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International Conference on Infrared, Millimeter, and Terahertz Waves (IRMMW-THz)

The structure of azimuthal eigenmodes of the optical-terahertz biphoton field

Pavel A. Prudkovskii, Lev S. Dvernik

Published Nov 8, 2020• 0 citations
Publisher

Abstract

The angular structure of an optical-terahertz biphoton field generated by strongly non-degenerate parametric down-conversion is studied theoretically. Azimuthal eigenmodes of scattered radiation are found, in the basis of which the nonlinear interaction operator has a diagonal form. The solution of the evolution equations for these eigenmodes allows us to find a scattering matrix describing the intensity and correlation properties of nonclassical optical-terahertz scattered radiation at arbitrary parametric gain and at different frequencies of the idler terahertz wave.

DOI
10.1109/irmmw-thz46771.2020.9370605

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The angular structure of an optical-terahertz biphoton field generated by strongly non-degenerate parametric down-conversion is studied theoretically. Azimuthal eigenmodes of scattered radiation are found, in the basis of which the nonlinear interaction operator has a diagonal form. The solution of the evolution equations for these eigenmodes allows us to find a scattering matrix describing the intensity and correlation properties of nonclassical optical-terahertz scattered radiation at arbitrary parametric gain and at different frequencies of the idler terahertz wave.
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.
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 possibility to manage and control spectral and spatial properties of optical-terahertz nonclassical fields generated in strongly nondegenerate parametric down-conversion is demonstrated experimentally using Mach-Zehnder nonlinear interferometer and analyzed theoretically in terms of Schmidt modes. The interferometer can be used for measuring the dispersion properties of different materials in the terahertz frequency range. The key point is that the information about these properties is extracted from the measurements in the optical channel due to strong frequency-angular correlations between optical and terahertz photons. The developed theoretical approach is used to predict properties of the optical-terahertz fields and photon correlations in different regimes of nondegenerate parametric down-conversion. The considered interferometer is shown to be a promising source of terahertz fields with new features and frequency-filtered terahertz Schmidt modes.
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.
Abstract Parametric down conversion in a strongly non-degenerate regime with output terahertz (THz) and optical beams is investigated. The theoretical approach based on the concept of independent Schmidt modes is developed and the shapes and weights of optical and THz Schmidt modes are analyzed both in a far-field and near-field regions. Analytical approximation for examined radial Schmidt modes is found. Strong azimuthal correlations between optical and THz photons are established. THz photons are shown to be involved simultaneously both in parametric down conversion and sum frequency generation processes. Photons in THz, Stocks and anti-Stocks channels are demonstrated to be strongly entangled. Methods to examine the properties of the THz radiation by measuring the correlations between generated Stocks and anti-Stocks components are suggested.
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.