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Optics and Spectroscopy

Effect of saturation in the field of coherent and intrinsic spontaneous radiation

Sergey G. Rautian, Э. Г. Сапрыкин, А. А. Черненко

Published Feb 1, 2005• 7 citations
Publisher

Abstract

Saturation effects in gaseous media in the presence of a high-intensity resonant laser field and in the field of incoherent radiation caused by the intrinsic spontaneous emission are considered. A simple nonlinear set of kinetic equations is proposed for describing the saturation effect in the case of optically thin media and nondegenerate levels. The Bennett structure and the band of homogeneous saturation, whose parameters are interdependent, exist in the velocity distribution. The regularities in the behavior of the band and the Bennett structure under variation in the transition parameters and the intensity of laser radiation are elucidated.

DOI
10.1134/1.1870069

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A theoretical analysis is made of the resonant interaction between a traveling monochromatic light wave of arbitrary intensity and polarization and the 1/21/2 and 10 transitions in gas atoms in a magnetic field. An analysis is made of the influence of atomic collisions and coherence of the Zeeman sublevels of the terms on the structure of nonlinear magnetooptic resonances in the amplitude and polarization characteristics of the wave. Some features of nonlinear magnetooptic resonances for laser excitation of atoms from the ground state are noted. A study is made of the Faraday rotation and self-rotation of the polarization ellipse of the radiation as a function of the detuning of the wave frequency, the saturation parameter, and the optical density of the gas. The stability of the polarization of light in the medium is discussed. It is noted that these laws may be used to analyze and control the radiation characteristics of lasers and amplifiers when the level of saturation of a resonant gaseous medium in a magnetic field is high.

