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Laser Physics

Propagation of the ultrashort laser pulses through the quantum nonlinear medium with resonant properties

A. V. Gulyaev, Olga V. Tikhonova

Published May 1, 2010• 6 citations
Publisher

Abstract

The propagation of ultrashort few-cycle laser pulses through a quantum nonlinear medium with resonant properties is studied using the method of slowly varying amplitudes with allowance for dispersion effects. A self-consistent system of nonlinear wave equation for the evolution of laser field and the nonstationary Schrödinger equation that determines the material polarization response is numerically solved. Specific features of the propagation of laser pulse caused by a relatively large spectral width and the nonadiabatic character of the laser pulse are established. The rise of the slowly dumping polarization at the eigenfrequency of the medium and the consequent stretching of the laser pulse are observed. The role of the resonant absorption of the laser energy in the medium is analyzed. The nonlinear spectral broadening is demonstrated for the laser pulse propagating through the medium.

DOI
10.1134/s1054660x10100014

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The propagation of ultrashort few-cycle laser pulses through a quantum nonlinear medium with resonant properties is studied using the method of slowly varying amplitudes with allowance for dispersion effects. A self-consistent system of nonlinear wave equation for the evolution of laser field and the nonstationary Schrödinger equation that determines the material polarization response is numerically solved. Specific features of the propagation of laser pulse caused by a relatively large spectral width and the nonadiabatic character of the laser pulse are established. The rise of the slowly dumping polarization at the eigenfrequency of the medium and the consequent stretching of the laser pulse are observed. The role of the resonant absorption of the laser energy in the medium is analyzed. The nonlinear spectral broadening is demonstrated for the laser pulse propagating through the medium.
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.
We investigate the propagation of laser pulses in media with non-stationary optical and magnetic response. A new amplitude integro-differential equation, governing the evolution of wave packets with one and few cycles under the envelope, is derived. The application of slowly varying amplitude approximation to this equation reduces it to a nonlinear Slowly Varying Equation of Amplitudes (SVEA) in a second approximation of the linear dispersion. It is important to point out that the SVEA obtained in media with non-stationary optical and magnetic response is similar to the SVEA equation with stationary magnetic response. The only difference is in the expressions for the group velocity and for the dispersion parameters. In particular, in paramagnetic media near to the magnetic resonances and also in experiments with a strong DC longitudinal magnetic field, it is possible to attain negative group velocity and group velocity, higher than the velocity of light in vacuum.
A system of equations is formulated describing the evolution of a slowly varying envelope of an arbitrarily polarized ultrashort pulse of electromagnetic radiation in a medium with its resonant properties determined by an ensemble of isolated quantum dots. It is assumed that the concentration of quantum dots is small and that the whole system is equivalent to a gas of resonant four-level atoms. Particular solutions are found that correspond to the propagation of a stationary optical pulse. It is shown by numerical solution of the generalized truncated Maxwell-Bloch equations that steady-state propagation is possible only for circularly polarized light pulses, whereas the pulses of arbitrary polarization either decay and experience the dispersion-related broadening or are converted into circularly polarized solitary waves.
The propagation of an arbitrary polarized few-cycle ultrashort laser pulse in a degenerate three-level medium is investigated by using an iterative predictor-corrector finite-difference time-domain method. It is found that the polarization evolution of the ultrashort laser pulse is dependent not only on the initial atomic coherence of the medium but also on the polarization condition of the incident laser pulse. When the initial effective area is equal to $2\ensuremath{\pi}$, complete linear-to-circular and circular-to-linear polarization conversion of few-cycle ultrashort laser pulses can be achieved due to the quantum interference effects between the two different transition paths.
An analytic solution is obtained for the self-consistent equations describing propagation of an ultrashort pulse in a resonant two-level medium. The first approximation in respect of the dispersion is used to allow for phase modulation and for the dependence of the group velocity on the intensity and on the running value of the frequency. The conditions for the formation of a shock wave are established. It is shown that asymmetric broadening of the spectrum of a pulse results in coherent absorption, as a result of which the propagation of this pulse in such a medium leaves behind a polarization at the atomic transition frequency responsible for the radiation represented by the pulse.