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Physical Review A

Generation of optical signal and terahertz idler photons by spontaneous parametric down-conversion

G. Kh. Kitaeva, Vladimir V. Kornienko, A.A. Leontyev, Andrey V. Shepelev

Published Dec 27, 2018• 38 citations
Publisher

Abstract

Frequency-angular characteristics of signal and idler photons generated under spontaneous parametric down-conversion are studied in a strongly frequency nondegenerate regime, without paraxial approximation, accounting for possible inherent absorption of idler waves in a nonlinear crystal, classical thermal field fluctuations, and the multimode character of parametric interaction induced by transverse spatial limitation of the pump beam. Spatial limitation is shown to lead to a huge increase in angular divergence of the idler photons generated at terahertz frequencies. General expressions are obtained for the frequency-angular sensitivity function of the nonlinear-optical terahertz wave detector and for power densities of the signal and idler photon fluxes. The absorption-induced difference in the parametric conversion coefficients for the noise and externally incident radiation of the idler frequency is shown to be described by approximately the same loss factor for all active spatial idler modes. Two different parametric contributions of the internal thermal noise to the number of output idler photons were revealed with different dependence on the idler-wave absorption. Expressions for the loss factors, which describe absorption-induced effects in signal and idler channels, are obtained and shown to be turning into one another by changing the sign of the absorption coefficient. Relative contribution of thermal and quantum field fluctuations into the intrinsic radiation of a nonlinear crystal at signal and idler frequencies is analyzed accounting for the crystal absorption properties.

DOI
10.1103/physreva.98.063844

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Frequency-angular characteristics of signal and idler photons generated under spontaneous parametric down-conversion are studied in a strongly frequency nondegenerate regime, without paraxial approximation, accounting for possible inherent absorption of idler waves in a nonlinear crystal, classical thermal field fluctuations, and the multimode character of parametric interaction induced by transverse spatial limitation of the pump beam. Spatial limitation is shown to lead to a huge increase in angular divergence of the idler photons generated at terahertz frequencies. General expressions are obtained for the frequency-angular sensitivity function of the nonlinear-optical terahertz wave detector and for power densities of the signal and idler photon fluxes. The absorption-induced difference in the parametric conversion coefficients for the noise and externally incident radiation of the idler frequency is shown to be described by approximately the same loss factor for all active spatial idler modes. Two different parametric contributions of the internal thermal noise to the number of output idler photons were revealed with different dependence on the idler-wave absorption. Expressions for the loss factors, which describe absorption-induced effects in signal and idler channels, are obtained and shown to be turning into one another by changing the sign of the absorption coefficient. Relative contribution of thermal and quantum field fluctuations into the intrinsic radiation of a nonlinear crystal at signal and idler frequencies is analyzed accounting for the crystal absorption properties.
We study conditions for the generation of strongly correlated photons of two extremely different frequency ranges, optical and terahertz, via the spontaneous parametric down-conversion effect in a nonlinear medium. Analytical expressions for the correlation function are derived using equations of the generalized Kirchhoff law for the second-order field moments with account of both classical thermal and quantum vacuum field fluctuations, possible inherent absorption of the medium at terahertz frequencies, and angular divergences of signal and idler radiation caused by a transverse limited spatial profile of the Gaussian pump beam. Associated with the current absence of terahertz photon counting detectors and coincidence schemes, the possible experimental limitations in measuring the second-order optical-terahertz field correlations are studied. Numerical calculations of noncollinear eee-geometry parametric down-conversion in a Mg:LiNbO3\mathrm{Mg}:\mathrm{LiNb}{\mathrm{O}}_{3}Mg:LiNbO3​ crystal demonstrate angular characteristics, particular features of the temperature and spectral behavior of the second-order quantum correlation function of optical-terahertz biphotons.
The impact of spatial limitation of the nonlinear interaction volume on the spontaneous parametric down-conversion spectra in a strongly nondegenerate regime is analyzed from the point of absolute calibration of the terahertz-wave nonlinear-optical detectors. We show that the idler wave angular resolution of the calibration method can be inherently low (about 1 to 10 degrees in lithium niobate crystals), and to fill all the input modes with external idler radiation, one has to take special care on geometry of the nonlinear interaction. Angular sensitivity distribution function is constructed, and a consecutive description is provided for both the parametric down-conversion and the external idler radiation detection processes.
Frequency-angular distributions of optical signals generated via spontaneous parametric downconversion with the Stokes idler frequency shifts 0.2–5 THz are studied simultaneously with the same distributions in the anti-Stokes range while the nonlinear Mg:LiNbO3 crystal is cooled from 300 K to 4.2 K. The temperature dependencies of the angular distributions at fixed idler frequencies are analyzed using a theoretical Klyshko–Kirchhoff approach with account of thermal field fluctuations and inherent crystal absorption at terahertz frequencies. Although all the measurements are performed in the optical range, we demonstrate how such analysis enables to predict the temperature behavior of the total number of spontaneous parametric downconversion-generated idler photons in the terahertz range, the temperature variation of the optical-terahertz biphoton function, and to study the contributions of classical thermal and pure quantum field fluctuations to parameters of biphotons. It is shown that the temperature-induced growth of the numbers of signal and idler photons and their non-normalized correlation function is provided by overwhelming increase in classical fluctuations, while the pure quantum contributions to these parameters are not so sensitive to the crystal temperature.
The conditions for the generation and detection of quantum-correlated pairs of optical and terahertz photons in the process of strongly frequency-nondegenerate parametric down-conversion of light are investigated. An approach based on increasing the frequency of the optical pump is proposed, whereby the power of a weak flux of terahertz idler photons can be measured for a wide range of parametric gain coefficients, down to the onset of the spontaneous down-conversion regime, using the same terahertz detector with a limited dynamic range. It is shown experimentally that the doubling of the frequency of pulsed laser pump leads to a 5-fold reduction in the lowest value of parametric gain that is still sufficient for detecting terahertz idler photons with a cooled hot-electron bolometer.
We study parametric down-conversion (PDC) of optical laser radiation in the strongly frequency non-degenerate regime which is promising for the generation of quantum-correlated pairs of extremely different spectral ranges, the optical and the terahertz (THz) ones. The possibility to detect tenuous THz-frequency photon fluxes generated under low-gain spontaneous PDC is demonstrated using a hot electron bolometer. Then experimental dependences of the THz radiation power on the detection angle and on the pump intensity are analyzed.
The effect of the structure of angular modes of an optical–terahertz biphoton field appearing in strongly nondegenerate parametric down-conversion on the possibility of measuring nonclassical correlation properties of this field has been studied theoretically. It has been shown that the nonlinear interaction operator describing parametric down-conversion can be diagonalized in the space of azimuth angles if idler radiation has a terahertz frequency. This feature makes it possible to determine azimuthal eigenmodes and the scattering matrix at arbitrary coefficients of the parametric gain. The determined scattering matrix has been used to find the dependences of the normalized correlation function and the noise reduction factor of the optical–terahertz biphoton field on the angular apertures of detectors recording the signal and idler radiation.