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Optics Letters

Higher-order photon statistics of single-mode laser diodes and microchip solid-state lasers

Tsong‐Shin Lim, Jyh‐Long Chern, Kenju Otsuka

Published Dec 15, 2002• 2 citations
Publisher

Abstract

We examine higher-order photon statisitics of laser diodes (LDs) and microchip solid-state lasers (SSLs). When the lasers are operated above lasing threshold, significantly different features of fluctuations are exhibited, which are the result of the asymmetric non-Gaussian distribution characteristics that are always present in SSLs, whereas, in contrast, Gaussian fluctuation persists in LDs. It is found that the deterministic dynamic trajectory in phase space, which is controlled by the ratio between the fluorescence and the photon lifetimes, is crucial to the corresponding behavior of higher-order statistics.

DOI
10.1364/ol.27.002197

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The intensity fluctuations of laser light are derived from photon number rate equations. In the limit of short times, the photon statistics for small laser devices such as typical semiconductor laser diodes show thermal characteristics, even above threshold. In the limit of long-time averages represented by the low-frequency component of the noise, the same devices exhibit squeezing. It is shown that squeezing and thermal noise can coexist in the multimode output field of laser diodes. This result implies that the squeezed light generated by regularly pumped semiconductor laser diodes is qualitatively different from single-mode squeezed light. In particular, no entanglement between photons can be generated by use of this type of collective multimode squeezing.
We use balanced homodyne detection to characterize light from a diode laser as it crosses the threshold. We measure the single-time second-order correlation function g(2), and also extract the photon number distribution. Just above the laser threshold, we find that the measured g(2) exceeds the prediction of the semiclassical single-mode laser model. From the reconstructed photon number distributions, we conclude that this excess is due to emission from nonlasing modes. For higher pumping current, the light noise increases due to a different mechanism, possibly mode competition or mode partition noise.
Coherence properties of light beams generated by optical parametric oscillators (OPOs) are discussed in the region of threshold. Analytic expressions, that are valid throughout the threshold region, for experimentally measurable quantities such as the mean and variance of photon number fluctuations, squeezing of field quadratures, and photon counting distributions are derived. These expressions describe non-Gaussian fluctuations of light in the region of threshold and reproduce Gaussian fluctuations below and above threshold, thus providing a bridge between below and above threshold regimes of operation. They are used to study the transformation of fluctuation properties of light as the OPOs make a transition from below to above threshold. The results for the OPOs are compared to those for the single-mode and two-mode lasers and their similarities and differences are discussed.
Lasing transition is known to be analogous to the second-order phase transition. Furthermore, for some cases, it is possible to define the Ginzburg-Landau (GL) potential, and the GL theory predicts the photon statistical properties of lasers. However, the GL potential for lasers is surprising, because lasers are operating far from equilibrium. In this paper, we theoretically examine the validity of the GL theory for lasers in terms of various parameters, particularly, the ratio between photon and carrier lifetimes. For this purpose, we use stochastic rate equations and higher-order photon correlation functions. With higher-order photon correlation measurements, we can check whether or not laser dynamics are described by the GL theory. We demonstrate that, for low-βββ lasers, the GL theory is applicable even when the photon lifetime is comparable to the carrier lifetime and that photon-carrier relaxation oscillation is the fundamental origin of the breakdown of the GL theory, which can be understood in the framework of center manifold reduction.
The evolution of the first and second moments of the photon density distribution for a two-mode laser system was studied by proposing appropriate transition rate expressions and using the Kubo equations developed for a Chapman-Kolmogorov system. A numerical analysis technique was used in solving the rate equations and computer plots were generated for various combinations of laser parameter values. Anomalously large fluctuations, similar to those occurring in single-mode lasers, were observed during photon buildup of the modes. When only one mode was oscillating, a photon buildup in the non-lasing mode was seen to cause similar fluctuations in the lasing mode. In all cases, these fluctuations were accompanied by a strong linear relationship between the modes. (Author)
A quantitative analysis is made of quantum fluctuations in the number of photons in the resonator of a single-mode laser considered in a quasi-linear approximation. An expression is obtained for a general four-level system, which is exact above the lasing threshold, but can also be used to calculate the fluctuations in the case of three- and two-level lasers. Above the threshold when certain relationships between the spontaneous decay constants are satisfied, the photon statistics are of the sub-Poisson type in four- and three-level systems. However, for other relationships between the decay constants, pumping rate, and average number of photons, fluctuations in the resonator obey both the Poisson and super-Poisson statistics with variances much greater than the average number of photons. Both Poisson and super-Poisson statistics with large values of the variance are found for a two-level system. The results of calculations indicate that, in general, there is no coherent Glauber state of the field in a laser resonator when the threshold is significantly exceeded.