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Physical Review A

Measurements of photon statistics in second-harmonic generation

Yujiang Qu, Surendra Singh

Published Mar 1, 1995• 17 citations
Publisher

Abstract

Statistical properties of second-harmonic photons generated by a single-mode laser operating near threshold are investigated by means of photoelectric counting measurements. It is found that second-harmonic photons display superthermal fluctuations below threshold where pump statistics are thermal. Above threshold, as the pump field becomes coherent, second-harmonic photons approach Poisson statistics. These measurements, interpreted as two-photon statistics of the fundamental beam, provide experimental evidence for the dependence of the fluctuation properties of a light beam on the process of detection.

DOI
10.1103/physreva.51.2530

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Statistical properties of second-harmonic photons generated by a single-mode laser operating near threshold are investigated by means of photoelectric counting measurements. It is found that second-harmonic photons display superthermal fluctuations below threshold where pump statistics are thermal. Above threshold, as the pump field becomes coherent, second-harmonic photons approach Poisson statistics. These measurements, interpreted as two-photon statistics of the fundamental beam, provide experimental evidence for the dependence of the fluctuation properties of a light beam on the process of detection.
Fluctuation properties of the fundamental light beam in intracavity second harmonic generation (ISHG) are studied theoretically. It is shown that the field produced by the ISHG can be described as a superposition of a coherent component and bivariate Gaussian noise field. Using this property of the ISHG field a generating function for photon counting statistics is obtained. From this generating function various expressions for quantities characterizing statistical properties such as photon counting distribution, factorial moments, and statistics of times are calculated. Curves are presented to illustrate the behavior. These results for the ISHG are also compared with those obtained for the optical parametric oscillators.
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.
The effect of the quantum properties of light on nonlinear processes has been well studied theoretically. It has been shown that the efficiency of n-photon nonlinear processes in many cases scales as the normalized n-th order correlation function. For light with high intensity correlation function, the efficiency of the n-th harmonic generation will be considerably higher than for coherent light. The experimental observation of this effect remained difficult until recently, because of the absence of bright sources with strong and fast intensity fluctuations. For the experimental demonstration of statistical effects in optical harmonic generation we use as a pump the radiation of high-gain parametric down conversion. Such light shows quantum properties (e.g. quadrature or two-mode squeezing) and has large number of photons in one mode. The normalized n-th order correlation function for this light is (2n - 1)!!, which makes it more attractive for nonlinear processes than both coherent and thermal light. For the generation of optical harmonics we used broadband parametric down conversion around frequency-degeneracy (1600 nm) produced in 1cm BBO crystal from Ti:Sapphire laser (800 nm, 1.6ps, 5kHz, 3W mean intensity). Due to spectral filtering and post-selection technique we could vary the statistics of light from coherent to super-bunched, which allowed us to demonstrate the efficiency enhancement for second-, third-, and fourth-harmonic generation. The obtained experimental results show a good agreement with the theory.
Changes in the statistical properties of light undergoing second-harmonic generation are investigated in the photon-number-resolving domain. We theoretically demonstrate that when a portion of multimode thermal light produced by parametric down-conversion is up-converted, both the second-harmonics and the residual beam at the fundamental wavelength are endowed with super-thermal photon-number distributions. The experimental results, which were obtained by exploiting the photo-number-resolving capability of hybrid photodetectors, are in excellent agreement with the theoretical expectations.
Second-harmonic generation (SHG) has been predicted to be very sensitive to photon bunching. Because of its two-photon nature SHG would be more efficient with bunched than with random or antibunched photon sequences of the same mean intensity. We use this phenomenon to demonstrate the bunching of photons in time. The fundamental beam, derived from a laser operating near threshold, was focused into a 90° temperature phase matched nonlinear crystal. The operating point of the laser was varied in the neighborhood of threshold, and a feedback loop stabilized its intensity at each operating point. It is well known that the character of laser light changes in passing the threshold of laser action. Underlying photon sequences are bunched below threshold and random above threshold.