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Journal of International Crisis and Risk Communication Research

Two-photon evolution equation for multiport optical systems

Armando Pérez-Leija, Markus Gräfe, Maxime Lebugle, René Heilmann, Stefan Nolte, H. M. Moya-Cessa, Demetrios N. Christodoulides, Alexander Szameit

Published Jan 1, 2015• 0 citations
Publisher

Abstract

In this work we demonstrate, theoretically and experimentally, that two-photon probability amplitudes describing propagation of light in any two-photon state are governed by an evolution equation identical to a 2D tight-binding equation. © 2015 OSA.
DOI
10.1364/cleo_at.2015.jw2a.20

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The spatiotemporal two-photon probability amplitude that describes light in a two-photon entangled state obeys equations identical to the Wolf equations, which are satisfied by the mutual coherence function for light in any quantum state. Both functions therefore propagate similarly through optical systems. A generalized van Cittert-Zernike theorem explains the predicted enhancement in resolution for entangled-photon microscopy and quantum lithography. The Wolf equations provide a particularly powerful analytical tool for studying three-dimensional imaging and lithography since they describe propagation in continuous inhomogeneous media.
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Exact versus tight-binding models in longitudinally modulated PT\mathcal{PT}PT-symmetric coupled waveguides
The tight-binding (TB) model is a widely adopted approximation scheme for describing light propagation in waveguide arrays. Despite its success, its validity in PT\mathcal{PT}PT-symmetric systems characterized by strong longitudinal modulation has not been rigorously benchmarked against exact analytical solutions. In this work, we address this gap by performing a comparative analysis between exact continuous solutions derived from zzz-dependent supersymmetric (SUSY) transformations and their corresponding discrete TB approximations. To achieve this, we develop a theoretical model for two PT-symmetric coupled waveguides subject to longitudinal modulation. We then evaluate the performance of the TB framework against the exact SUSY benchmark. Our results delineate the specific validity range of the TB approximation, demonstrating its proficiency in reproducing spatial intensity distributions. However, we also identify its limitations in accurately capturing the complex oscillatory phase dynamics inherent to this non-Hermitian evolution.