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Physical Review A

Inhomogeneously broadened laser with a saturable absorber

Mansour Mortazavi, Surendra Singh

Published Jan 1, 1987• 5 citations
Publisher

Abstract

A quantum theory for a laser with inhomogeneously broadened active and absorber atoms is presented. Photon-number distributions are derived for both on- and off-resonance operation of the laser, and the results are compared with the results of earlier investigations.
DOI
10.1103/physreva.35.429

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Effect of Relaxation Parameters on the Quantum Theory of an Inhomogeneously Broadened Laser

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The results of the Riska-Stenholm quantum theory for an inhomogeneously broadened laser are re-derived without using the Doppler limit approximation which restricts the utility of this theory. The photon distribution peak is seen to occur at a significantly lower photon number and the threshold condition is dependent on Yablku, where Yab is the relaxation parameter and ku the Doppler parameter. The dimensionless intensity parameter is obtained and the results are compared with the existing theories of Riska and Stenholm and of Scully and Lamb.

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Off-resonance operation of inhomogeneously broadened two-photon lasers

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We generalize Lamb's quantum theory of lasers to treat the off-resonance operation of two-transition lasers in inhomogeneously broadened media. The master equation is derived from the density-matrix equation of motion in the Doppler limit. We first find the stationary-state solution from which we then obtain such operation characteristics as the threshold condition, the mean photon number, and the half-width of photon distribution. Compared with the one-transition laser, it is found that in the two-transition laser it is much easier to start oscillation and to obtain higher gain. Furthermore, we find that the two-transition laser is less sensitive to the detuning effect and its deviation from the coherent state is smaller than that of the one-transition laser. The remarkably different hole-burning phenomenon is also discussed.

Physical Review A•Sep 1, 1988•1 citation
The results of the semi-classical theory for the laser are compared with the results of the quantum theory given by Scully and Lamb (1967). It is found that the spatial structure of the cavity mode leads to important corrections. For moving atoms the cavity mode is smeared, and a generalized form of the Scully-Lamb theory (for resonance between the atomic transitions and the cavity mode) leads to agreement with the semi-classical theory. The photon distribution for the case with moving atoms is obtained and compared with the results of the Scully-Lamb theory.
The results of the quantum theory of a laser given by Riska and Stenholm (see ibid., vol.3, p.536 (1970)) for the case of inhomogeneous broadening and detuning are re-derived by avoiding the Doppler limit approximation to show the exact influence of relaxation parameters on the theory. The threshold condition is seen to be dependent on gamma ab /ku where gamma ab is the relaxation parameter and ku the Doppler parameter. Its value is found to be higher than earlier results. It is noted that the photon distribution function at resonance is much closer to the corresponding distribution obtained from exact calculations for the tuned case. The photon number at the peak of the distribution curve is much lower than earlier values for comparable situations.
Many quantum optical systems exhibit first-order phase transition analogy.1 Fluctuations of the optical field in such systems are due to spontaneous emission noise. The nature of these fluctuations for various systems has been discussed using various approaches. Fully quantum mechanical and Langevin equation treatments have been given for the dye laser2,3 and the laser with a saturable absorber (LSA) with homogeneously broadened media.2,4 For inhomogeneously broadened media, such treatments are either valid for low intensities or do not fully take into account the effect of quantum noise.5 In this contribution we present a fully quantum mechanical treatment for the LSA with an inhomogeneously broadened absorber using the Foch state representation of the density matrix.2,6
The results of the Riska-Stenholm quantum theory for an inhomogeneously broadened laser are re-derived without using the Doppler limit approximation which restricts the utility of this theory. The photon distribution peak is seen to occur at a significantly lower photon number and the threshold condition is dependent on Yablku, where Yab is the relaxation parameter and ku the Doppler parameter. The dimensionless intensity parameter is obtained and the results are compared with the existing theories of Riska and Stenholm and of Scully and Lamb.
We generalize Lamb's quantum theory of lasers to treat the off-resonance operation of two-transition lasers in inhomogeneously broadened media. The master equation is derived from the density-matrix equation of motion in the Doppler limit. We first find the stationary-state solution from which we then obtain such operation characteristics as the threshold condition, the mean photon number, and the half-width of photon distribution. Compared with the one-transition laser, it is found that in the two-transition laser it is much easier to start oscillation and to obtain higher gain. Furthermore, we find that the two-transition laser is less sensitive to the detuning effect and its deviation from the coherent state is smaller than that of the one-transition laser. The remarkably different hole-burning phenomenon is also discussed.