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Physical Review A

Atomic coherence effects in a two-mode laser with coupled transitions

Govind Prasad Agrawal

Published Aug 1, 1984• 3 citations
Publisher

Abstract

An analytical nonperturbative theory of a two-mode laser with coupled transitions is presented. The gain medium is modeled as a homogeneously broadened $\ensuremath{\Lambda}$-type three-level system. Stable stationary solutions of such a two-mode laser are studied with particular attention paid to the two-photon-induced atomic coherence effects. Our analysis shows that the nonradiative collisional decay of atomic coherence affects substantially the extent of mode competition. In particular, the coexistence domain of the two modes increases with a faster decay of the quadrupole atomic coherence that also leads to an increase in the power extraction efficiency.

DOI
10.1103/physreva.30.884

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An analytical nonperturbative theory of a two-mode laser with coupled transitions is presented. The gain medium is modeled as a homogeneously broadened \ensuremathΛ\ensuremath{\Lambda}\ensuremathΛ-type three-level system. Stable stationary solutions of such a two-mode laser are studied with particular attention paid to the two-photon-induced atomic coherence effects. Our analysis shows that the nonradiative collisional decay of atomic coherence affects substantially the extent of mode competition. In particular, the coexistence domain of the two modes increases with a faster decay of the quadrupole atomic coherence that also leads to an increase in the power extraction efficiency.
Aid or competition between two laser modes oscillating on different transitions of a three-level medium are studied following the method of Lamb. An arbitrary amount of Doppler broadening is allowed for. The "electric-quadrupole" term generated by back-to-back transitions of the two modes but having vanishing electric dipole moment is found to have little effect on the oscillation intensities in typically observed circumstances. This fact justifies, in part, the rate-equation approximation commonly used in multilevel analysis. For a bidirectional ring cascade configuration, however, this coherence term can be important because of constructive interference familiar from two-photon, Doppler-free spectroscopy. The ordinary (i.e., hole-burning) cross-saturation terms for cascade transitions produce mutual mode aid, rather than competition as in the competitive cases. A curious consequence of this difference is greater accuracy in the third-order theory of cascade transitions than in that of competitive transitions, as a result of partial cancellation of errors incurred through neglect of higher orders. The treatment is generalized to multilevel media (four or more levels) with numerical illustration and discussion of the method's relationship to laser oscillation involving diatomic molecules.
The quantum-statistical properties of the optical field of a two-mode laser with two coupled transitions have been studied by means of a generalization of the Scully and Lamb theory. The photon number distribution and the mode intensity distribution are obtained in the steady state for a system of homogeneously broadened atoms in resonance with the laser field. It is shown that the mode-coupling constant $\ensuremath{\xi}$ is unity and that near threshold the results of earlier treatments are recovered. Furthermore, it is shown that certain limit measures for the relative intensity fluctuations predicted by the semiclassical Fokker-Planck treatments based on the third-order theory are valid even in the limit of arbitrarily high gain levels.
A V-type three level system with two closely spaced upper levels interacting with a single mode of the electromagnetic field is studied for the absorptive and dispersive lineshapes. A semiclassical description for the atom-field interaction is being adopted to obtain the usual optical Bloch equations. The approximate analytical solutions for the density matrix elements are obtained by solving coupled optical Bloch equations. Through the off-diagonal density matrix elements, the introduction of phase angles between the levels participating in dipole allowed transitions are automatic. It is shown that these phases are appreciable if the applied electromagnetic field is strong. These field dependent phases (coherence) are responsible for the reduction of the inversionless gain and the absorptionless dispersion. For large decay constants, it is found that the energy gap between the upper two levels has no role to play on the laser without inversion and on the absorptionless dispersion. However, for large population per unit decay, a significant increase of the absorptionless dispersion and the inversionless gain is obtained. The condition for large population decay and a possible experimental realization of the field dependent phases are discussed.
The optical bistable behavior of V-type three-level atomic system in a unidirectional ring cavity driven by a coherent field is studied.A single mode laser field is applied to two transitions simultaneously.The interference between decay channels is very important.Studies show that atomic coherent effects could significantly decrease the optical bistability threshold.We also analyze the effect of the atomic cooperation parameter,the width between two upper levels,and the detuning on the optical bistability.
We apply Lugiato's theory of open systems to the single-mode laser model of Haken and co-workers, in order to investigate the effect on laser dynamics of processes involving one photon and two atoms. A Fokker-Planck time-evolution differential equation is obtained for the field quasiprobability distribution $P(\ensuremath{\beta}, {\ensuremath{\beta}}^{*}, t)$, which includes terms proportional to the squared number of atoms N2{N}^{2}N2. A detailed analysis reveals a twofold effect of these terms. The main effect that becomes relevant well above threshold is a broadening of the stationary field-intensity distribution. This broadening is due to a "cooperative noise," whose source is a squared polarization created by the two-atom processes. These processes also give rise to a very weak loss mechanism, which affects the maximum of the stationary intensity distribution in the threshold region, slightly increasing the threshold for the laser emission.