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Optics and Spectroscopy

Resonances of intensities and oscillation frequencies in ring gas lasers. I

T. V. Radina

Published Mar 1, 2009• 1 citation
Publisher

Abstract

Narrow resonances of the intensities and oscillation frequencies of counterpropagating waves in the vicinity of the center of the quantum transition in a pure-isotope ring gas laser have been studied. It is shown that the origin of resonances is related to the presence of sources causing unequal losses and/or frequencies of the counterpropagating waves in the laser cavity. The resonance change of intensities, which is accompanied by the resonance behavior of the medium dispersion for each of the waves, is not related to resonance changes of the saturated gain coefficients of the nonlinear medium. The resonances are caused by the redistribution of energy between the waves. The character of resonance changes of frequencies and intensities depends on the nature of nonreciprocity present in the cavity.

DOI
10.1134/s0030400x09030229

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Narrow resonances of the intensities and oscillation frequencies of counterpropagating waves in the vicinity of the center of the quantum transition in a pure-isotope ring gas laser have been studied. It is shown that the origin of resonances is related to the presence of sources causing unequal losses and/or frequencies of the counterpropagating waves in the laser cavity. The resonance change of intensities, which is accompanied by the resonance behavior of the medium dispersion for each of the waves, is not related to resonance changes of the saturated gain coefficients of the nonlinear medium. The resonances are caused by the redistribution of energy between the waves. The character of resonance changes of frequencies and intensities depends on the nature of nonreciprocity present in the cavity.
We have developed a theory for nondegenerate oscillations in optical resonators containing an intracavity phase-conjugate element. The phase-conjugate element consists of a nonlinear transparent medium that is pumped externally by a pair of counterpropagating laser beams of the same frequency and intensity. Phase conjugation of an input beam of slightly different frequency occurs because of nondegenerate four-wave mixing. The theory takes into account linear absorption (or gain) in the medium and is applied to study the threshold behavior of phase-conjugate oscillators. For the special case of no conventional mirrors, the phase-conjugate oscillator reduces to an ordinary phase-conjugate mirror, and our general formulation yields the results of previous studies. Our analysis shows that the parametric gain required for oscillation increases (or decreases) as a result of linear absorption (or gain) in the medium, and oscillation can occur at a frequency different from that of the pump beams in the presence of large linear gain (or loss). The effects of linear absorption (or gain) on the filter operation are also examined.
Experiments on open transitions of the D 1 line of alkali metals (Cs and Rb isotopes) reveal the dual structure of saturated absorption resonance in the signal of a high-intensity optical wave in the presence of a low-intensity counterpropagating wave. Theoretical analysis shows that the observed shape of the resonance is associated with the openness of the atomic transition as well as with the Doppler effect for atoms in a gas. The results are of general physical significance for nonlinear spectroscopy and can also find application in metrology (frequency and time standards on open transitions).
The effect of a double structure of saturated absorption resonance in the field of counterpropagating light waves interacting with an atomic gas is studied. The experimental observation of this effect was first reported in 2011 in a work by our colleagues at the P.N. Lebedev Physical Institute of the Russian Academy of Sciences (Laboratory of Frequency Standards). The essence of the effect lies in the fact that, on exciting an open dipole transition, another, narrower, resonance of an opposite sign can be observed at the center of the ordinary saturated absorption resonance. A theoretical analysis of this effect has also been performed in this work in terms of a simple spectroscopic model of an atom with two nondegenerate energy levels without taking into account higher spatial harmonics of atomic polarization and polarizations of light waves (scalar model). The present work is devoted to the development of a theory of the formation of a central narrow resonance for the example of a real F g = 1 → F e = 1 atomic transition and to the study of its main characteristics (amplitude, width, contrast, and amplitude-to-width ratio). In addition, the theoretical results obtained without taking into account the influence of higher spatial harmonics and with inclusion of the influence of first higher harmonics are compared. This comparison shows that their influence on the parameters of the new nonlinear resonance is strong even in moderately intense light fields (R ~ γ, where R is the Rabi frequency). The results of this study can be of interest for quantum metrology, as well as for many experiments in which the laser-radiation frequency is stabilized by the saturated absorption resonance on open dipole transitions in atoms and molecules.
When a gas laser plasma is illuminated by unequally intense laser beams traveling in opposing directions, its index of refraction becomes significantly nonreciprocal. We have studied this effect by measuring the beat frequency between the counter-rotating beams in a 6328Å He-Ne ring laser under controlled conditions. Frequency locking was effectively eliminated by using a Faraday effect beat frequency bias element. The measured beat frequency became a strong function of two independent parameters: the ring resonator tuning and the beam intensity difference. A second Faraday effect element was introduced to control non-reciprocal losses within the ring resonator. Servo loops controlling both the total laser intensity and the intensity ratio between the counterrotating beams permitted direct measurement of the non-reciprocal gain caused by saturation, or hole burning. The effects observed are contained in Aronowitz' theoretical description of ring lasers.
We present an examination of the stability and time-dependent behavior of a semiclassical model of the ring laser with a saturable absorber, in the vicinity of multiple steady-state solutions. We consider particularly the case in which the cavity is tuned away from the resonance frequency of the gain medium. The model considers the absorbing and amplifying media to consist of two-level atoms. Only homogeneous spectral broadening and unidirectional propagation of the light are considered. We are able to treat the steady state with an approximate mean field solution and also with its exact longitudinal dependence. The latter is found numerically from an implicit function solution to the Maxwell-Bloch equations in the steady state. There may be as many as four steady-state solutions for a given set of parameter values. When there are four solutions, we find that three solutions are of one intensity class (high or low) and that one is of a second intensity class (low or high). When the absorbing and emitting atoms are in resonance and the cavity is tuned to their line-center frequency, two of the members of the three-solution class have the same intensity. This degeneracy is broken by detuning.
We demonstrate lasing into counterpropagating modes of a ring cavity using a gas of cold atoms as a gain medium. The laser operates under the usual conditions of magneto-optical trapping with no additional fields. We characterize the threshold behavior of the laser and measure the second-order optical coherence. The laser emission exhibits directional bistability, switching randomly between clockwise and counterclockwise modes, and a tunable nonreciprocity is observed as the atoms are displaced along the cavity axis.