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High Power Laser and Particle Beams

Spatial and temporal characteristics of ultrashort laser pulses propagation in resonance media

Wang Ganquan, xie li-hong, Jianying Zhou

Published May 15, 2005• 0 citations
OpenAlex

Abstract

Laser propagating through resonance media taking into account of spatial effect was discussed by simultaneously solving the Maxwell-Bloch equations with definite differential method. Results indicate that the propagation of a 2π pulse form would no longer be a soliton, its profile would expand, and the degree of distortion depends on the interaction intensity of laser and material: stronger interaction causes more distortion till the profile split. The interaction intensity was decided by such elements as the laser frequency, laser intensity, the dipole of material, detuning and the concentration of resonance particles．

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Laser propagating through resonance media taking into account of spatial effect was discussed by simultaneously solving the Maxwell-Bloch equations with definite differential method. Results indicate that the propagation of a 2π pulse form would no longer be a soliton, its profile would expand, and the degree of distortion depends on the interaction intensity of laser and material: stronger interaction causes more distortion till the profile split. The interaction intensity was decided by such elements as the laser frequency, laser intensity, the dipole of material, detuning and the concentration of resonance particles．
The spatial effect of ultrashort pulse laser propagating through the cylindrical symmetry resonance media was discussed by solving the Maxwell-Bloch equations simultaneously with the definite differential method.Results indicate that the propagating of a 2π pulse form would no longer be a soliton when spatial effect was taken into account,its profile would distort, and the degree of distortion depends on the interaction intensity of laser and material: the stronger interaction,the more distortion till the profile split.The interaction intensity was decided by such elements as the laser intensity,the dipole of material,and the concentration of resonance particles.Two problems were solved in numerical calculation,one was that a term of 1/r in Maxwell was divergence in the cylindrical center where r=0,another was that the value of optical field at the cylindrical center was difficult to be decided when the cylindrical center set as a boundary condition in the Maxwell equation.So the values of optical field need just calculating from the cylindrical center to the cylindrical boundary,comparing with that from one cylindrical boundary to another cylindrical boundary,nearly half CPU time and RAM are saved.
The propagation regularity of the laser in the 1D resonance media was studied by solving the Maxwell-Bloch equations with definite difference method.It was found that the 2π pulse would not propagate as a soliton but split if the dipole moment or the particles concentration of the resonance media was over a certain value.When two 2π pulses of different pulse widthes propagated through the resonance media,the shorter-duration pulse would catch up with the longer one.If the peak area signs of the two pulses were the same,the optical field indensity would not change obviously,it would add up and a powerful pulse with larger peak area but shorter duration would be generated.Therefore a powerful field could be generated on a fix position by adjusting the pulse width or time lapse of the two pulses properly.
The propagation of a polarized ultrashort laser pulse is analyzed by the inverse scattering method under initial conditions including a spatial pulse profile, a state of the medium, and a “switched-on” resonant atom-field interaction. Magnetic degeneracy of atomic levels is taken into account. The Maxwell-Bloch equations are rewritten in Hamiltonian form without redefining the spatial and temporal variables. The inverse scattering method is based on an analysis of a new spectral problem. Gelfand-Levitan-Marchenko-type equations are derived, a soliton solution is obtained, and the changes in parameters of two solitons after their collision are calculated. A possible experimental setup for implementing the system under analysis is discussed.
Exact single-soliton solutions of the modified system of Maxwell-Bloch equations, in which the dipole-dipole interactions of the atoms of a dense resonant medium are taken into account, are obtained. Two propagation regimes are analyzed: “coherent,” where the pulse duration is much shorter than both relaxation times ( T p ≪ T 1 , T 2 ), and “incoherent,” where the pulse duration falls between the relaxation times ( T 2 ≪ T p ≪ T 1 ). It is predicted, for the first time, that soliton propagation of an ultrashort pulse is possible in a dense resonant absorbing medium in an incoherent interaction regime. The differences between the amplitude and phase characteristics of the solitons considered and the corresponding characteristics of the solitons for McCall-Hahn self-induced transparency are noted.
Propagation and amplification of an ultrashort laser pulse in a two-level medium is numerically investigated with the use of the finite-difference time-domain (FDTD) procedure simultaneously solving Maxwell and Schrodinger equations with no assumptions characteristic of slowly varying envelope approximation. Comparison of the results of FDTD numerical simulations with the predictions of the pulse area theorem has demonstrated that the developed numerical procedure provides an adequate description of pulse evolution in a two-level medium. Amplification of ultrashort light pulses in a two-level medium is analyzed. Two methods of improving the gain of ultrashort pulses in a two-level medium by modulating the spatial distribution of dipole moments of resonant transitions and using initially chirped frequency-detuned pulses are explored.
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.