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Journal of South China Normal University

THE CHARACTERISTICS OF ULTRASHORT LASER PULSES PROPAGATION IN CYLINDRICAL SYMMETRY RESONANCE MEDIA

Wang Ganquan

Published Jan 1, 2009• 0 citations
OpenAlex

Abstract

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.

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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.
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 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.
When cylindrical symmetry is assumed, a numerical study of coherent on-resonance self-focusing of laser pulses in atomic media reveals a well-defined dependence on the interaction's parameters for the focusing distance and the maximal on-axis energy density reached at the focus. We interpreted this focusing to be the result of a diaphragm effect at the edge of the pulse. This can be readily explained by considering the transverse dependence of local self-induced transparency phenomena first described by McCall and Hahn [Phys. Rev. Lett. 18, 908 (1967); Phys. Rev. 183, 457 (1969)]. From this interpretation and the well-known Maxwell-Bloch equations, we derived a theoretical quantitative model for coherent on-resonance large-scale self-focusing, that is to say, focusing of the beam as a whole. Our main results include the above-mentioned exact parametric dependence for the focusing distance, as well as predictions about the ratios of on-axis energy densities and pulse transverse sizes between the input and focus planes. All of these predictions appear to corroborate the results of an experiment on a Tm169{\mathrm{Tm}}^{169}Tm169 vapor.
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.
In this paper the phase-dependent features of ultrashort laser pulse resonant propagation in a two-level dipolar molecule are demonstrated by solving full Maxwell–Bloch equations. The electronic properties of dipolar molecule 4-trans-[p-(N, N-Di-n-butylamino)-p -stilbenylvinyl] pyridine (DBASVP) molecule, one-dimensional asymmetric organic molecule, is calculated by density functional theory at ab initio level. The numerical results show that the carrier propagation and the spectrum evolution of the pulse are sensitive to its initial phase and the phase sensitivity is more obvious for larger area pulse. The phase-dependent feature is more evident in dipolar molecule because the permanent dipole moment makes the nonlinear effects stronger.