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The European Physical Journal D

Quantum derivation of the excess noise factor in lasers with non-orthogonal eigenmodes

Philippe Grangier, J.-Ph. Poizat

Published Aug 1, 1999• 25 citations
Publisher
DOI
10.1007/s100530050353

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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.
A quantum theory for the noise of optical pulses in actively mode-locked lasers is presented. In the presence of phase modulation and/or group velocity dispersion, the linear operator that governs the time evolution of the pulse fluctuations inside the laser cavity is not Hermitian (or normal) and the eigenmodes of this operator are not orthogonal. As a result, the eigenmodes have excess noise and the noise in different eigenmodes is highly correlated. We construct quantum operators for the pulse photon number, phase, timing, and frequency fluctuations. The nonorthogonality of the eigenmodes results in excess noise in the pulse photon number, phase, timing, and frequency. The excess noise depends on the frequency chirp of the pulse and is present only at low frequencies in the spectral densities of the pulse noise operators.