Tight focusing of polychromatic waves using angular spectrum compensation in spatially dispersive media

TL;DR

This paper introduces a general angular spectrum compensation method for tight wave focusing applicable to monochromatic, polychromatic, and diffusive waves, enabling subwavelength confinement and novel light sheet formations in dispersive media.

Contribution

The paper presents a new, unified approach for wave focusing through angular spectrum compensation, extending to various wave types and establishing an analogy with relativistic frequency transformations.

Findings

Enables subwavelength confinement of waves in dispersive media.

Allows formation of light sheets and evanescent modes.

Provides a theoretical framework linking wave focusing and relativistic transformations.

Abstract

A general method for tight focusing of waves, based on compensation of the angular spectrum, is established. We apply the method to monochromatic, polychromatic and diffusive waves. Diffusive and monochromatic waves may form spatially localized waves in free space, whereas polychromatic waves form light sheets or non-decaying traveling evanescent modes confined to subwavelength regions in media where the frequency depends on the wave vector. We suggest an analogy between our compensation method and the transformation of frequencies between inertial, relativistic coordinate systems.