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Soviet Journal of Quantum Electronics

Theory of parametric scattering and method of absolute measurement of the brightness of light

G. Kh. Kitaeva, Давид Николаевич Клышко, I V Taubin

Published Mar 31, 1982• 14 citations
Publisher

Abstract

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.

DOI
10.1070/qe1982v012n03abeh012180

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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.
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.
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.
The parametric approximation is used in a statistical analysis of the frequency conversion of an optical field by a noncentrosymmetric crystal which couples an input wave of frequency 0 < ω < ωL/2 to output waves of frequency ω+nωL(n = 0, ±1, ±2, ...; ωL is the pump frequency). An expression is obtained for the characteristic function of the output field which is described in terms of a matrix of the coupling coefficients in the case of Gaussian (displaced) statistics of the input field with independent modes. The mutual statistics of the output waves with n ≥ 0 and n' < 0 is not Gaussian but corresponds, in the lowest approximation with respect to the pump wave and in the absence of the input field, to a spontaneous (direct or cascade) decay of pump photons into photon pairs. The intensity of the radiation represented by the n ≥ 0 modes is equal to the intensity of the radiation emerging from a classical converter which receives one photon in each mode with n' < 0. The special case of three interacting modes with n = −1, 0, 1 (upconverter or light modulator) is considered in detail. The noise intensities and correlations between the numbers of photons in two and three modes are found for this case, and the spatial-temporal correlation function of the fields of the Stokes (n' = −1) and anti-Stokes (n = 1) frequencies is determined.
A new method of absolute calibration of photodetectors based on a nonclassical effect in nonlinear optics is discussed. The combined influence of a monochromatic flux of pump photons and quantum vacuum noise on a nonlinear crystal with no center of symmetry results in the appearance of rigorously correlated pairs of photons with continuous spectral distribution in the spontaneous parametric scattering of light (spontaneous parametric downconversion) process. The presence of an optical field in a broad spectral range created by the two-photon states (biphotons) makes it possible to develop a new method of measuring the spectral distribution of the absolute value of the quantum efficiency of photodetectors, both in photon counting and in analog regimes, that does not use any calibrated standard light sources (étalons). The feasibility of the method is demonstrated on different types of photomultiplier tube.
Frequency-angular distributions of signal wave intensity are calculated for spontaneous parametric down-conversion and parametric frequency conversion in spatially nonuniform nonlinear media. Wave reflection from interfaces is taken into account, and both regular and irregular nonuniform distributions of second-order nonlinear susceptibility are considered. A unified approach using a scattering matrix and a generalized Kirchhoff law is applied in calculations of spontaneous and stimulated processes in dissipative nonlinear media. Interference of electromagnetic zero-point fluctuations of the vacuum, nonlinear interference, and nonlinear diffraction are examined for media with various absorptive properties. Theoretical foundations are developed for diagnostics of nonuniform distributions of the second-order susceptibility, based on measurement of the line profiles of nonlinear signals.
A theoretical study is made of the process in which incident pump photons that interact with a nonlinear medium (such as a crystal lacking inversion symmetry) are spontaneously split into lower-frequency signal and idler photons. The down-converted fields are quantized and described by a continuum of modes, a subset of which interacts with each photodetector. It is shown that when two ideal photodetectors are appropriately located so that they receive the conjugate signal and idler photons, then the joint probability of two-photon detection by the two detectors can equal the single-photon detection probability. The time correlation between the two detected photons is shown to be limited either by the resolving time of the detectors, or by the bandwidth of the down-converted light, and to be independent of the coherence time of the pump field or of the length of the nonlinear medium. These conclusions are compared with the results of recent experiments.