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OSA Advanced Photonics Congress

Generation of Spectrally Factorizable Counterpropagating Photon Pairs in Photonic Crystal Waveguides

Sina Saravi, Thomas Pertsch, Frank Setzpfandt

Published Jan 1, 2018• 0 citations
Publisher

Abstract

We show how photonic crystal waveguides can generate and engineer spectrally factorizable photon pair states, through modally phase-matching a counterpropagating spontaneous parametric down-conversion process, without the need for periodic poling.
DOI
10.1364/np.2018.npm2i.6

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In this thesis, I overcome the challenges and fill the gaps in knowledge for the design and analysis of photonic crystal slab waveguides (PCSWs) as spontaneous parametric down-conversion (SPDC) sources of photon-pairs, as well as to investigate their potential for engineering the properties of the photon-pair quantum state. I have developed the required formalism for analyzing both the quantum process of SPDC and its classical counterpart of second-harmonic generation (SHG). In studying SHG, I verified my formalism through comparing its results with direct nonlinear simulations. In these formulations, special attention was given to treating lossy modes, as they prove to be an inherent part of the SPDC designs in PCSWs. Moreover, I have found a practical set of PCSW designs, phase-matched for three-wave-mixing processes, while demonstrating that PCSWs can offer a strong control over the phase-matching configuration. This includes reaching phase-matching between modes of different propagation directions, reaching simultaneous phase-matching between multiple processes, and controlling the group velocity of the modes at the point of phase-matching. These capabilities proved to be the key to discovering the unique strength of PCSWs for the SPDC application. Through the use of various phase-matching configurations, I showed how compact SPDC sources can be designed using PCSWs that are capable of creating entanglement and tuning its extent in different degrees of freedom, with specific examples for path and spectral degrees of entanglement, all in a fully integrated way and directly at the generation step. This work also includes my experimental results on characterizing lithium niobate nanostructured ridge waveguides, demonstrating phase-matched SHG. Finally, I propose the concept of atom-mediated SPDC, for interfacing a single-emitter source with a photon-pair source, relying on the bandgap evanescent modes of a periodic waveguide.

•Jan 1, 2018•1 citation
We demonstrate numerically that photonic crystal slab waveguides can generate spectrally unentangled biphoton states, highly desired for heralding of single photons. We achieve this by modally phase matching a counterpropagating spontaneous parametric down-conversion process, in a fully integrated scheme and without the need for periodic poling. Such a configuration is an ideal integrated source of heralded single photons, as it spatially separates the photons of a pair at the source without any extra components, while allowing for generation of spectrally narrow photons on a very short length scale.
In this work, we propose and theoretically analyze a new scheme for generation of counterpropagating photon pairs in photonic crystal waveguides through the process of spontaneous four-wave mixing. Using the fundamental properties of periodic Bloch modes in a standard photonic crystal waveguide, we demonstrate how modal phase-matching can be reached between forward-propagating pump modes and counterpropagating signal and idler modes, for generation of degenerate and non-degenerate photon pairs. We then show how this scheme can be used for generation of photon pairs that are nearly uncorrelated in the spectral degree of freedom. Such a source will be highly interesting as a heralded source of single photons, especially as the spectrally separable signal and idler photons are also spatially separated directly at the source. We conduct our investigation based on a design in silicon, yet our design concept is general and can in principle be applied to any nanostructured material platform.
We propose the use of nonlinear periodic waveguides for direct and fully integrated generation of counterpropagating photon pairs by spontaneous parametric down-conversion. Using the unique properties of Bloch modes in such periodic structures, we furthermore show that two counterpropagating phase-matching conditions can be fulfilled simultaneously, allowing for the generation of path-entangled Bell states in a single periodic waveguide. To demonstrate the feasibility of our proposal, we design a photonic crystal slab waveguide made of lithium niobate and numerically demonstrate Bell-state generation.
Counter-propagating parametric conversion processes in non-linear bulk crystals have been shown to feature unique properties for efficient narrowband frequency conversion. In quantum optics, the generation of photon pairs with a counter-propagating parametric down-conversion process (PDC) in a waveguide, where signal and idler photons propagate in opposite directions, offers unique material-independent engineering capabilities. However, realizing counter-propagating PDC necessitates quasi-phase-matching (QPM) with extremely short poling periods. Here, we report on the generation of counter-propagating single-photon pairs in a self-made periodically poled lithium niobate waveguide with a poling period on the same order of magnitude as the generated wavelength. The single photons of the biphoton state bridge GHz and THz bandwidths with a separable joint temporal-spectral behavior. Furthermore, they allow the direct observation of the temporal envelope of heralded single photons with state-of-the art photon counters.
In this thesis, I overcome the challenges and fill the gaps in knowledge for the design and analysis of photonic crystal slab waveguides (PCSWs) as spontaneous parametric down-conversion (SPDC) sources of photon-pairs, as well as to investigate their potential for engineering the properties of the photon-pair quantum state. I have developed the required formalism for analyzing both the quantum process of SPDC and its classical counterpart of second-harmonic generation (SHG). In studying SHG, I verified my formalism through comparing its results with direct nonlinear simulations. In these formulations, special attention was given to treating lossy modes, as they prove to be an inherent part of the SPDC designs in PCSWs. Moreover, I have found a practical set of PCSW designs, phase-matched for three-wave-mixing processes, while demonstrating that PCSWs can offer a strong control over the phase-matching configuration. This includes reaching phase-matching between modes of different propagation directions, reaching simultaneous phase-matching between multiple processes, and controlling the group velocity of the modes at the point of phase-matching. These capabilities proved to be the key to discovering the unique strength of PCSWs for the SPDC application. Through the use of various phase-matching configurations, I showed how compact SPDC sources can be designed using PCSWs that are capable of creating entanglement and tuning its extent in different degrees of freedom, with specific examples for path and spectral degrees of entanglement, all in a fully integrated way and directly at the generation step. This work also includes my experimental results on characterizing lithium niobate nanostructured ridge waveguides, demonstrating phase-matched SHG. Finally, I propose the concept of atom-mediated SPDC, for interfacing a single-emitter source with a photon-pair source, relying on the bandgap evanescent modes of a periodic waveguide.