Rayleigh Anomaly Induced Phase Gradients in Finite Nanoparticle Chains

TL;DR

This paper presents a theoretical analysis of Rayleigh anomaly-induced phase gradients in finite nanoparticle chains, revealing their impact on diffraction directions and providing analytical solutions for chain dynamics with potential applications in optical wave control.

Contribution

It introduces an analytical approach based on the discrete dipole approximation and recursive relations, including a novel Fibonacci series description of dipole moments in nanoparticle chains.

Findings

Rayleigh anomalies cause significant phase gradients in finite chains.

Analytical solutions describe the chain's dipole moments and scattering behavior.

Results suggest new ways to control optical wave propagation in nanoparticle arrays.

Abstract

We report on the theoretical study of anomalous phase gradients induced by Rayleigh anomalies in finite nanoparticle chains. These phase gradients, defined with respect to the phase of the applied plane wave, cause a deviation of the diffraction directions from the chain relative to the direction expected from the grating equation for infinite chains. To study the effect theoretically, we use an analytical approach based on the discrete dipole approximation, which reveals the combinatorial nature of the multi-scattering process that governs the chain dynamics. We find an approximate closed-form solution to the particles' dipole moments by describing the single reciprocal system with a successive solution of two non-reciprocal, one-way systems. Within this framework, we obtain the chain excitation by means of interference between different scattering paths. Moreover, we show that the dipole moments along the chain are governed by recursive relations dictated by the generalized Fibonacci series. The presented results provide a new perspective for understanding nanoparticle arrays' dynamics. Specifically, the unique approach for analytically analyzing the spatial excitations of the array inclusions may shed new light on emerging applications of periodic traveling wave antennas in the optical regime, such as LIDARs, topological states analysis and arbitrary beam shaping schemes.