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Chinese Physics

New amplitude equation of single-mode laser

Zhang Li, Cao Li, Wu Da-Jin

Published Jan 1, 2003• 22 citations
Publisher

Abstract

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.

DOI
10.1088/1009-1963/12/1/306

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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.
By means of the unified coloured noise approximation and phase lock, we study in this paper the stationary intensity distribution of the single-mode laser cubic model driven by coloured pump noise with cross-correlation between the real and imaginary parts of the quantum noise. We present a thorough discussion of how the cross-correlation λ q between the real and imaginary parts of the quantum noise and the self-correlation time τ of the pump noise determine the behaviours of the mean intensity ⟨ I ⟩ and variance λ 2 (0) for both below and above the threshold operation and many new phenomena are discovered. When the laser is operated above the threshold, increasing the cross-correlation intensity λ q makes the ⟨ I ⟩–τ curves exhibit a ``re-entrant phase transition''. Whether the laser is above or below the threshold, the whole ⟨ I ⟩–τ curve moves down as λ q increases; however, when λ q = 1 (perfect cross-correlation), the curve abruptly runs up. A nonzero value of cross-correlation time τ (τ≠0) leads to the entire λ 2 (0)– p ′ curve being suppressed (here p ′ is the pump noise intensity). This indicates the increasing precision of the laser beam due to the existence of the self-correlation time τ. The behaviour of the λ 2 (0)– p ′ curve as a function of λ q is similar to that of the ⟨ I ⟩–τ curve against λ q : that is, whether the laser is above or below the threshold, the λ 2 (0)– p ′ curve moves up as λ q increases; however, when λ q = 1, the curve suddenly moves down. Through the study in this paper, we can find a way to optimize for output laser intensity.
A single-mode dye-laser model incorporating pump white noise through gain-parameter fluctuations is analyzed. It includes a fluctuating saturation term. Intensity fluctuations, a first-order-like transition, and intensity correlation functions are calculated and discussed. It is found that effects previously claimed to be a consequence of the presence of colored noise in the context of loss-noise models can be also explained by white gain noise, except for the existence of two time regimes in the early decay of intensity correlation functions.
Using the linear approximation method, we calculated the steady-state mean normalized intensity fluctu-ation for a loss-noise model of a single-mode laser driven by a pump noise and a quantum noise, whose real part andimaginary part are cross-correlated. We analyzed the valid range for thelinear approximation method by studying theinfluences on the steady-state mean normalized intensity fluctuation by the cross-correlation coefficient, the intensities ofthe quantum and pump noise, the net gain, and the amplitude and frequency of the input signal, and we found that thevalid range becomes wider when the cross-correlation between the real and imaginary part of quantum noise is weaker,the noise intensities of quantum and pump are weaker, the laser system is far from the threshold and the signal hassmaller amplitude and higher frequency.
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.
Using the linear approximation method, we calculated the steady-state mean normalized intensity fluctuation for a loss-noise model of a single-mode laser driven by a pump noise and a quantum noise, whose real part and imaginary part are cross-correlated. We analyzed the valid range for the linear approximation method by studying the influences on the steady-state mean normalized intensity fluctuation by the cross-correlation coefficient, the intensities of the quantum and pump noise, the net gain, and the amplitude and frequency of the input signal, and we found that the valid range becomes wider when the cross-correlation between the real and imaginary part of quantum noise is weaker, the noise intensities of quantum and pump are weaker, the laser system is far from the threshold and the signal has smaller amplitude and higher frequency.