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The European Physical Journal A

Fokker-Planck equation, distribution and correlation functions for laser noise

H. Risken, Ch. Schmid, Wolfgang Weidlich

Published Aug 1, 1966• 101 citations
Publisher
DOI
10.1007/bf01326279

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A single-mode laser noise model driven by quadratic pump noise and quantum noise with cross-correlation between the real and imaginary parts of the noises is proposed. The approximate Fokker-Planck equation (AFPE) of the model for the laser phase and the laser amplitude is derived. It is found that the laser phase is controlled intensively by the correlation between the real and imaginary parts of the pump noise and that of the quantum noise. The correlation between the real and imaginary parts of quantum noise ${\ensuremath{\lambda}}_{q}$ tends to lead the laser phase to be locked at some values and the correlation between the real and imaginary parts of the pump noise ${\ensuremath{\lambda}}_{p}$ tends to destroy or confine the laser phase lock. Quantitative results are presented and discussed in detail. As an important application of the above-mentioned results, we take a phase lock approximation to get a Langevin equation for the laser field amplitude and an AFPE of the laser intensity.

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Theory of Some Laser Noise Effects

Y. K. Wang, Willis E. Lamb

Using semiclassical theory, we investigate the shot- and thermal-noise effects on the behavior of a laser. The Fokker-Planck equations for the probability distribution of the laser field are derived. These equations are approximately solved, using a Gaussian function, from which we calculate the spectral profile of the laser field. The width constant for the thermal noise is related to the temperature of the cavity.

Physical Review A•Aug 1, 1973•5 citations
A single-mode laser noise model driven by quadratic pump noise and quantum noise with cross-correlation between the real and imaginary parts of the noises is proposed. The approximate Fokker-Planck equation (AFPE) of the model for the laser phase and the laser amplitude is derived. It is found that the laser phase is controlled intensively by the correlation between the real and imaginary parts of the pump noise and that of the quantum noise. The correlation between the real and imaginary parts of quantum noise ${\ensuremath{\lambda}}_{q}$ tends to lead the laser phase to be locked at some values and the correlation between the real and imaginary parts of the pump noise ${\ensuremath{\lambda}}_{p}$ tends to destroy or confine the laser phase lock. Quantitative results are presented and discussed in detail. As an important application of the above-mentioned results, we take a phase lock approximation to get a Langevin equation for the laser field amplitude and an AFPE of the laser intensity.
The linear theory of the correlated-emission laser (CEL) is studied using the quantum-mechanical definition of the phase of the electromagnetic field recently introduced by Barnett and Pegg [J. Mod. Opt. 36, 17 (1989); Phys. Rev. A 39, 1665 (1989)]. From the master equation for the density matrix of the field, a Fokker-Planck equation for the phase probability function is derived, and the phase properties of the CEL discussed. The Adler equation and the equation of motion for the variance of the phase difference are derived. The Fokker-Planck equation satisfied by the phase probability function is compared with the corresponding equations for the P, Q, and Wigner quasiprobability distributions, specialized to the case when amplitude fluctuations are negligible. We show that the phase probability function and the Wigner function satisfy the same equation, and conclude that, of the three quasiprobability functions studied, only the Wigner function is reliable for calculating directly the phase properties. The commonly used P function overestimates the laser linewidth by a factor of 2.