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IEEE Journal of Quantum Electronics

Noise spectra and noise correlation functions of the single-mode laser with a low-Q cavity

T. Ogawa

Published Jan 1, 1989• 3 citations
Publisher

Abstract

The noise characteristics of a single-mode laser with a low-Q cavity are investigated theoretically. After the electric field is adiabatically eliminated from the Maxwell-Bloch equations, coupled Langevin equations with both additive and multiplicative white noises are examined. The equations are solved using Rice's method in a framework of quasilinear Fourier analysis. Noise spectral densities are calculated analytically to study the dependence of the relative intensity noise (RIN) on the pumping. Through an investigation of the auto- and cross-correlations of the light intensity and population noises, their variances are obtained in order to compare their properties to the good-cavity case. The stationary intensity cumulants, the photon counting coefficient, and the photon counting probability are explicitly derived and compared with the results of a Fokker-Planck analysis previously carried out for both the good- and bad-cavity cases.>

DOI
10.1109/3.35732

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The noise characteristics of a single-mode laser with a low-Q cavity are investigated theoretically. After the electric field is adiabatically eliminated from the Maxwell-Bloch equations, coupled Langevin equations with both additive and multiplicative white noises are examined. The equations are solved using Rice's method in a framework of quasilinear Fourier analysis. Noise spectral densities are calculated analytically to study the dependence of the relative intensity noise (RIN) on the pumping. Through an investigation of the auto- and cross-correlations of the light intensity and population noises, their variances are obtained in order to compare their properties to the good-cavity case. The stationary intensity cumulants, the photon counting coefficient, and the photon counting probability are explicitly derived and compared with the results of a Fokker-Planck analysis previously carried out for both the good- and bad-cavity cases.>
The steady-state fluctuations of an inhomogeneously broadened two-mode laser with both additive and multiplicative white noise are investigated theoretically. A Fokker-Planck equation of the intensity-distribution function is presented. Analytic expressions of the autocorrelation and cross correlation of the steady-state two-mode intensities are derived for equal pump parameters of the two modes. Large intensity fluctuations occur when the laser is operated below threshold. However, when the laser is operated far above threshold, there is almost no difference between the laser models with and without multiplicative noise.
The statistical noise properties of the laser radiation in a low-Q (bad) cavity are theoretically investigated. The bad-cavity laser system is shown to be exactly equivalent to the stochastic Toda oscillator (STO) in the case of negligible polarization noise. Transforming the STO Langevin equation to the Fokker-Planck equation with a position-dependent diffusion coefficient, analytical expressions of the probability distribution are obtained as particular solutions in a stationary state with the aid of the expansion into a complete orthogonal set. We predict novel statistical features of the laser light, e.g., a power tail of the intensity distribution function, non-Gaussian nature of the field fluctuation, and super-Poissonian photoelectron statistics. General solutions are also given in a closed form in terms of the matrix continued fraction to compare with the particular solutions. The good-cavity case is reanalyzed in our formalism to root out differences between them.
The saturation effects in a single-mode laser with multiplicative white noise are investigated through a full saturation laser model. The corresponding Fokker-Planck equation is transformed to a radial Schr\"odinger equation and the intensity correlation time and effective eigenvalues are calculated. Compared with experimental measurements, excellent agreement is obtained and the cavity decay rate is also determined. Relatively large errors occur in the third-order theory and the measured data.
Abstract The noise feature of a single-mode class-A laser amplifier is investigated by solving the Maxwell–Bloch equations of motion in the presence of the fluctuation force of cavity Langevin. The aim is to calculate the simultaneous fluctuations that are superimposed on the amplitude and phase of the cavity electric field, as well as the atomic population inversion. The correlation function of these fluctuations yields the amplitude, phase, and spontaneous emission noise fluxes, respectively. The amplitude and spontaneous emission noise fluxes exhibit the Lorentzian profiles in both the below-threshold state and the injection-locking region of the above-threshold state. While noise is typically viewed negatively in science and engineering, this research highlights its positive role as a valuable tool for measuring the optical properties of a laser amplifier. For instance, the degree of first-order temporal coherence (DFOTC) is derived by taking the Fourier transform of the amplitude noise flux. The damping rate of DFOTC is associated with the coherence time of the light emitted by the laser amplifier. Furthermore, the uncertainty relation between noise bandwidth and coherence time is confirmed. Finally, it is demonstrated that the input pumping noise flux, together with the output amplitude and spontaneous emission noise fluxes, satisfy the principle of flux conservation.
Based on the Fokker-Planck description of a single-mode laser model with correlations between the real and imaginary parts of the quantum noise as well as the pump noise,the dynamical properties of the laser system were studied by using of the mean relaxation time approximation method.The intensity correlation function and the associated mean relaxation time were calculated.It is found that the presence of correlations between the real and imaginary parts of the quantum noise always slows down the relaxation of the light intensity fluctuation when the laser is operated over the threshold.
The noise feature of a single mode class-A laser is investigated in the presence (amplifier) and absence (free-running) of an input signal. The Maxwell-Bloch equations of motion have been solved after adding the cavity Langevin force to calculate fluctuations that imposed to the atomic population inversion and the amplitude and phase of cavity electric field. The correlation function of these fluctuations is then used to derive the spontaneous emission, amplitude, and phase noise fluxes in the below and above-threshold states. The bandwidth of noise fluxes is not only adjusted by the amplitude and frequency detuning of input signal, but also by the laser pumping and cavity damping rates. On the other hand, the degree of first-order temporal coherence (DFOTC) is turned out as the correlation function of the amplitude fluctuation so that its Fourier transform led to the amplitude noise flux. The coherence time plays a dual role in order that it is equal to the damping rate invers of DFOTC and at the same time has an uncertainty relation with the bandwidth of amplitude noise flux. Finally, the flux conservation requires a balance between the input pumping noise flux and the output amplitude and spontaneous emission noise fluxes.