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arXiv:1609.05350 · Journal of the Optical Society of America B

Coupled parametric processes in binary nonlinear photonic structures

M. Yu. Saygin, A. S. Chirkin

Published Nov 18, 2016• 0 citations
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Abstract

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.

DOI
10.1364/josab.33.002577

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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.
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.
The teleportation of entangled optical images is for the first time considered. The scheme offered is based on process of four-partite state generation in coupled parametric interactions realizing in an aperiodic nonlinear photonic crystal. The coupled nonlinear optical process consists of one parametric down-conversion process which is followed by two up-conversion ones. We study nonclassical properties of the generated fields by analyzing the EPR correlations for different pairs of modes and carry out the comparison of the EPR correlations of the input and images output images and also calculate fidelity of the teleportation exploiting the covariance matrices of the images. We take into account the difference of spatial frequency bandwidths of the entangled images and fields generated in the coupled process. It has been established that under certain parameters of the scheme one can be obtain rather high fidelity of the teleportation and good preservation of the quantum correlations of the input images for all details of the images.
Quasi-phase-matched parametric downconversion via cascaded optical nonlinearities in an aperiodically poled MgO:LiNbO3 superlattice was studied in theory and experiment. Due to the cascading effect and the abundant reciprocal structure in an aperiodic optical superlattice, multiple-wavelength parametric downconversion in a wide spectrum range can be obtained. Enhancement of the conversion efficiency and output stability through coupling of two nonlinear processes is demonstrated. The result also reveals that the cascaded parametric downconversion process can be used to efficiently downconvert the fundamental wavelength to a longer wavelength of the infrared region. The process can be additionally served as an efficient mechanism to enhance THz wave propagation in a nonlinear optical medium.
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).
Summary form only given. Parametric downconversion (PDC) allows the generation of highly coherent, spectrally pure single photons for quantum photonics. In a typical heralded PDC source, the signal photon emerges in a spectrally mixed state due to strong (anti)correlation in the joint spectrum of PDC photon pairs.One method for reducing spectral correlations is spectral filtering, but this compromises the heralding efficiency and the brightness of the source. A more sophisticated method for increasing the heralded photon purity is group-velocity matching, which works by erasing part of the timing information between the pump and PDC photons. What group-velocity matching cannot address, however, are the remaining correlations in the joint spectrum that come from the sinc-shaped phase-matching function (PMF) typical to standard PDC crystals. Further source engineering is therefore required to remove these correlations. Several studies have introduced domain-engineering techniques for shaping the phase matching function (PMF) in periodically poled crystals to improve single photon purities [1-4]. We present a new technique for tailoring crystal nonlinearities which combines the advantages of a deterministic method for domain engineering [4] and an annealing method developed for classical applications in higher-harmonic generation [5]. In our method, we first choose each domain orientation such that the generated field amplitude along the crystal matches the target field amplitude obtained by integrating the desired nonlinearity profile. Using a one-block structure instead of a two-blocks structure (as in [4]) results in a higher flexibility of the algorithm in tracking the target function and yields to more accurate results. We then use an annealing algorithm to slightly vary the width of each domain, further improving the effective PMF. Our technique outperforms its predecessors, particularly for short crystals, leading to high single photon purities, as shown in Fig.1. We experimentally characterise our method through a high-precision measurement of multiphoton interference between two heralded photons generated by two independent sources.We also notice that by considering a complex target field amplitude function it is possible to generalise the algorithm in [5] to any constant domain width (not necessarily equal to the coherence length), leading to a better approximation of the desired phase matching function, especially in the very short crystal regime. Moreover, tracking both the real and imaginary components of the target function allows us to approximate more exotic cases such as chirped nonlinearity profiles. Since scalable quantum photonics will require integrated architectures in which nonlinear processes are typically employed for single-photon generation, it will be interesting to explore new techniques similar to in-fibre Bragg grating structures which might yield quasi-periodic four-wave mixing and apply our algorithm to these new platforms.
Quasi-phase-matched parametric downconversion via cascaded optical nonlinearities in an aperiodically poled MgO:LiNbO3 superlattice was studied in theory and experiment. Coupling equations reveal that multiple-wavelength parametric downconversion in a wide infrared spectrum range can occur in a single crystal. Enhancement of the conversion efficiency and output stability through coupling of two nonlinear processes is demonstrated. The result also reveals that cascaded parametric downconversion process can be used to efficiently downconvert the fundamental wavelength to longer wavelength of infrared region.