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Measurements of photon correlations in quasi-coherent optical fields

J. Klebba

Published Jan 1, 1970• 0 citations
OpenAlex

Abstract

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.

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Two-photon correlation measurement provides a promising way to experimentally demonstrate the statistical nature of a light source, which is very significant for the deep understanding of the photon-generating process and the diagnosing of the coherence property. Quantitatively two- photon correlation is described by second-order coherence. Usually the behavior of the second-order coherence against any of the parameters defining the phase volume is different for different photon statistics. The Poisson photon statistics for coherent light gives its second-order coherence as a flat response; The Bose-Einstein photon statistics for chaotic light gives its second-order coherence as a bunching effect; While the Sub-Poisson photon statistics for non-classical light gives its second-order coherence as an anti-bunching effect. 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However there exists a general problem, to which no attention has ever been paid, in measuring the two-photon correlation of non-stationary light such as synchrotron radiation (SR) by the HBT method. Here the "non-stationary" means a sense of classical mechanics that the observed intensity has some deterministic time structure. The systematic time structure of SR decided by the bunch distribution of the electric current in a storage ring will give rise to a large amount of unexpected accidental correlation, which in fact has nothing to do with the inherent photon statistics of light source and usually l000～l0000 times larger than the true two-photon correlation due to the short bunch separation length (2ns) and the short coherence time (～0.1ps) which is not comparable to the time resolution (1ns) of the measuring system. The existence of the accidental correlation would severely prevent us from observing the bunching effect of the true two-photon correlation. Therefore to suppress the much larger accidental correlation and to extract the small true two-photon correlation, a novel intensity interferometer has been developed for soft X-ray synchrotron radiation. This intensity interferometer consists of an optical vacuum chamber and an electric correlator. All the essential optical elements which includes a wire scanner, a precise diffraction slit, a grating monochromator with a coherence time modulator, a beam divider and two fast-response photon detectors (microchannel plates) are mounted in this high vacuum chamber. The electric correlator completes the multiplication of the two broad band electric currents coming from the photoelectric detectors. The basic idea to suppress the much larger accidental correlation is to modulate the coherence time by modulating the entrance slit width of the monochromator by a piezoclectric translator. The two sets of light intensity are simultaneously modulated too. 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•Mar 24, 1999•0 citations
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.
A procedure for the measurement of intensity correlations of the type $〈:\stackrel{^}{I}(\mathrm{x}, t)\stackrel{^}{I}(\mathrm{x}, t+\ensuremath{\tau}):〉$ and $〈:\stackrel{^}{I}(\mathrm{x}, t)\ifmmode\times\else\texttimes\fi{}\stackrel{^}{I}(\mathrm{x}, t+{\ensuremath{\tau}}_{1})\stackrel{^}{I}(\mathrm{x}, t+{\ensuremath{\tau}}_{2}):〉$ with the use of a time-to-amplitude converter is developed. The procedure is used to measure second- and third-order intensity fluctuation correlation functions of the optical field produced by a gas laser operated at various levels near its threshold of oscillation. The results are shown to be in agreement with the predictions of laser theories.
In this study, we measured the temporal correlations in the electromagnetic field radiated by a laser in the threshold region of oscillation, from 110\frac{1}{10}101​ to 10 times threshold intensity. The experimental results are compared with theoretical predictions based on solutions of a Fokker-Planck equation. We stabilized the intensity of a He-Ne cw gas laser by means of a long-time-constant servo system which controlled the cavity length. Using a fast photomultiplier as detector, we recorded the photoelectron count distribution within a short counting time (3 \ensuremath{\mu}sec) while the photomultiplier was exposed to the laser light. From the photoelectron count distribution measurement, we calculated second, third, and fourth normalized cumulants of the intensity probability density function of the light field. The normalized cumulant is a measure of "pure" correlations among photons because the contributions from lower-order correlations are removed. The statistics of the photoelectron count distribution shows that the intensity fluctuations at about 110\frac{1}{10}101​ threshold are nearly those of a Gaussian field, and continuously approach those of a constant-amplitude field as the intensity is raised to about 10 times threshold. The normalized second, third, and fourth cumulants of the intensity probability density function of the laser light were also measured at 17 and 42% of threshold intensity as the counting time was increased from 3 to 1000 \ensuremath{\mu}sec. The results agree with predictions computed under the assumption that the dependence of the correlation functions on the time variables is the same as for Gaussian light.
