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Measurement Science and Technology

A new technique for measuring light statistics

M V Lebedev, A. I. Filin, O. V. Misochko

Published May 14, 2001• 2 citations
Publisher

Abstract

A new technique to measure light statistics has been developed. The efficacy of the technique has been proved by measuring the statistics of a light field created by a well known light source - a low pressure 86Kr lamp. The sensitivity and temporal resolution of the technique allow photon bunching to be detected in a weak chaotic thermal light.

DOI
10.1088/0957-0233/12/6/312

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A new technique to measure light statistics has been developed. The efficacy of the technique has been proved by measuring the statistics of a light field created by a well known light source - a low pressure 86Kr lamp. The sensitivity and temporal resolution of the technique allow photon bunching to be detected in a weak chaotic thermal light.
Light from thermal blackbody radiators such as stars exhibits photon bunching behavior at sufficiently short timescales. However, with available detector bandwidths, this bunching signal is difficult to observe directly. We present an experimental technique to increase the photon bunching signal in blackbody radiation via spectral filtering of the light source. Our measurements reveal strong temporal photon bunching from blackbody radiation, including the Sun. This technique allows for an absolute measurement of the photon bunching signature g (2) (0), and thereby a direct statement on the statistical nature of a light source. Such filtering techniques may help revive the interest in intensity interferometry as a tool in astronomy.
Thermal light sources exhibiting photon bunching have been suggested for sensing applications that exploit timing correlations of stationary light, including range finding, clock synchronization, and non-line-of-sight imaging. However, these proposals have remained unrealized in practice because available sources of photon bunching either possess coherence times too short to be timing resolved by photodetectors, or produce brightness levels too low to tolerate realistic return losses. In this work, we demonstrate a low-loss method for generating photon bunching with a conversion efficiency nearly 9 orders of magnitude higher than that achieved by many other bunching processes.
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.
Thermal light such as blackbody radiation including starlight has been known to exhibit photon bunching behaviour. This is the characteristic property of thermal photons to propagate closer together than as described by random Poissonian timing statistics. Although first theorised in the 1960s, attempts to directly probe the temporal coherence of starlight has remained challenging due to the very short timescales required. This work aims to address that by using narrowband spectral filtering to increase the timescale sufficiently for a direct measurement. We present calibration tests using laboratory light sources towards an observatory measurement.