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Applied Physics Letters

MEASUREMENTS OF PHOTON CORRELATIONS OF SECOND HARMONIC GENERATED LIGHT

F. Davidson, J. Klebba, C. L. Laurence, Frank K. Tittel

Published Aug 1, 1970• 4 citations
Publisher

Abstract

Results of measurements of the second-order intensity correlation function of the optical field produced by cw optical second harmonic generation in a LiNbO3 crystal pumped by a He–Ne laser operating in two independent axial modes are reported. The observed correlation function is shown to be in agreement with theoretical descriptions of second harmonic generation and with coherence theory.

DOI
10.1063/1.1653329

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Results of measurements of the second-order intensity correlation function of the optical field produced by cw optical second harmonic generation in a LiNbO3 crystal pumped by a He–Ne laser operating in two independent axial modes are reported. The observed correlation function is shown to be in agreement with theoretical descriptions of second harmonic generation and with coherence theory.
The purpose of this investigation was to construct the experimental apparatus for measuring second-order intensity correlation functions of the type T2,2 (x,t,x,t+T) = < : I(x,t)I(x,t+T):>. This measurement was applied to the radiation field produced by a two axial mode Helium-Neon gas laser in order to verify the intensity fluctuation correlations due to the beating of the two axial modes of the laser. The axial mode separation was measured for comparison with a scanning Fabry Perot interferometer and also an RF spectrum analyzer. The correlation measurement was also applied to the second harmonic radiation field produced by the. parametric interaction in a LiNb03 crystal pumped with two axial modes. The experimental determination of the correlation <:I(x,t)I(x,t+T):> involves a time-spectroscopy measurement in which one photon is detected at point x, and another at point x, T seconds later, and measuring the probability of two-fold coincident detection as a function of T. The radiation field was split into two beams at a partially transmitting reflector, each of which was directed incident on the photocathode of a photomultiplier tube. The photoelectron pulses from the tubes were amplified and standardized. These standardized pulses were then temporally correlated with the use of a time-to-amplitude converter (TAC) and a multi-channel pulse height analyzer (MA). The time-to-amplitude conversions generated by the TAC were stored in the channels of the PHA, which was a direct measure of the two-fold delayed coincidence detection rate, R(T). The second-order intensity correlation functions <:I(x,t)I(x,t+T):> are determined from measurements of R(T). The fluctuating components of the second-order intensity correlation functions were found to be in agreement with what would be expected on a classical basis. Correspondingly, the capability is demonstrated of the experimental apparatus measuring a quantity relating to the second-order intensity correlation function.
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.
Summary form only given. The second-order correlation function of the intensity is a measurement of the intensity fluctuations and their enhancement or suppression relative to an ideal laser field. It is a sensitive probe of the dynamic processes involved in producing the light. We have measured the correlation function of the photons escaping from a cavity QED system consisting of a high-finesse interferometer traversed by an atomic beam of optically pumped Rb atoms. We observe nonclassical correlations, exhibiting antibunching and sub-Poissonian statistics.
An intensity-correlation experiment is proposed to test the second-order coherence of laser light from a cw-operated laser based on the Glauber formalism. The calculation utilizes the known form of the density matrix for radiation from a randomly excited source such as a discharge tube which is equivalent to filtered black-body radiation, and represents the laser radiation field by a coherent state. The intensity correlation calculated exhibits the standard Hanbury Brown-Twiss term and an extra term due to intensity interference between the Fourier components of the thermal field and the laser mode.