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Soviet Journal of Quantum Electronics

Resonance interaction of a strong monochromatic wave with excited ions in a magnetic field

A. P. Kol'Chenko, Gennady I. Smirnov

Published Nov 30, 1975• 0 citations
Publisher

Abstract

A theoretical analysis is made of the influecne of a magnetic field on the gain of a monochromatic traveling-wave field in a medium composed of charged two-level particles (ions). An expression is obtained for the traveling-wave gain, allowing for the drift of ions and weak saturation. It is shown that the drift results in the asymmetry of the gain profile.

DOI
10.1070/qe1975v004n11abeh011997

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IEEE Journal of Quantum Electronics•Apr 1, 1966•2 citations
A theoretical analysis is made of the influecne of a magnetic field on the gain of a monochromatic traveling-wave field in a medium composed of charged two-level particles (ions). An expression is obtained for the traveling-wave gain, allowing for the drift of ions and weak saturation. It is shown that the drift results in the asymmetry of the gain profile.
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.
A theoretical analysis is made of the nonlinear (in respect of the radiation intensity) rotation of the plane of polarization occuring in an atomic medium subjected to a static magnetic field near one-photon (two-level atoms) and two-photon (three-level atoms) resonances. A study is also made of the influence of a strong monochromatic pump wave on the propagation of a weak nonmonochromatic wave. The wave functions and quasienergies are calculated for a three-level system in static magnetic and monochromatic electromagnetic fields near a two-photon resonance. It is shown that the Verdet constant and the refractive index of such a system depend on the magnitude and relative sign of the frequency detuning from resonance. Proximity to a two-photon resonance destroys the polarizability of a medium for either sign of the detuning.
The gain experienced by a weak electromagnetic wave traveling in the opposite direction to a strong wave through a gaseous medium subjected to a sufficiently strong magnetic field is calculated for any values of the angular momenta of dipole transition levels allowing for atomic depolarizing collisions. It is shown that information on all the relaxation characteristics of an atomic transition and on the levels participating in this transition can be obtained using the model of depolarizing collisions.
The Coulomb broadening of a magneto-optical resonance of degenerate two-level ions in the field of a standing wave is calculated. Under the conditions of linear polarisation of this wave, of the normal Zeeman effect, and of weak saturation, the broadening is described by familiar expressions for multistage and two-photon resonances in separate three-level subsystems and the coefficients in these expressions depend on the angular momenta. The profile of a nonlinear resonance in the dependence of the output power of a single-frequency Zeeman ionic laser on the applied magnetic field consists of a narrow central interference peak, a wide diffusion part, and Lorentzian wings. It is shown that, in the case of a broad lower active level, the J → J+1 transitions are more favourable for the observation of a two-photon resonance and the relative amplitude of the resonance is not less than 2/7.
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 ${({\ensuremath{\omega}}_{1}\ensuremath{-}{\ensuremath{\omega}}_{2})}^{\ensuremath{-}m}$.