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

TL;DR

This paper analytically explores how torsion in a (2+1)-dimensional spacetime with a spiral dislocation affects light trajectories and wave propagation, revealing torsion's role as a geometric waveguide and frequency filter.

Contribution

It provides an exact analytical study of null and scalar wave behavior in torsion-only spacetime, highlighting torsion's effects on light deflection, localization, and frequency filtering, distinct from curvature effects.

Findings

Torsion modifies null ray trajectories, creating a finite turning radius and angular deflection.

Wave analysis shows a diverging refractive index near the dislocation core, leading to wave localization.

Torsion acts as a geometric regulator, inducing anisotropy, filtering, and confinement of waves.

Abstract

We present an exact analytical investigation of null trajectories and scalar wave propagation in a $(2+1)$-dimensional spacetime containing a spiral dislocation-a topological defect characterized by torsion in the absence of curvature. For null rays, the torsion parameter $\beta$ modifies the affine structure, enforcing a finite turning radius $r_{\min} = \sqrt{b^2 - \beta^2}$ and inducing a torsion-mediated angular deflection that decreases monotonically with increasing $\beta$. The photon trajectory deviates from the curvature-induced lensing paradigm, exhibiting a purely topological exclusion zone around the defect core. In the wave regime, we recast the Helmholtz equation into a Schr\"odinger-like form and extract a spatially and spectrally dependent refractive index $n^2(r,k)$. This index asymptotically approaches unity at large distances, but diverges strongly and negatively near the dislocation core due to torsion-induced geometric terms. The resulting refractive index profile governs the transition from propagating to evanescent wave behavior, with low-frequency modes experiencing pronounced localization and suppression. Our findings reveal that torsion alone, absent any 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 engineered to replicate non-Riemannian geometries.