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Bulletin of the Russian Academy of Sciences Physics

Mathematical Modeling a Source for the Formation of Ghost Images with the Help of a Periodically Poled Nonlinear Crystal: Quantum Polarization Characteristics by Considering Diffraction

Aleksandr V. Belinsky, Ranjit Singh

Published Jan 1, 2021• 1 citation
Publisher

Abstract

Abstract The authors consider the generation of correlated multiphoton quantum states using periodically poled nonlinear crystals with quadratic nonlinearity. The spatial and polarization characteristics of the generated correlated beams are studied. Statistical quantum polarization Stokes operators and coefficients of intermode correlation are calculated.

DOI
10.3103/s1062873821010056

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Abstract The authors consider the generation of correlated multiphoton quantum states using periodically poled nonlinear crystals with quadratic nonlinearity. The spatial and polarization characteristics of the generated correlated beams are studied. Statistical quantum polarization Stokes operators and coefficients of intermode correlation are calculated.
Abstract A study is performed of a degenerate parametric process in which two orthogonally polarized counterpropagating modes are generated and propagate in a periodically poled nonlinear crystal. A scheme for quantum ghost imaging is proposed. It is established that beam diffraction has a negligible effect on the second-order coefficients of correlation. This offers good prospects for the formation of high-quality ghost images, since diffraction is normally the factor that has the worst effect on their spatial resolution.
Abstract A degenerate parametric process and the complete upward generation of ordinary and extraordinary optical waves inside a periodically poled nonlinear crystal (PPNC) with quadratic nonlinearity are considered. A quantum theory is developed for describing statistical characteristics of the polarized states of light in a PPNC. It is found that the degree of polarization can be controlled by creating an imbalance in the intensity of modes at frequencies of ordinary and extraordinary optical waves (i.e., reducing the average number of photons in one and increasing it in the other).
Theoretical analysis is presented on quantum state evolution of polarization light waves at frequencies ωoω_{o}ωo​ and ωeω_{e}ωe​ in a periodically poled nonlinear crystal (PPNC). It is shown that the variances of all the four Stokes parameters can be squeezed.
We consider a nondegenerate parametric process ω 3 → ω 1 + ω 2 and simultaneous sum frequency generation ω 1 + ω 3 → ω 4 and ω 2 + ω 3 → ω 5 in periodically poled quadratic crystals. An algorithm is proposed for the numerical description of the system evolution with full allowance for the quantum-mechanical interaction of all five plane monochromatic modes and pump depletion. The behaviour of the average number of photons of interacting modes and their mutual correlations is studied. An effect of inversion of the mutual correlation of the modes of the generated light is found.
Abstract We demonstrate theoretically cascaded fourth and second harmonics generation in a periodically oriented nonlinear crystal with a half-order of the periodical orientation. We consider a cascaded process in which four photons of the fundamental harmonic are initially converted into an intermediate photon of the fourth harmonic, which parametrically decays at the second stage into two photons of the second harmonic. We show that fractional phase matching can be achieved by using an asymmetric periodically poled grating. To describe the propagation and transformation of light inside a nonlinear crystal, the quantum spatial Heisenberg equations have been applied, using which the average numbers of photons of the fourth and second harmonics have been calculated as functions of the nonlinear crystal length.