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Physical Review A

Semiclassical dynamics of excess quantum noise

Martin P. van Exter, N. J. van Druten, A. M. van der Lee, S. M. Dutra, Gerard Nienhuis, J. P. Woerdman

Published Mar 5, 2001• 10 citations
Publisher

Abstract

A semiclassical theoretical framework is presented to describe the essential features of the excess quantum noise that occurs in systems with nonorthogonal eigenmodes. Excess noise is shown to be always spectrally colored, instead of white, so that the Petermann excess noise factor is best written as $K(\ensuremath{\omega})$ instead of K. The consequences of this spectral coloring are analyzed for lasers, both below and above the lasing threshold.

DOI
10.1103/physreva.63.043801

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A semiclassical theoretical framework is presented to describe the essential features of the excess quantum noise that occurs in systems with nonorthogonal eigenmodes. Excess noise is shown to be always spectrally colored, instead of white, so that the Petermann excess noise factor is best written as K(\ensuremathω)K(\ensuremath{\omega})K(\ensuremathω) instead of K. The consequences of this spectral coloring are analyzed for lasers, both below and above the lasing threshold.
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.
To meet recent experimental advances, we generalize the intuitively appealing nonorthogonal-mode theory of excess quantum noise by introducing a Maxwell-Bloch description of the gain medium. The resulting equations extend the nonorthogonal-mode approach beyond the class A linear-gain regime providing a general starting point for theoretical descriptions of excess quantum noise. As an illustration of our theory, we derive rate equations describing excess quantum noise in class B lasers and obtain the non-Lorentzian spectrum due to the coloring of excess noise in class A lasers accounting for gain saturation.
We propose a generalized radiation-field quantization formalism, where quantization does not have to be referenced to a set of power-orthogonal eigenmodes as conventionally required. This formalism can be used to directly quantize the true system eigenmodes, which can be non-power-orthogonal due to the open nature of the system or the gain/loss medium involved in the system. We apply this generalized field quantization to the laser linewidth problem, in particular, lasers with non-power-orthogonal oscillation modes, and derive the excess-noise factor in a fully quantum-mechanical framework. We also show that, despite the excess-noise factor for oscillating modes, the total spatially averaged decay rate for the laser atoms remains unchanged.