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Europhysics Letters (EPL)

Vectorial excess noise factor in common lasers

Olivier Émile, M. Brunel, A. Le Floch, Fabien Bretenaker

Published Jul 15, 1998• 31 citations
Publisher

Abstract

The fundamental linewidth of usual lasers containing linear phase and loss anisotropies is experimentally and theoretically investigated. It is proved that the eigenstates of such lasers are in general nonorthogonal, leading to the prediction of an important excess noise factor. The experiment evidences an enhancement of the Schawlow-Townes linewidth up to a factor of nearly one hundred, in good agreement with theory.

DOI
10.1209/epl/i1998-00334-5

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The fundamental linewidth of usual lasers containing linear phase and loss anisotropies is experimentally and theoretically investigated. It is proved that the eigenstates of such lasers are in general nonorthogonal, leading to the prediction of an important excess noise factor. The experiment evidences an enhancement of the Schawlow-Townes linewidth up to a factor of nearly one hundred, in good agreement with theory.
A recent theory of the fundamental laser linewidth developed by the authors is extended to include the effects of the Henry \ensuremath{\alpha} parameter. The usual (1+${\mathrm{\ensuremath{\alpha}}}^{2}$) enhancement of the linewidth is shown to be increased for arbitrary output coupling by spatial hole burning. A total enhancement factor is derived that multiplies the Schawlow-Townes linewidth and takes into account line broadening due to amplification of quantum noise as well as that due to phase-amplitude coupling.
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Using a semiclassical approach we derive a general expression for the quantum-limited linewidth of a single-mode laser. We include both nonuniform properties of the laser medium and localized losses at mirrors and apertures. For such systems the transverse modes are known to be nonorthogonal, giving rise to an enhancement of the laser noise. The transverse factor varies, in general, along the propagation direction. The combination of transverse and longitudinal noise enhancement is far from trivial. In particular, we show that for an aperture in the cavity, the transverse excess noise factor is the geometric mean of the factors pertaining to the two regions in which the aperture divides the cavity.
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 theoretically investigate the quantum dynamics of an unstable resonator laser. Compared to a stable cavity laser of equal gain and loss it exhibits a K-fold enhanced linewidth. This excess noise factor K is a measure of the nonorthogonality of the resonator eigenmodes and amounts to an enlargement of the quantum vacuum fluctuations. Using a quantum treatment starting from first principles based on the nonorthogonal eigenmodes, we put previous theoretical predictions onto a more firm ground. While we find a position-dependent enhancement of the spontaneous emission rate into an empty mode of only K,\sqrt{K},K​, the constructive quantum interference of the spontaneous emission with a single oscillating mode lets the Petermann excess noise factor K reappear in the phase diffusion (laser linewidth). Hence locally enhanced spontaneous emission as well as noise enhanced by interference (amplified spontaneous emission) play an equal role in the origin of excess noise.
We describe the quantum-noise behavior of a laser that has nonorthogonal polarization modes. The nonorthogonality of the modes leads to excess quantum noise. Theoretically, we derive the excess noise dynamics of the laser, including the saturation of the gain medium. Experimentally, we have measured the noise dynamics in the polarization, intensity and phase degrees of freedom of a 3.51-$\ensuremath{\mu}\mathrm{m}\mathrm{}$ HeXe laser and we obtain good agreement with theory. When the modes are made nonorthogonal we observe: (i) excess intensity and phase noise, (ii) spectral coloring of the excess intensity noise and (iii) correlations between the polarization-angle noise and the intensity noise. The excess phase noise is found to be partly suppressed by the polarization-anisotropic part of the saturation of the gain medium.