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Soviet Journal of Quantum Electronics

Competition between modes generated due to adjacent transitions

D. S. Bakaev, Yu. A. Vdovin

Published Jan 31, 1987• 0 citations
Publisher

Abstract

An analysis is made of competition between modes emitted due to adjacent transitions having a common upper level. Conditions are obtained for the onset of lasing due to one transition in the presence of lasing of arbitrary intensity due to the other transition in standing- and traveling-wave lasers. Both transitions were assumed to be homogeneously broadened. Allowance is made for level degeneracy, collisional broadening of the dipole-forbidden transition between the lower active levels, and collisions with the buffer gas that equalize the populations of the lower active levels. The ranges of single-mode and two-mode lasing are determined as a function of the radiation intensity, the spectroscopic parameters of the transitions, and their collisional broadening.

DOI
10.1070/qe1987v017n01abeh006423

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Journal of Experimental and Theoretical Physics•Aug 1, 2008•0 citations
An analysis is made of competition between modes emitted due to adjacent transitions having a common upper level. Conditions are obtained for the onset of lasing due to one transition in the presence of lasing of arbitrary intensity due to the other transition in standing- and traveling-wave lasers. Both transitions were assumed to be homogeneously broadened. Allowance is made for level degeneracy, collisional broadening of the dipole-forbidden transition between the lower active levels, and collisions with the buffer gas that equalize the populations of the lower active levels. The ranges of single-mode and two-mode lasing are determined as a function of the radiation intensity, the spectroscopic parameters of the transitions, and their collisional broadening.
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.
We show that the dip in the intensity line shape of a single-mode laser can appear at definite experimental conditions in cases both of nonhomogeneously broadened line as well as homogeneously broadened line of the atomic transition. In both cases the dip is explained by the nonlinear character of the phenomenon. The saturation of the population difference of the involved atomic energy levels has its maximum in the vicinity of the line center. Therefore the saturation of the amplification is at maximum near the atomic line center, and, as a consequence, the lasing power is reduced.
The emission linewidth in active medium emerges due to homogeneous and inhomogeneous broadening. We demonstrate that in lasers with inhomogeneous broadening there is a critical pump rate, above which the special mode forms. This mode consists of locked-in oscillations of cavity mode and of the active atoms with different transition frequencies. Below the critical value of the pump rate, the radiation spectrum of the laser has a Gaussian profile, provided that inhomogeneous broadening is dominant. Above the critical value of pump rate, the special mode mostly determines the laser radiation spectrum. As a result, the spectrum attains Lorentz shape characteristic for homogeneous broadening. The formation of the special mode precedes lasing and that the critical pump rate plays the role of lasing prethreshold. We suggest a system where such a transition could be experimentally observed separately from lasing. We obtain expressions for the threshold and generation frequency of a single-mode laser where both homogeneous and inhomogeneous broadening are present.
In the present work, an analytical calculation of the value of xo is presented for the same physical conditions as in [5, 6], with one additional approximation. In a gas laser, movement of the atoms has the result that the periodic structure of the standing wave field of the laser modes is weakly reflected in the spatial distribution of the population inversion [7]. On this basis we shall carry out the calculation of xo assuming that the intensity of the fields ml and ma is constant along the axis of the laser. We thus exclude from consideration a certain range of phenomena related to the effect of a spatial displacement between the standing waves m~ and ma on the mode competition. We consider this reasonable, since those phenomena were analyzed in sufficien.t detail in [3], where the basic attention of the work was directed at analysis of the competition effect for various values of q. Following Evseev et al. [5,6] we shall use the fact that, near the boundaries of the two-frequency and slngle-frequency regimes (x =  the intensity of one of the modes is much larger than the intensity of the other, almost to the point of suppression. We shall assume at the outset that lasing takes place in one strong mode, for example m,, caused by saturation of the active medium. We shall initially assume the mode ma to be suppressed and '~eak, i.e., not saturating the active medium. In the steady state, the saturated amplification gt of the mode m~ in the active medium is equal to the losses T. The saturated amplification ga of the weak mode may be larger than, smaller than, or equal to T, depending on x. In the first case, the field of the mode ma will grow and two-frequency operation, not slngle-frequency, will be stable, while the third is realized for x =  Based on the results of [8] it is possible to obtain the following expressions for gt and ga:
A new version of obtaining short-wave lasing on transition between highly excited states and the ground state of active atoms in the buffer gas atmosphere is studied theoretically. The mechanism of obtaining population inversion on such a transition is associated with the establishment of the local Boltzmann distribution of populations in a group of highly excited levels due to frequent collisions. If the excitation of the upper-lying level is performed by two laser radiation sources with frequencies ω 1 and ω 2 , short-wave lasing can be obtained at a frequency close to the total frequency ω 1 + ω 2 . The conditions for the emergence of population inversion are analyzed and simple analytic formulas are derived. It is shown that collision-induced enhancement of short-wave radiation can occur for pumping intensities on the order of 100 W/cm 2 . For pumping intensities on the order of 1000 W/cm 2 , the amplification factor for short-wave radiation may attain values of 3 cm −1 (for an active atom concentration of N ∼ 10 15 cm −3 ), which is sufficient for the development of lasing per path through an active medium (superradiance condition) for a length of the active medium on the order of 10 cm.