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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Resonant self-focusing of periodically modulated laser beams

Vladimir Leonardovich Derbov, Inna L. Plastun

Published Jun 4, 2002• 5 citations
Publisher

Abstract

On-resonance self-action of a beam with periodically modulated amplitude in a two-level saturable absorber is studied numerically. When the period of modulation is comparable with relaxation times, one cannot describe the medium by means of susceptibility, and the response of the medium to the amplitude variation is not immediate. We solve the Bloch equations in each point of the medium to find this response correctly. Transient behavior followed by stable oscillations of population difference and polarization vector is shown to depend strongly on the frequency and amplitude of modulation. Beam propagation is considered using a simplified model of a thin absorber followed by free space, the propagation distance being small compared with the modulation wavelength. Manifestations of non-stationary response of the medium in the output intensity behavior are analyzed.

DOI
10.1117/12.469587

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On-resonance self-action of a beam with periodically modulated amplitude in a two-level saturable absorber is studied numerically. When the period of modulation is comparable with relaxation times, one cannot describe the medium by means of susceptibility, and the response of the medium to the amplitude variation is not immediate. We solve the Bloch equations in each point of the medium to find this response correctly. Transient behavior followed by stable oscillations of population difference and polarization vector is shown to depend strongly on the frequency and amplitude of modulation. Beam propagation is considered using a simplified model of a thin absorber followed by free space, the propagation distance being small compared with the modulation wavelength. Manifestations of non-stationary response of the medium in the output intensity behavior are analyzed.
We study the self-action of an amplitude-modulated beam in a two-level saturable absorbing medium. We also consider the radial quadratic dependence of the linear refraction index to apply the results to doped waveguides. As the modulation period approaches the relaxation times, the medium response is no more instantaneous, so that one should solve the full set of Maxwell-Bloch equations. We propose a second-order scheme with the Gauss-Laguerre transformation of the transverse field pattern. A simplified approach based on the synchronous interaction approximation is used for thin layers. We analyze the transient behavior of the medium response and its manifestation in the modulation of the beam diffracting after a thin saturable absorber. Nonlinear distortions of the modulation signal passed through a doped waveguide appear to be unexpectedly small compared with those of the local polarization and population difference.
Numerical modeling of self-action of a beam, whose amplitude is periodically modulated in time, in a two-level saturable absorbing medium is reported. For describe a beam self-action we solve numerically the full set of Maxwell-Bloch equations. We study the influence of the non-stationary self-action of the beam on the transmission of modulation signal through the medium. It is shown that in the time dependence of the polarization and population difference the nonlinear distortions of the modulation signal can be much stronger than in the output field intensity.
We study the self-action of an amplitude-modulated beam in a two-level saturable absorbing medium. We also consider the radial quadratic dependence of the linear refraction index to apply the results to doped waveguides. As the modulation period approaches the relaxation times, the medium response is no more instantaneous, so that one should solve the full set of Maxwell-Bloch equations. We propose a second-order scheme with the Gauss-Laguerre transformation of the transverse field pattern. A simplified approach based on the synchronous interaction approximation is used for thin layers. We analyze the transient behavior of the medium response and its manifestation in the modulation of the beam diffracting after a thin saturable absorber. Nonlinear distortions of the modulation signal passed through a doped waveguide appeared to be unexpectedly small compared with those of the local polarization and population difference.
We report numerical modeling of self-action of a beam, whose amplitude or phase is periodically modulated in time, in a gradient waveguide medium doped with two-level saturable active centers. For frequencies close to the dopant absorption line and modulation periods close to its relaxation time the response of the medium is no more instantaneous, and the description in terms of susceptibility fails. We account for the delayed response of the medium by solving numerically the full set of Maxwell-Bloch equations. In case of modulation wavelength and the diffraction length larger than the propagation distance we also make use of a simplified scheme based oil synchronous interaction approximation. Using these schemes we study the influence of the non-stationary self-action of the beam on the transmission of modulation signal through the doped waveguide. It is shown that in the time dependence of the polarization and population difference the nonlinear distortions of the modulation signal can be much stronger than in the output field intensity.
Full space-time numerical modeling of near-resonance self-action of a beam, whose frequency is harmonically modulated in time, is presented. Maxwell-Bloch equations describing the propagation of the beam through a two-level medium with saturable absorption and refraction are solved using an original stable numerical scheme for multidimensional nonlinear Schrodinger equations. Delayed redistribution of intensity over the beam cross-section due to nonlinear self-focusing and self-phase-modulation effects is shown to affect the phase and the amplitude dynamics of the output signal in a rather nontrivial way, depending on the carrier laser frequency.