Janus Waves

TL;DR

This paper introduces Janus waves, a family of conjugate superposed waves with unique propagation and focusing properties, demonstrated through analytical, numerical, and experimental methods, including Airy and ring-Airy beams.

Contribution

It presents the concept of Janus waves, providing analytical formulas and experimental validation for their unique focusing behavior, especially in accelerating Airy and ring-Airy beams.

Findings

Janus waves consist of conjugate twin waves with distinct focusing properties.

Analytical formulas describe intensity distribution after focusing.

Experimental demonstrations confirm theoretical predictions for Airy and ring-Airy beams.

Abstract

We show the existence of a family of waves that share a common interesting property affecting the way they propagate and focus. These waves are a superposition of twin waves, which are conjugate to each other under inversion of the propagation direction. In analogy to holography, these twin "real" and "virtual" waves are related respectively to the converging and the diverging part of the beam and can be clearly visualized in real space at two distinct foci under the action of a focusing lens. Analytic formulas for the intensity distribution after focusing are derived, while numerical and experimental demonstrations are given for some of the most interesting members of this family, the accelerating Airy and ring-Airy beams