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Quantum Electronics

Resolving power of a quantum photometer

G. Kh. Kitaeva, Alexander N. Penin

Published Aug 31, 1994• 2 citations
Publisher

Abstract

An analysis is made of the spectral and spatial resolving powers of a quantum photometer, which is an instrument for absolute (free of reference standards) measurement of the spectral density of the energy brightness of electromagnetic radiation on the basis of three-frequency parametric conversion. General expressions are obtained for the frequency and angular intervals, and also for elements of the area of the beam cross section over which averaging is carried out in the determination of the spectral density of the brightness. The dependence is determined of the resolving power of a quantum photometer on the characteristics of a parametric converter and of a recording system used in this photometer.

DOI
10.1070/qe1994v024n08abeh000180

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An analysis is made of the spectral and spatial resolving powers of a quantum photometer, which is an instrument for absolute (free of reference standards) measurement of the spectral density of the energy brightness of electromagnetic radiation on the basis of three-frequency parametric conversion. General expressions are obtained for the frequency and angular intervals, and also for elements of the area of the beam cross section over which averaging is carried out in the determination of the spectral density of the brightness. The dependence is determined of the resolving power of a quantum photometer on the characteristics of a parametric converter and of a recording system used in this photometer.
A proposal is made to use the relationship between the spontaneous and stimulated multiphoton transitions in determination of the spectra] brightness B and the effective temperature of noncoherent light. It is shown that the signal/noise ratio M of a parametric amplifier and frequency converter operating under constant pumping conditions is equal to B expressed in units of hc 2 /λ 5 = B vac , i.e., to the number n of photons per mode in the converted radiation (this number is known as the degeneracy factor). The strong frequency and angular selectivity of the coherent frequency subtraction ensures a high resolution of the proposed "photon counter". Since the relationship M = n is independent of the rate of pumping, conversion efficiency, etc., such a counter may be considered as a new type of spectral brightness and radiation temperature standard. Another possible metrological application of the parametric amplifier noise arises from the simultaneity and close coupling of the directions of emission of the idler and signal photons. This feature may be used in a source emitting a known number of photons with known momenta and directions of emission; in particular, this approach should make it possible to determine the absolute quantum efficiency of a photomultiplier.
In this paper we present schemes of experimental setups for the radiation spectral brightness measurements in the range of 0.6 - 5 (mu) for N varying from 10-1 to 102 (if, for example, (lambda) equals 1 (mu) , this range of N corresponds to the brightness temperature range from 6 (DOT) 103 to 106 K), and for photomultipliers quantum efficiency measurements in the range of 0.4 - 5 (mu) with a dynamical range 10 - 1012 photon/sec and accuracy not worse than 1%. The new measurement methods are based on the utilization of the parametric light scattering phenomenon which is a spontaneous decay of laser pump photons in correlated photon pairs in crystals with quadratic nonlinear susceptibility. The first of two methods allows measurement of the radiation spectral brightness N in absolute units ('photons per mode') in visible and infrared range. The quantity N is related to the energetic brightness spectral density B through the equation B equals (hc2/(lambda) 5)N, where h is the Plank constant, c - the light velocity, (lambda) - the wavelength. The method is absolute and does not require any reference source or detector of radiation. Quantum noise of a parametric down-convertor, caused by the zero vacuum fluctuations with an effective brightness Nvac equals 1 photon per mode, is the reference in this case. The second method concerns the quantum efficiency of photodetectors determination, and it is based on the connection between the statistics of photocurrent and the radiation which causes it. The parametric scattering is a unique source of rather intensive and directed radiation flow consisting of photon pairs. Such a flow can be used to determine the absolute quantum efficiency of photodetectors.
An investigation is made of the feasibility of absolute measurements of the brightness of light from the signal-to-noise ratio M of a parametric frequency converter with reflection and absorption in a nonlinear crystal. A model of a plane-parallel layer and a constant monochromatic pump source of frequency ω 0 is used. Equations are derived to describe the transmission and reflection of waves with frequencies ω 1 and ω 2 = ω 0 – ω 1 in the layer. The resultant four-dimensional scattering matrix determines the quantum noise of the converter in accordance with the "nonlinear" Kirchhoff law. It is found that the number of photons per mode N in the incident light is equal to M multiplied by a correction factor close to unity, which depends on the absorption coefficient and on the refractive index.
The black body remains the most prominent source of light for absolute radiometry. Its main alternative, synchrotron radiation, requires costly and large facilities. Quantum optics offers a new radiometric source: parametric down-conversion (PDC), a nonlinear optical process, in which pairwise photon correlations enable absolute calibration of photodetectors. Since the emission rate crucially depends on the brightness of the electromagnetic field, quantum-mechanical fluctuations of the vacuum7 can be seen as a seed of spontaneous PDC, and their amplitude is a natural radiometric standard. Thus, they allow for the calibration of the spectral radiance of light sources by measuring the ratio between seeded and unseeded PDC. Here, we directly use the frequency spectrum of the electromagnetic vacuum to trigger spontaneous PDC and employ the generated light to infer the spectral response of a spectrometer over a broad spectral range. Then, we deduce the absolute quantum efficiency from the spectral shape of PDC in the high-gain regime, without relying on a seed or reference detector. Our results compare well with the ones obtained with a reference lamp, demonstrating a promising primary radiation standard.
A method to measure the correlation function of a biphoton field, which does not require single-photon detectors and photocount coincidence schemes, has been proposed and experimentally approved. It is based on the statistical analysis of current data from analog detectors. On an example of the operation of a scheme with analog photomultiplier tubes in the signal and idler channels of degenerate parametric down conversion, it has been shown that this new approach allows one to obtain correlation function values coinciding with the results of the standard photon counting technique. It has been shown how the absolute values of photon numbers and radiation power in the signal channel of the down conversion scheme are determined from the measured correlation function. Analog detection can expand the spectral and dynamic ranges of electromagnetic radiation for the application of quantum optic technologies. A method for the reference-free measurement of the spectral sensitivity of an analog photosensor module has been demonstrated as the first example of application.
Approaches to the standard-free calibration of the quantum efficiency of a wide class of analog detectors based on the measurement of statistical characteristics of fields generated by parametric down-conversion are analyzed. General expressions are obtained for the noise reduction factor of the difference photocurrent and for the covariance of photocurrents in the signal and idler channels that take into account the possibility of strong fluctuations in the amplitudes of single-photon response functions of the detectors used. It is shown that the measurement of the noise reduction factor of the difference photocurrent using detectors that cannot operate in the photon counting mode is on its own insufficient to directly characterize the level of two-mode squeezing in the down-conversion field and to determine the quantum efficiency of photosensitive elements without additional calibration procedures. A method to determine the quantum efficiency of such detectors based on measuring the dependence of the normalized covariance of photocurrents on the parametric gain is proposed.