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Physics Letters A

Stationary properties in a single-mode laser with cross-correlation between quantum noise terms

S.Z. Ke, Cao Li, D.J. Wu, K.L. Yao

Published Mar 1, 2001• 30 citations
Publisher
DOI
10.1016/s0375-9601(01)00112-8

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A two-dimensional single-mode laser model is investigated, with cross-correlations between the real and imaginary parts of the quantum noise as well as the pump noise. The general closed form of the laser intensity Langevin equation (GILE) is obtained under a stable locked phase resulting from the cross-correlation λ q between the real and imaginary parts of the quantum noise. Because of the presence of a new term containing λ q , we can unify the two opposite intensity Langevin equations which correspond to the two special cases for |λ q |→0 and |λ q |→1 in the GILE. It is expected that the transient and stationary properties of the laser model can be changed qualitatively when λ q varies.
The white-gain model and the white-loss model of a single-mode laser are investigated in the presence of cross-correlations between the real and imaginary parts of quantum noise as well as pump noise. It was found that, like the white cubic model (2001 Chin. Phys. Lett. 18 370), the amplitude equations are all decoupled from the phase equations for the two models and the same novel term appears in the amplitude equations of the two models. So we can put the amplitude equations of all the models into a general form, that is, the new amplitude equation. We further use this new amplitude equation to study specifically the stationary properties of the laser intensity for the white-gain model.
Exact formulas for the effective eigenvalue characterizing the initial decay of intensity correlation functions are given in terms of stationary moments of the intensity. Spontaneous emission noise and nonwhite pump noise are considered. Our results are discussed in connection with earlier calculations, simulations, and experimental results for single-mode dye lasers, two-mode inhomogeneously broadened lasers, and two-mode dye ring lasers. The effective eigenvalue is seen to depend sensitively on noise characteristics and symmetry properties of the system. In particular, the effective eigenvalue associated with cross correlations of two-mode lasers is seen to vanish in the absence of pump noise as a consequence of detailed balance. In the presence of pump noise, the vanishing of this eigenvalue requires equal pump parameters for the two modes and statistical independence of spontaneous emission noise acting on each mode.