Soviet Journal of Quantum Electronics•Mar 31, 1988•2 citations
Saturation effects in gaseous media in the presence of a high-intensity resonant laser field and in the field of incoherent radiation caused by the intrinsic spontaneous emission are considered. A simple nonlinear set of kinetic equations is proposed for describing the saturation effect in the case of optically thin media and nondegenerate levels. The Bennett structure and the band of homogeneous saturation, whose parameters are interdependent, exist in the velocity distribution. The regularities in the behavior of the band and the Bennett structure under variation in the transition parameters and the intensity of laser radiation are elucidated.
The shape of the resonance of a saturated absorption is calculated at an arbitrary intensity of a probe field. It is revealed that, in the case of orthogonal polarizations of strong and probe fields, an increase in the intensity of the probe field can invert the shape of the nonlinear resonance of clearing of the medium, changing it to the resonance of absorption. The saturation of optical transitions by intrinsic spontaneous radiation increases the contrast of the inverted resonance of saturation and narrows its width. In the case of parallel polarizations of the optical fields, an absorption peak can arise in the shape of the nonlinear resonance upon splitting of the lower state.
Using Lamb's model, we analyze the effects of gain saturation by strong traveling-wave fields in dilute laser media. Using approximate solutions of an integral equation for the population inversion density (PID), the index of refraction and incremental gain are studied for arbitrarily strong fields. Effects of atomic motion are included for a Maxwellian velocity distribution, but pressure effects are neglected. The case of a monochromatic field leads to the saturation results of Gordon, White, and Rigden, which are studied as a function of frequency. For a small ratio of natural to Doppler linewidths, there is a transition from inhomogeneous to homogeneous broadening for sufficiently strong fields. An effect of particular interest is the generation of waves at $2{\ensuremath{\omega}}_{1}\ensuremath{-}{\ensuremath{\omega}}_{2}$, $2{\ensuremath{\omega}}_{2}\ensuremath{-}{\ensuremath{\omega}}_{1}$, and higher order sidebands by two strong input signals at ${\ensuremath{\omega}}_{1}$ and ${\ensuremath{\omega}}_{2}$. The source of the parametric gain at these frequencies is the time-dependent gain saturation due to the presence of multiple strong fields. For ${\ensuremath{\omega}}_{1}\ensuremath{-}{\ensuremath{\omega}}_{2}$ small compared to the decay rates ${\ensuremath{\gamma}}_{a}$ and ${\ensuremath{\gamma}}_{b}$ of the laser levels, the gain at these intermodulation sidebands is computed as a function of the field strengths. The limiting cases of homogeneous and inhomogeneous (due to atomic motion) broadening are studied in detail. These two cases give essentially the same results, for a given unsaturated gain. Numerical results indicate that a first-order side-band intensity at least 10% as large as that of the inducing fields can be easily observed in practice. The integral equation for the PID is converted into an infinite set of linear algebraic equations for a typical solid-state laser. The conditions under which this set of equations can be limited to a finite number is discussed, and the dependence of the sideband gain on ${\ensuremath{\omega}}_{1}\ensuremath{-}{\ensuremath{\omega}}_{2}$ is calculated. For large ${\ensuremath{\omega}}_{1}\ensuremath{-}{\ensuremath{\omega}}_{2}$, the gain at the mthm\mathrm{th}mth sideband decreases as ${({\ensuremath{\omega}}_{1}\ensuremath{-}{\ensuremath{\omega}}_{2})}^{\ensuremath{-}m}$.
Using Lamb's model, we analyze the effects of gain saturation by strong traveling-wave fields in dilute laser media. Using approximate solutions of an integral equation for the population inversion density (PID), the index of refraction and incremental gain are studied for arbitrarily strong fields. Effects of atomic motion are included for a Maxwellian velocity distribution, but pressure effects are neglected. The case of a monochromatic field leads to the saturation results of Gordon, White, and Rigden, which are studied as a function of frequency. For a small ratio of natural to Doppler linewidths, there is a transition from inhomogeneous to homogeneous broadening for sufficiently strong fields. An effect of particular interest is the generation of waves at $2{\ensuremath{\omega}}_{1}\ensuremath{-}{\ensuremath{\omega}}_{2}$, $2{\ensuremath{\omega}}_{2}\ensuremath{-}{\ensuremath{\omega}}_{1}$, and higher order sidebands by two strong input signals at ${\ensuremath{\omega}}_{1}$ and ${\ensuremath{\omega}}_{2}$. The source of the parametric gain at these frequencies is the time-dependent gain saturation due to the presence of multiple strong fields. For ${\ensuremath{\omega}}_{1}\ensuremath{-}{\ensuremath{\omega}}_{2}$ small compared to the decay rates ${\ensuremath{\gamma}}_{a}$ and ${\ensuremath{\gamma}}_{b}$ of the laser levels, the gain at these intermodulation sidebands is computed as a function of the field strengths. The limiting cases of homogeneous and inhomogeneous (due to atomic motion) broadening are studied in detail. These two cases give essentially the same results, for a given unsaturated gain. Numerical results indicate that a first-order side-band intensity at least 10% as large as that of the inducing fields can be easily observed in practice. The integral equation for the PID is converted into an infinite set of linear algebraic equations for a typical solid-state laser. The conditions under which this set of equations can be limited to a finite number is discussed, and the dependence of the sideband gain on ${\ensuremath{\omega}}_{1}\ensuremath{-}{\ensuremath{\omega}}_{2}$ is calculated. For large ${\ensuremath{\omega}}_{1}\ensuremath{-}{\ensuremath{\omega}}_{2}$, the gain at the mthm\mathrm{th}mth sideband decreases as ${({\ensuremath{\omega}}_{1}\ensuremath{-}{\ensuremath{\omega}}_{2})}^{\ensuremath{-}m}$.
Nonlinear absorption of a probe field is analyzed taking into account intrinsic spontaneous radiation (the self-saturation effect). Systems of two and three nondegenerate levels, as well as a system of two levels with the angular momenta equal to unity, are considered. Changes produced by the self-saturation in the population, polarization, and nonlinear interference effects, as well as in the field splitting of lines, are determined. In certain situations, incoherent spontaneous radiation enhances the interference phenomena.
The form of the saturated absorption resonance for atomic transition J=1-J=1 at arbitrary intensities of a probe light field is calculated. The influence of the saturation effect of optical transitions by own spontaneous radiation on the form of a nonlinear resonance is researched. It is revealed, that in case of orthogonal polarizations of strong and probe fields the increase of the probe field intensity can result in inversion of the shape of a nonlinear resonance. The saturation effect of optical transitions by own spontaneous radiation increases contrast of the inverted resonance of saturation and narrows its spectrum. In case of parallel polarizations of optical fields the peak of absorption can arise in the shape of nonlinear resonance at splitting of the lower atomic state.
A theoretical analysis is made of the resonant interaction between a traveling monochromatic light wave of arbitrary intensity and polarization and the 1/21/2 and 10 transitions in gas atoms in a magnetic field. An analysis is made of the influence of atomic collisions and coherence of the Zeeman sublevels of the terms on the structure of nonlinear magnetooptic resonances in the amplitude and polarization characteristics of the wave. Some features of nonlinear magnetooptic resonances for laser excitation of atoms from the ground state are noted. A study is made of the Faraday rotation and self-rotation of the polarization ellipse of the radiation as a function of the detuning of the wave frequency, the saturation parameter, and the optical density of the gas. The stability of the polarization of light in the medium is discussed. It is noted that these laws may be used to analyze and control the radiation characteristics of lasers and amplifiers when the level of saturation of a resonant gaseous medium in a magnetic field is high.