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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Frequency conversion in regular and stochastic quasi-phase matched structures

Zh. D. Genchev

Published Oct 2, 2009• 0 citations
Publisher

Abstract

The influence of disordering of one-dimensional quasi-phase matched structures in nonlinear optical crystals on spectral characteristics of parametric processes is studied. Two different correlation functions are introduced for describing the random change of the sign of the second-order nonlinear susceptibility. The optimal conditions for quasi-phase matching of the interacting waves are found. The second aim of the paper is the investigation of important features of spontaneous parametric down-conversion (SPDC) in a homogeneous nonlinear slabs with emphasis of spatial inhomogeneity of interacting waves (in paraxial approximation). We estimate the absolute values of the emission rate of photon pairs produced by SPDC when all fields are in single Gaussian modes.

DOI
10.1117/12.848026

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The influence of disordering of one-dimensional quasi-phase matched structures in nonlinear optical crystals on spectral characteristics of parametric processes is studied. Two different correlation functions are introduced for describing the random change of the sign of the second-order nonlinear susceptibility. The optimal conditions for quasi-phase matching of the interacting waves are found. The second aim of the paper is the investigation of important features of spontaneous parametric down-conversion (SPDC) in a homogeneous nonlinear slabs with emphasis of spatial inhomogeneity of interacting waves (in paraxial approximation). We estimate the absolute values of the emission rate of photon pairs produced by SPDC when all fields are in single Gaussian modes.
The influence of disordering of quasi-phase-matched structures on the properties of biphoton fields generated by spontaneous parametric down-conversion in periodically poled crystals is studied in the general form, taking into consideration arbitrary one-dimensional spatial distribution of the crystal second-order susceptibility. It is shown that the spectral amplitudes of the biphoton wave function become complex and gain frequency- and angle-dependent phase shifts in the structures with unequal lengths of domains. Effects of the spectrum broadening and the phase shifting are expressed in terms of the crystal non-linear transfer function. Spectrum of the first-order correlation function is found to be strictly dependent on the transfer function module, but insensitive to the phase shifts. Availability of the phase shifts makes the second-order temporal correlation function of the broadened as-generated biphoton field to be almost the same as in case of a single-domain crystal. At the same time, possibility of strong temporal biphoton compression appears further if an additional phase-compensating element is placed after the aperiodically poled crystal.
We study spontaneous parametric down conversion (SPDC) in a one-dimensional photonic crystal designed to operate in a doubly resonant configuration, where the frequencies of the pump and the generated photons are both tuned to band-edge resonances. We investigate the spectral correlations of the generated photons as a function of the spectral width of the pump, and demonstrate that the SPDC generation rate can scale with the fifth power of the structure length in the limit of a quasi-continuous-wave pump. We show that such an unusual scaling can be simply connected with the scaling of second-harmonic generation in the same structure, illustrating the general link between spontaneous and stimulated parametric nonlinear processes.
For advanced quantum information technology, sources of photon pairs in quantum mechanically factorable states are of great importance for realizing high-fidelity photon-photon quantum gate operations. Here we experimentally demonstrate a technique to produce spectrally factorable photon pairs utilizing multi-order quasi-phase-matching (QPM) conditions in spontaneous parametric downconversion (SPDC). In our scheme, a spatial nonlinearity profile of a nonlinear optical crystal is shaped with current standard poling techniques, and the associated phase-matching function can be approximated to a Gaussian form. By the measurement of a phase-matching function and the second-order autocorrelation function, we demonstrate that telecom-band photon pairs produced by our custom-poled crystal are highly factorable with > 95% single-photon purity.
The existing widely-accepted theory of photon-pair generation via spontaneous down-conversion (SPDC) in nonlinear optical crystals and waveguides is incomplete, as it fails to account for the important physical phenomenon of parametric resonances. We demonstrate that exponential gain of classical fields in the regime of parametric resonance corresponds to resonant delocalization in the Glauber-Fock model of quantum SPDC. We propose a quantitative measure of localisation of Floquet eigen-modes as an analogue of classical gain to identify regimes of resonant delocalization. Using this method, we are able to reconstruct the classical "Arnold tongues" map of domains of instabilities for SPDC. We also predict novel regimes of resonant delocalization in the two-level model describing quantum frequency conversion processes.
The process of spontaneous parametric down-conversion (SPDC) inXXX(2)-materials, in which a pump (P) photon of wavelength λpcan split into a pair of entangled signal (S) and idler (I) photons of lower energy, is an instrumental tool in optical quantum technologies. Recently, there has been a growing interest in pair generation in sub-wavelength-thin nonlinear crystals [1], [2], especially because they are not restricted by the phase-matching condition and exhibit SPDC in a very wide spectral and angular range. This also motivates their use in quantum imaging applications, for pushing the resolution of such schemes to the limit [3], [4]. Despite its seemingly simple appearance, there has not yet been a comprehensive theoretical analysis of photon-pair generation in a thin unstructured nonlinear slab. Specifically, a proper theory should embed the Fabry-Pérot type of interferences that the signal and idler photons experience in such a nonlinear etalon during SPDC. In our work, we develop the theory for description of SPDC in thin nonlinear etalons and calculate far-field properties of the generated pairs. We use the Green's function (GF) quantization approach for description of pairgeneration [5], combined with analytical expressions for the GF of multilayer systems [6], to develop our formalism. Because of the generality of the GF method, this formalism can describe any thickness of the slab, ultra-thin or thick, and far-field radiation in the non-paraxial regime. Fig. 1 (a) schematic of spdc in a nonlinear etalon.ϵ1,ϵ2\epsilon_{1},\epsilon_{2}ϵ1​,ϵ2​andϵ3\epsilon_{3}ϵ3​are linear permittivities of the mediums. Medium 2 with thicknesshhhhas a second-orderχ(2)\chi^{(2)}χ(2)nonlinearity. (b-e) Joint detection probabilities of different detection configurations and etalon thicknesses.