We study a possibility of measuring the time-resolved second-order autocorrelation function of one of two beams generated in type-II parametric down-conversion by means of temporal magnification of this beam, bringing its correlation time from the picosecond to the nanosecond scale, which can be resolved by modern photodetectors. We show that such a measurement enables one to infer directly the degree of global coherence of that beam, which is linked by a simple relation to the number of modes characterizing the entanglement between the two generated beams. We illustrate the proposed method by an example of photon pairs generated in a periodically poled potassium titanyl phosphate (KTP) crystal with a symmetric group velocity matching for various durations of the pump pulse, resulting in different numbers of modes. Our theoretical model also shows that the magnified double-heralded autocorrelation function of one beam exhibits a local maximum around zero delay time, corresponding to photon bunching at a short time scale.
Two-photon correlation measurement provides a promising way to experimentally demonstrate the statistical nature of a light source, which is very significant for the deep understanding of the photon-generating process and the diagnosing of the coherence property. Quantitatively two- photon correlation is described by second-order coherence. Usually the behavior of the second-order coherence against any of the parameters defining the phase volume is different for different photon statistics. The Poisson photon statistics for coherent light gives its second-order coherence as a flat response; The Bose-Einstein photon statistics for chaotic light gives its second-order coherence as a bunching effect; While the Sub-Poisson photon statistics for non-classical light gives its second-order coherence as an anti-bunching effect. Therefore the measurement of two-photon correlation is proved to be a good finger print to check whether light is in coherent state or incoherent state such as thermal state or non-classical state. Historically the measurement of two-photon correlation was first performed by Hanbury-Brown and Twiss (HBT) in 1956. They used a linear mixer to realize the correlation of the two currents from the photoelectric detectors illuminated by a stationary thermal light souece, a mercury arc, and the photo-bunching effect was first successfully observed in the visible region of 435.8 nm. HBT method is no doubt a good way to extract the small excess two-photon correlation for a stationary light because the background, that is the DC components, has been cut off automatically by the broad band amplifiers, which is in fact the key of the success of HBT experiment. However there exists a general problem, to which no attention has ever been paid, in measuring the two-photon correlation of non-stationary light such as synchrotron radiation (SR) by the HBT method. Here the "non-stationary" means a sense of classical mechanics that the observed intensity has some deterministic time structure. The systematic time structure of SR decided by the bunch distribution of the electric current in a storage ring will give rise to a large amount of unexpected accidental correlation, which in fact has nothing to do with the inherent photon statistics of light source and usually l000～l0000 times larger than the true two-photon correlation due to the short bunch separation length (2ns) and the short coherence time (～0.1ps) which is not comparable to the time resolution (1ns) of the measuring system. The existence of the accidental correlation would severely prevent us from observing the bunching effect of the true two-photon correlation. Therefore to suppress the much larger accidental correlation and to extract the small true two-photon correlation, a novel intensity interferometer has been developed for soft X-ray synchrotron radiation. This intensity interferometer consists of an optical vacuum chamber and an electric correlator. All the essential optical elements which includes a wire scanner, a precise diffraction slit, a grating monochromator with a coherence time modulator, a beam divider and two fast-response photon detectors (microchannel plates) are mounted in this high vacuum chamber. The electric correlator completes the multiplication of the two broad band electric currents coming from the photoelectric detectors. The basic idea to suppress the much larger accidental correlation is to modulate the coherence time by modulating the entrance slit width of the monochromator by a piezoclectric translator. The two sets of light intensity are simultaneously modulated too. When the frequency of modulation is f, the third harmonics 3f is detected with a loch-in amplifier because the 3f components include only the true two-photon correlation. Practically it is difficult to modulate with frequency f without any higher order harmonics distortion which might add some false 3f components. To overcome this difficulty we have used a sharp bandpass filter of l00～350 MHz in each branch of the correlator, which is lower than the RF frequency 500 MHz and much higher than 1.6 MHz, the revolution frequency of the stored beam of the 2.5 GeV storage ring. This new apparatus has been operated successfully in the measurement of the horizontal two-photon correlation for the first harmonic of undulator radiation with photon energy of 70 eV at the Photon Factory, KEK. By narrowing the precise slit width which correspondingly changes the spatial coherence of the incident SR, a bunching effect of the normalized excess two-photon correlation has been clearly observed. This explicit bunching effect implies that synchrotron radiation is chaotic radiation. Further investigation shows that although second-order coherence is completely determined by the first-order coherence for the case of chaotic light, the measured information from the light source is essentially different. The two-photon correlation of synchrotron radiation does not depend on the response time of the detectors but gives the information of instantaneous emittance of the stored beam with the time scale of coherence time τC. By fitting the experimental data, the horizontal instantaneous emittance of the stored beam is estimated to be 40nmrad. This intensity interferometer can be utilized to characterize the coherence properties of incomplete FELs, such as SASE, because if they are fully coherent light sources the normalized excess two-photon correlation would have a flat response, but not showing a photon-bunching effect.