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IEEE Journal of Quantum Electronics

Evidence of nonuniform phase-diffusion in a bad-cavity laser

S. J. M. Kuppens, Martin P. van Exter, M. van Duin, J. P. Woerdman

Published Jul 1, 1995• 20 citations
Publisher

Abstract

The quantum-limited linewidth of a short HeNe 3.39-/spl mu/m laser was measured and seen to increase with increasing nonuniformity of the intracavity intensity distribution. Experiments were done inside as well as outside the bad-cavity regime; in this regime the polarization of the gain medium cannot be adiabatically eliminated but acts as a memory. Good quantitative agreement with theory is obtained inside as well as outside the bad-cavity regime. The effect of nonuniformity is well described by the longitudinal Petermann K-factor. The bad-cavity and nonuniformity effects can be separated from each other as predicted by theory.>

DOI
10.1109/3.391086

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Physical Review A•Aug 1, 1992•24 citations
The quantum-limited linewidth of a short HeNe 3.39-/spl mu/m laser was measured and seen to increase with increasing nonuniformity of the intracavity intensity distribution. Experiments were done inside as well as outside the bad-cavity regime; in this regime the polarization of the gain medium cannot be adiabatically eliminated but acts as a memory. Good quantitative agreement with theory is obtained inside as well as outside the bad-cavity regime. The effect of nonuniformity is well described by the longitudinal Petermann K-factor. The bad-cavity and nonuniformity effects can be separated from each other as predicted by theory.>
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.
A recent SSS-matrix-based theory of the quantum-limited linewidth, which is applicable to general lasers, including spatially nonuniform laser cavities operating above threshold, is analyzed in various limits. For broadband gain, a simple interpretation of the Petermann and bad-cavity factors is presented in terms of geometric relations between the zeros and poles of the SSS matrix. When there is substantial dispersion, on the frequency scale of the cavity lifetime, the theory yields a generalization of the bad-cavity factor, which was previously derived for spatially uniform one-dimensional lasers. This effect can lead to sub--Schawlow-Townes linewidths in lasers with very narrow gain widths. We derive a formula for the linewidth in terms of the lasing mode functions, which has accuracy comparable to the previous formula involving the residue of the lasing pole. These results for the quantum-limited linewidth are valid even in the regime of strong line pulling and spatial hole burning, where the linewidth cannot be factorized into independent Petermann and bad-cavity factors.
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.
The simple intuitive picture of phase diffusion in a traveling wave is introduced to calculate the fundamental (Schawlow-Townes) limit to the laser linewidth. Contrary to the usual phase-diffusion model, our variety is not limited to the regime of low outcoupling; it predicts an enhancement of the linewidth for large outcoupling. It is demonstrated that the results of the traveling-wave phase-diffusion model are identical to those of the theory of nonorthogonal eigenmodes. Finally, the effects of saturation on the linewidth are estimated.
We present a theory of the homogeneously broadened laser that is based on the simple boundary conditions that govern the connection of intracavity traveling fields and the leaking vacuum field at the cavity mirrors. The approach is uniformly valid for arbitrary output-mirror transmissions. We compute the intrinsic linewidth of the laser both below and above threshold and for arbitrary mirror outcoupling. In the limit of complete output-mirror transmission, for which any semblance of the cavity to a lasing cavity is completely untenable and the laser is severely below threshold, we show that the laser linewidth reduces to the natural linewidth of spontaneous emission by atoms in free space. Above threshold, in contrast with most previously obtained results, the fundamental linewidth exhibits a power-independent contribution that arises from gain saturation that is spatially nonuniform.