We introduce a "statistical microscope" which allows the accurate determination of a small number of infrared photons inside a laser cavity by optical (rather than electron) multiplication. For this purpose, we induce a loss switch in a CO 2 laser and then measure the statistical distribution of passage times through a threshold value within the linear regime. Our approach is model independent, since the measured cumulants provide both average values and associated error bars. Furthermore, our method discriminates the initial photon number from noise contributions along the amplifying path, thus it does not depend on the statistical features of the amplifying process.
We introduce a "statistical microscope" which allows the accurate determination of a small number of infrared photons inside a laser cavity by optical (rather than electron) multiplication. For this purpose, we induce a loss switch in a CO 2 laser and then measure the statistical distribution of passage times through a threshold value within the linear regime. Our approach is model independent, since the measured cumulants provide both average values and associated error bars. Furthermore, our method discriminates the initial photon number from noise contributions along the amplifying path, thus it does not depend on the statistical features of the amplifying process.
We measure the statistical distribution of buildup times for the field of a single-mode CO2 laser when cavity losses have rapidly changed from a large to a small value. The ratio between the average buildup time and its statistical spread is shown to be a sensitive test of the quantum fluctuations in the off state. This method operates as a ``statistical microscope,'' permitting the accurate determination of a small mean photon number in the infrared region by optical amplification, and a discrimination of the initial mean photon number from noise contributions along the amplification process. Following the buildup, the laser pulse decays on two time scales. The faster one, due to the radiation coupling, can be fitted by a Toda oscillator model; the slower one, due to the collisional dynamics of the excited population, provides a quantitative evaluation of two distinct population decay rates, one within the rotational manifold and the other one out of the vibrational band.
Laser fluctuations are measured and characterized with a new technique based on the concept of first-passage-time distributions. This first-passage-time technique makes it possible to discern quantum noise in a dye laser even in the presence of pump fluctuations that are many orders of magnitude larger. We report new analytic and experimental results for the mean, variance, and skewness of the first-passage-time distributions. The analytic results agree well with numerical computations and experimental measurements. Our technique is particularly suited to the quantitative description of laser fluctuations above threshold; it complements the conventional photoelectric counting and correlation methods which are valuable for lasers below and near threshold but are difficult to implement for lasers far above threshold. The limits of validity of the theory containing a cubic nonlinearity are examined in the context of passage-time measurements. The effects of multiplicative noise and saturation on the variance of the intensity fluctuations are also discussed. A new signature of multiplicative noise is predicted.
We report a measurement workflow free of systematic errors consisting of a reconfigurable photon-number-resolving detector, custom electronic circuitry, and faithful data-processing algorithm. We achieve an unprecedented accurate measurement of various photon-number distributions going beyond the number of detection channels with an average fidelity of 0.998, where the error is primarily caused by the sources themselves. Mean numbers of photons cover values up to 20 and faithful autocorrelation measurements range from g^{(2)}=6×10^{-3} to 2. We successfully detect chaotic, classical, nonclassical, non-Gaussian, and negative-Wigner-function light. Our results open new paths for optical technologies by providing full access to the photon-number information without the necessity of detector tomography.
We derive the photon-number probability distribution and the resulting degree of second-order optical coherence for light emission from a uniformly distributed active species within a multiple-light-scattering medium. This is obtained from a master equation describing the probability distribution for photons in the vicinity of position r, traveling with a wave vector k, related, in turn, to a coarse-grained average of the optical Wigner coherence function. Using a simple model for isotropic, spatially uncorrelated scatterers, this reduces to a generalization of the master equation of a conventional laser in which the medium behaves like a random collection of low-quality factor cavities that are coupled by photon diffusion between a given cavity and its neighbors. Laserlike coherence, on average, is obtained in the random laser above a specific pumping threshold. Photon-number statistics above and below the lasing threshold are computed by first assuming that the atomic response to the local electromagnetic fields is nearly instantaneous. Corrections to this simple model, arising from nonadiabatic atomic dynamics, are then estimated. The dependence of the photon statistics on scatterer density, gain concentration, and position within a sample reveal that, on average, increase of the scattering strength (decrease of the photon transport mean free path) in the medium leads to a sharper peak in the local photon-number distribution, characteristic of increased local coherence in the optical field. We also evaluate the coherence of the output field at points outside the random-laser medium. This is a weighted average of radiation emitted at different positions in the sample, exhibiting varying degrees of coherence due to variations in the local pumping intensity.
Laser amplification kicks off with just a few photons in the cavity, a regime where standard additive Langevin noise cannot capture the real fluctuations. To understand how this amplification begins, we map out a single-mode photon-carrier model that links macroscopic lasers directly into nanolasers. Stationary rate equations reveal that stimulated emission takes over across a tight pump window. In nanolasers, however, spontaneous processes coexist across a much broader range. Because steady-state averages miss the individual events that lead to the macroscopic photon number, we frame the stochastic dynamics around the actual discrete transitions, deriving a state-dependent diffusion approximation. The destruction of an excited carrier concurrent with the generation of a photon creates a negative photon-carrier cross-correlation. This unavoidably leads to a correlated, multiplicative Gaussian-noise framework. We track the resulting discrete dynamics with an established, event-based Laser Markov Chain (LMC) which stochastically samples pump, relaxation, emission, and cavity-loss events keeping all physical quantities as non-negative integers. Comparing its predictions to those of our multiplicative model proves that the latter reproduces excellently well the statistical behavior of photons and carrier, as long as a continuous diffusion description holds. Once the emission drops into the few-photon regime, however, the discrete model becomes indispensable. On the other hand, at large photon counts relative fluctuations shrink to a level where the state-dependence of the diffusion matrix can be ignored, to leading order, thus returning to the classic Langevin description of the system's stochastic dynamics.
The transient statistical properties of a single-mode laser field are investigated both experimentally and theoretically. The physical system is a Q-switched He-Ne gas laser oscillating on the 6328-\AA{} transition. The measurements are performed by photon-counting techniques, using the so-called linear method which enables resolving times to be in the nsec region. The effects of the photomultiplier and of the attenuators on the statistics are taken into account. The measurements are interpreted in terms of the available laser theories as well as in terms of a simple phenomenological model which attributes the statistical spread to the initial photon distribution, neglecting the stochastic forces in the course of the buildup. Finally, some of the approximations of the theories are discussed, and the sensitivity of a transient measurement is compared with that of a stationary-intensity-correlation measurement.