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Soviet Journal of Quantum Electronics

Limits of stability of two-mode emission in a strong field

I. V. Evseev, V. M. Ermachenko

Published Jul 31, 1976• 1 citation
Publisher

Abstract

A theoretical analysis is made of the two-mode emission from a gas laser in the vicinity of the symmetric position of the modes relative to the center of the gain profile when the intensities of the modes in the symmetric position cannot be regarded as low. The example of a homogeneously broadened spectral line is used in an investigation of the range of stable two-mode emission as a function of the relative excitation of the medium.

DOI
10.1070/qe1976v006n07abeh011652

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A theoretical analysis is made of the two-mode emission from a gas laser in the vicinity of the symmetric position of the modes relative to the center of the gain profile when the intensities of the modes in the symmetric position cannot be regarded as low. The example of a homogeneously broadened spectral line is used in an investigation of the range of stable two-mode emission as a function of the relative excitation of the medium.
A theoretical analysis is made of the stability range of stimulated emission of two modes with orthogonal and parallel polarizations. The case of transitions between active levels of momenta ja = jb = 1 in a relatively strongly excited medium is considered. It is found that, in contrast to the case of parallel polarizations, emission of two modes with orthogonal polarizations is possible even when the mode spacing is small. Investigation is made of the influence of the quadrupole polarization of the medium on the width of the two-mode emission range. It is shown that the results obtained by calculating the polarization of the medium to within terms cubic in respect of the field amplitude describe correctly relatively highly excited active media.
A theoretical analysis is made of the characteristics of a single- and two-mode gas laser with an anisotropic resonator in an axial magnetostatic field with arbitrary relative excitation of the active medium for an atomic transition with total level momenta of 0 and 1. Using an example of a homogeneously broadened spectral line, it is shown that the results of calculations made to within terms cubic with respect to the electric field give a correct qualitative description of the characteristics of two-mode lasing.
The instabilities in homogeneously broadened lasers, which we described in the previous chapter, have a paradigmatic importance because they arise in models which allow one to perform the linear-stability analysis in a simple analytic form. The treatment of the corresponding instabilities in the case of in homogeneously broadened lasers is substantially more complex in general. However, it is very interesting because, as we shall see, the instabilities arise in parametric domains that are much more accessible from the experimental viewpoint. A related issue is that of the possibility of multimodal emission in a laser. It is common knowledge that in order to attain multimode emission it is necessary to have a sort of in homogeneity in the gain medium, because in a completely homogeneous configuration all modes interact with all atoms, and the arising competition among modes implies that only one of them survives. There are basically two main kinds of in homogeneity, the first is of spatial nature and the other is of spectral nature. The first kind is realized in Fabry–Perot lasers, because different cavity modes interact with atoms at different spatial positions in the cavity thanks to the standing-wave configuration of the field and to the consequent phenomenon of spatial hole- burning (see Section 14.2 and Fig. 14.1). This circumstance is capable of weakening the mode–mode competition and allowing multimode operation. In unidirectional ring lasers, on the other hand, there is an “inhomogeneous” configuration in the case of inhomogeneous broadening, because different groups of atoms have different transition frequencies and therefore interact with different modes thanks to the spectral hole-burning (see Section 15.2 and Fig. 15.3). Again, this weakens the mode–mode competition and allows multimode operation. However, these are qualitative considerations, and the only reliable and quantitative method to determine the possibility of multimodal operation is the linear-stability analysis of the single-mode stationary solutions.
A theoretical investigation is made of the feasibility of simultaneous laser action due to adjacent transitions in atoms of a gaseous medium with level momenta j/sub b/..-->..j/sub c/ and j/sub b/..-->..j/sub a/. In the case of small relative excesses of the population inversions of the active levels over the threshold, an expression is derived for the region of simultaneous laser action with parallel and orthogonally polarized fields. The limiting cases of homogeneously and inhomogeneously broadened lines are studied. Calculations are made allowing for depolarizing atomic collisions. For a homogeneously broadened line and negligible degeneracy of the levels, a region of simultaneous laser action is found for an arbitrary relative excess of the population inversion over the threshold.
A gas laser oscillating steadily in a single mode is described theoretically using the "generalized Bloch equations" as the point of departure. The nonlinear susceptibility is calculated without utilizing perturbation techniques, so that the theory retains validity for laser fields of arbitrary intensity. Expressions are presented for (1) the "gain profile" which exhibits the phenomenon of dual "hole burning," (2) the powertuning characteristics, including the conditions for the appearance of the central tuning dip, and (3) the frequency of oscillation, in which are displayed the effects of mode pulling and pushing. Emphasis is on a strongly inhomogeneous line and a high-QQQ cavity, although some more general results are included as well. For excitations only slightly above threshold, a comparison is made with the Lamb single-mode theory, and in all cases agreement is found.