Self-similarity in azimuthal Walsh filters and corresponding far-field diffraction characteristics : a unique study to control tightly focused fields and coupling of light into metamaterials, plasmonic structure and waveguides

Abstract

In this paper, we propose illumination beam shaping using azimuthal Walsh filters derived from azimuthal Walsh functions, in and around the focal plane of a rotationally symmetric imaging system and studied for finding out self-similar groups and sub-groups for different orders to examine self-similarity existing between them and their corresponding transverse intensity distributions at the far-field plane. The unique rotational self-similarities observed in 2D intensity distributions at the transverse far-field plane for adjacent orders of azimuthal Walsh filters are also presented. Practical implementations of these filters are achievable by the availability of high speed spatial light modulators (SLMs) which can be successfully used to code and control illumination in and around the tightly focused field and coupling of light into metamaterials, plasmonic structures and waveguides. Further scope of research is intended to develop a new photonics platform based on dielectric surface wave harvesting model controlled by the dynamically variable illumination using azimuthal Walsh filters. Surface waves such as Bloch Surface Waves (BSW) and Surface Plasmons (SP) can be considered as the future enabling tools using this concept for probable applications in Photonics Research as well as in Industrial sectors, namely, quantum optics, telecom, sensing, computing, security, imaging and medical applications.