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Nanosystems Physics Chemistry Mathematics

Numerical solution of Schrödinger equation for biphoton wave function in twisted waveguide arrays

Dmitrii N. Vavulin, Andrey A. Sukhorukov

Published Oct 31, 2015• 3 citations
Publisher

Abstract

We consider the generation of entangled biphoton states with orbital-angular-momentum in triangular quadratic waveguide arrays with twisted geometry.For this purpose, we derive the Shrödinger equation for biphoton wave function and equation for pump field profile.We describe numerically the process of biphoton generation through spontaneous four-wave mixing.We suggest that biphoton correlations can be controlled by the amount of twist and pump field profile.

DOI
10.17586/2220-8054-2015-6-5-689-696

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We consider the generation of entangled biphoton states with orbital-angular-momentum in triangular quadratic waveguide arrays with twisted geometry.For this purpose, we derive the Shrödinger equation for biphoton wave function and equation for pump field profile.We describe numerically the process of biphoton generation through spontaneous four-wave mixing.We suggest that biphoton correlations can be controlled by the amount of twist and pump field profile.
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We describe the generation of photon pairs entangled in optical angular momentum through spontaneous four-wave mixing in circular arrays of nonlinear waveguides. We show that the incorporation of the array twist along the waveguides can enable robust generation even in the presence of defects and inhomogeneities. We present analytical results and numerical simulations based on coupled-mode equations for the classical pump field and a discrete Schr\"odinger equation for the biphoton wave function.
We suggest that closed-loop quadratic nonlinear waveguide arrays can be used as a compact interferometrically stable integrated source of discrete orbital-angular-momentum (OAM) entangled biphoton state. We describe analytically and numerically the process of biphoton generation through spontaneous parametric down-conversion in triangular waveguide arrays, and reveal that the generated biphoton quantum states can be precisely controlled by changing the pump phase and wavelength, including the case of photon-pair generation with pure OAM.
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