Optics in spiral dislocation spacetime: torsion as a geometric waveguide and frequency-filtering mechanism

Abstract

We present an exact analytical study of null trajectories and scalar wave propagation in a (2+1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(2+1)$$\end{document}-dimensional spacetime containing a spiral dislocation, a topological defect characterized by torsion in the absence of curvature. For null rays, the torsion parameter beta\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta $$\end{document} modifies the affine structure, enforcing a finite turning radius rmin=b2-beta 2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$r_{\min } = \sqrt{b<^>2 - \beta <^>2}$$\end{document}, and inducing a torsion-mediated angular deflection that decreases monotonically with increasing beta\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta $$\end{document}. The photon trajectory departs from the curvature-induced lensing paradigm, exhibiting instead a purely topological exclusion zone around the defect core. Moreover, the results can, in principle, be mapped onto laboratory frames and conditions. In the wave regime, we recast the Helmholtz equation into a Schr & ouml;dinger-like form and extract a spatially and spectrally dependent refractive index n2(r,k)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n<^>2(r,k)$$\end{document}. This index approaches unity asymptotically at large distances but diverges strongly and negatively near the dislocation core due to torsion-induced geometric contributions. The resulting refractive index profile governs the transition from propagating to evanescent wave behavior, with low-frequency modes undergoing pronounced localization and suppression. Our findings demonstrate that torsion alone, even in the absence of curvature, can act as a geometric regulator of both classical and quantum propagation, inducing effective anisotropy, frequency filtering, and confinement. This framework provides a rare exact realization of light-matter interaction in a torsion-dominated background, with potential applications in analog gravity systems and photonic metamaterials designed to emulate non-Riemannian geometries.