerns the transient process of self-induced transparency soliton formation, in particular, the compression of the pulse which seems to be more effective in the case of homogeneous broadening. The second question deals with the collisions of counter-propagating solitons. It is shown that the level of inhomogeneous broadening has a substantial effect on the elasticity of such collisions.