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Известия Российской академии наук Серия физическая

Frequency up-conversion of an even coherent state

Aleksandr V. Belinsky, Ranjit Singh

Published Sep 25, 2024• 0 citations
Publisher

Abstract

The problem of transferring the state of even coherent states from a low frequency to a high frequency is theoretically considered using a periodically-poled nonlinear crystal. With the help of the Wigner quasi-probability distribution function, a parallel implementation of two nonlinear processes is studied: parametric and sum frequency generation.

DOI
10.31857/s0367676524010072

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The problem of transferring the state of even coherent states from a low frequency to a high frequency is theoretically considered using a periodically-poled nonlinear crystal. With the help of the Wigner quasi-probability distribution function, a parallel implementation of two nonlinear processes is studied: parametric and sum frequency generation.
Two-dimensional lattices of the optical nonlinearity implemented by periodic poling inχ(2)\chi^{(2)}χ(2)materials afford additional degrees of freedom for enhanced gains in optical parametric generation [1–2] and the generation of multipartite photon entanglement in compact device formats [3]. So far all investigations have considered single-frequency excitation of the crystals in classical or quantum parametric downconversion regimes. However, the effects underpinned by the coherent coupling of multiple nonlinear resonances unique to 2D lattices, may be expected to further enlarge the spectrum of possibilities also in suitably seeded coherent parametric amplification and difference frequency generation (DFG) processes.
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.
We review recent experimental and theoretical progress in the study of optical parametric generation and cascaded frequency up conversion in two-dimensional purely nonlinear lattices, relying on acoherent coupling of multiple resonances in the quadratic lattice. Since their original proposal (1), two dimensional (2D) nonlinear photonic crystals in periodically poled materials have been the subject of a number of experimental and theoretical investigations, exploring the enhanced possibilities to engineer the nonlinear dynamics of quadratic interactions afiorded in such structures (2,3). Most of the studies have concerned frequency up-conversion, until the recent demonstration of twin-beam optical parametric generation (TB-OPG) in 2D hexagonally poled crystals (4,5). TB-OPG experiments in hexagonally poled MgO:LiTaO3 lattices demonstrated enhanced para- metric gains as well as a rich spectral and angular response underpinned bythe coherent coupling of concurrent nonlinear processes throughshared signal or idlermodes. They provided evidence forrich interaction scenarios, generating multiple outputs in the infrared as well in the visible and encompassing also self-phase modulation and cascaded upconversion processes arising from the interplay of multiple lattice resonances.A good agreement was found with a simple model in- volving the cross-seeding of two non-collinear OPG processes via a common signal (idler), while the development of advanced ad-hoc simulation tools enabled to fully account for the complex nonlinear dynamics in the 2D lattices and faithfully reproduce the rich spectral-angular response seen in the experiments (6).