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Physical Review A

Nonadiabatic linewidth of a Λ-type noninversion laser

Michael Fleischhauer, Ulrich W. Rathe, Marlan O. Scully

Published Aug 1, 1994• 4 citations
Publisher

Abstract

The linewidth of a \ensuremath{\Lambda}-type noninversion laser is calculated on the basis of a c-number Langevin approach in lowest order of the laser field. It is shown that the system behaves in general---that is, also in the good-cavity limit---nonadiabatically. In the nonadiabatic regime a substantial deviation of the laser linewidth from the Schawlow-Townes formula is found and a simple interpretation is given.

DOI
10.1103/physreva.50.1748

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The linewidth of a \ensuremath{\Lambda}-type noninversion laser is calculated on the basis of a c-number Langevin approach in lowest order of the laser field. It is shown that the system behaves in general---that is, also in the good-cavity limit---nonadiabatically. In the nonadiabatic regime a substantial deviation of the laser linewidth from the Schawlow-Townes formula is found and a simple interpretation is given.
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We perform a first-principles calculation of the quantum-limited laser linewidth, testing the predictions of recently developed theories of the laser linewidth based on fluctuations about the known steady-state laser solutions against traditional forms of the Schawlow-Townes linewidth. The numerical study is based on finite-difference time-domain simulations of the semiclassical Maxwell-Bloch lasing equations, augmented with Langevin force terms, and includes the effects of dispersion, losses due to the open boundary of the laser cavity, and non-linear coupling between the amplitude and phase fluctuations (α factor). We find quantitative agreement between the numerical results and the predictions of the noisy steady-state ab initio laser theory (N-SALT), both in the variation of the linewidth with output power, as well as the emergence of side-peaks due to relaxation oscillations.
We derive the quantum-limited linewidth of a bad-cavity laser, where the cavity-loss rate can be comparable to or larger than the gain bandwidth. We allow for incomplete inversion and arbitrary mirror losses and show how the position-dependent gain, refractive index, and populations co-determine the laser linewidth. The result obtained factorizes in parts that have straightforward physical interpretations. In the bad-cavity regime the laser linewidth is shown to be reduced as compared to the Schawlow-Townes expression as a result of anomalous dispersion associated with the optical gain. Saturation is shown to lead to a power-independent contribution to the laser linewidth; the magnitude of this contribution depends critically on the assumed pumping and decay rates.
In this paper the laser linewidth without rotating wave approximation is studied by keeping the ratio of the atomic natural decay rate to the radiation frequency to two orders.It is shown that while the linewidth is confined to the Schawlow-Townes formula,the non-rotating wave terms would cause the linewidth to increase since the non-rotating wave terms decrease the average photon number.The degree of increasing in linewidth depends not only on the square of the ratio of the atomic natural de-cay rate to radiation frequency,but also on the average photon number in rotating wave approxima-tion.The influence of the non-rotating wave terms on the laser linewidth is much larger than on the photon number fluctuations.
The problem of the quantum-limited or intrinsic linewidth of a good-cavity laser is revisited. Starting from the Scully-Lamb master equation, we present a fully analytical treatment to determine the correlation function and the spectrum of the cavity field at steady state. For this purpose, we develop an analytical approximation method that implicitly incorporates the microscopic fluctuations of both the phase and intensity of the field, and, in addition, takes full account of the saturation of the nonlinear gain. Our main result is a simple formula for the quantum-limited linewidth that is valid from near to far above threshold and also includes the presence of thermal photons. Close to the threshold, the linewidth is twice as large as predicted by the standard phase-diffusion treatment neglecting intensity fluctuations, and even 50% above threshold the increase is still considerable. In general, quantum fluctuations of the intensity are present and continue to influence the linewidth as long as the photon-number distribution is not strictly Poissonian. This inherent relationship is displayed by a formula relating the linewidth and the Mandel Q parameter. More than 100% above treshold the linewidth is found to be smaller than predicted by the standard treatment, since the simple phase-diffusion model increasingly overestimates the rate of phase fluctuations by neglecting gain saturation. In the limit of a very large mean photon number the expected perfectly coherent classical field is obtained.