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Bulletin of the Russian Academy of Sciences Physics

Modeling Nonlinear Optical Processes in a Periodically Poled Nonlinear Crystal

Aleksandr V. Belinsky, Ranjit Singh

Published Jan 1, 2019• 1 citation
Publisher

Abstract

Abstract Three nondegenerate processes are considered: the parametric and simultaneous generation of sum frequencies in a periodically poled nonlinear crystal. The behavior of the average number of photons of interacting modes and their mutual correlations of orders 3, 4, and 5 are studied numerically. A new effect of inversion of the mutual correlation of the modes of the generated radiation is observed at certain length of interaction.

DOI
10.3103/s1062873819010040

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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 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).
We study parametric interactions in a new type of nonlinear photonic structure, which is realized in the volume between a pair of nonlinear crystals. In this kind of structure, which we call binary, multiple nonlinear optical processes can be implemented simultaneously, owing to multiple phase-matching conditions, fulfilled separately in the constituent crystals. The coupling between the nonlinear processes by means of modes sharing similar frequency is attained by the spatially broadband nature of the parametric fields. We investigate the spatial properties of the fields generated in the binary structure constructed from periodically poled crystals for the two examples: (1) single parametric downconversion and (2) coupled parametric downconversion and upconversion processes. The efficacy of the fields’ generation in these examples is analyzed through comparison with the cases of a traditional single periodically poled crystal and an aperiodic photonic structure, respectively. For this, we have devised a method that allowed us to solve the field equations numerically without resorting to statistically modeling the input vacuum states. It has been shown that the relative shift between the periodic crystal lattices has a crucial effect on the generated spatial field spectrum and overall efficiency. In addition, the influence of the intercrystal distance on these characteristics has been studied. Therefore, our study suggests that one can construct optical elements with sophisticated nonlinear properties from simpler elements without significant sacrifice of efficacy.
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.
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We theoretically demonstrate cascaded fourth and second harmonic generation in a periodically-poled nonlinear crystal with a half-order of phase-matching period. We consider a cascaded process in which four photons of the fundamental harmonic firstly convert into an intermediate photon of the fourth harmonic, which parametrically decays into two photons of the second harmonic at the second stage. Phase-matching for this cascaded nonlinear conversion is provided by using an asymmetric periodical poling. We use the quantum spatial Heisenberg equations to describe light propagation and conversion inside the nonlinear crystal. With this approach, we calculate second and fourth harmonic average number of photons as a function of the nonlinear crystal length.