Exact versus tight-binding models in longitudinally modulated $\mathcal{PT}$-symmetric coupled waveguides

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Main Authors: Contreras-Astorga, Alonso, Galindo-Rodríguez, José Israel
Format: Preprint
Published: 2026
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author Contreras-Astorga, Alonso
Galindo-Rodríguez, José Israel
author_facet Contreras-Astorga, Alonso
Galindo-Rodríguez, José Israel
contents The tight-binding (TB) model is a widely adopted approximation scheme for describing light propagation in waveguide arrays. Despite its success, its validity in $\mathcal{PT}$-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 $z$-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.
format Preprint
id arxiv_https___arxiv_org_abs_2605_23853
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Exact versus tight-binding models in longitudinally modulated $\mathcal{PT}$-symmetric coupled waveguides
Contreras-Astorga, Alonso
Galindo-Rodríguez, José Israel
Mathematical Physics
Optics
Quantum Physics
The tight-binding (TB) model is a widely adopted approximation scheme for describing light propagation in waveguide arrays. Despite its success, its validity in $\mathcal{PT}$-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 $z$-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.
title Exact versus tight-binding models in longitudinally modulated $\mathcal{PT}$-symmetric coupled waveguides
topic Mathematical Physics
Optics
Quantum Physics
url https://arxiv.org/abs/2605.23853