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International Conference on Actual Problems of Electron Devices Engineering

Numerical simulation of CW laser beam propagation in saturable absorber

Inna L. Plastun, A.V. Trofimov

Published Sep 1, 2008• 0 citations
Publisher

Abstract

The numerical model of periodical modulated cw laser beam propagating through a saturable two-level absorber is presented. Within the framework of the scalar paraxial optics the investigated system is described by the set of normalized Maxwell-Bloch equations. To solve equations we use the second-order scheme based on the decomposition of the transverse field pattern in terms of Gauss-Laguerre modes, described in present paper.

DOI
10.1109/apede.2008.4720156

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The numerical model of periodical modulated cw laser beam propagating through a saturable two-level absorber is presented. Within the framework of the scalar paraxial optics the investigated system is described by the set of normalized Maxwell-Bloch equations. To solve equations we use the second-order scheme based on the decomposition of the transverse field pattern in terms of Gauss-Laguerre modes, described in present paper.
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 suggest an improved numerical algorithm for nonlinear paraxial optics that makes use of the modified quasi-fast-Fourier–Bessel transform and the special high-harmonic correction technique. The algorithm is applied to an initially cw near-resonance Gaussian beam propagating through a strongly saturated two-level medium. The spatial behavior is in good agreement with experiments and simulations by other authors. The spectral characteristics, which to our knowledge have not been previously studied, are shown to be drastically affected by the transverse pattern formation. The semianalytical approach of our earlier research is shown to provide a sufficient approximation of the beam, requiring only a few of the lowest-order dressed Laguerre–Gaussian modes.
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.
Self-action of a frequency-modulated laser beam, propagating through a two-level saturable absorber, is modeled numerically basing of the direct solution of Maxwell-Bloch equations. Following the common idea of spectroscopy, we plot the output intensity versus the input laser frequency that periodically changes in time. At modulation frequencies comparable with the relaxation rates the hysteresis loop is observed, i.e. the dependence of the transmitted intensity upon the instantaneous frequency depends on the direction of the frequency change. At large amplitudes of modulation coherent transient oscillations of the output intensity are observed.