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Optics Letters

Direct detection of super-thermal photon-number statistics in second-harmonic generation

Alessia Allevi, Maria Bondani

Published Jun 23, 2015• 25 citations
Publisher

Abstract

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.

DOI
10.1364/ol.40.003089

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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.
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.
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.
We use hybrid photodetectors endowed with partial photon-number resolution to characterize the photon-number distribution of twin-beam states produced at different intensity regimes up to pump depletion. To match the detectors’ dynamics, the light of signal and idler is strongly attenuated by neutral-density filters. Since the filters do not modify the nature of any classical-light statistics, we find that signal and idler are described by a multimode thermal distribution at any pump power. The number of modes decreases at increasing pump power until pump depletion, when the number starts increasing again. The effect is qualitatively interpreted as a selective mode amplification induced by the high-gain parametric process.
Second-harmonic generation in multimode laser beams is studied experimentally. A multimode laser beam derived from a laser oscillating simultaneously in many longitudinal modes that have the same transverse profile (TEM00{\mathrm{TEM}}_{00}TEM00​) is focused into a nonlinear crystal. Noncritical phase matching is utilized to generate the second harmonic. The number of longitudinal modes is systematically varied from 1 to 7 and the dependence of the efficiency of second-harmonic generation on the number of modes in the fundamental beam is studied. Experimental results clearly demonstrate the increasing degree of photon bunching in the fundamental beam as the number of modes increases. Experimental results are discussed and compared with the predictions of theoretical models.
Parametric down-conversion (PDC) is a technique of ubiquitous experimental significance in the production of nonclassical, photon-number-correlated twin beams. Standard theory of PDC as a two-mode squeezing process predicts and homodyne measurements observe a thermal photon number distribution per beam. Recent experiments have obtained conflicting distributions. In this article, we explain the observation by an a priori theoretical model solely based on directly accessible physical quantities. We compare our predictions with experimental data and find excellent agreement.