Refraction of space-time wave packets: I. Theoretical principles

TL;DR

This paper develops a theoretical framework for understanding how space-time wave packets refract at interfaces, revealing novel phenomena like group-velocity invariance and inversion, with experimental confirmation in subsequent studies.

Contribution

It introduces a new optical invariant called spectral curvature and formulates a law of refraction for space-time wave packets, expanding understanding beyond conventional optical fields.

Findings

Refractive phenomena such as group-velocity invariance and inversion are predicted.

The law of refraction depends on spectral curvature, a new invariant.

Experimental confirmation of the theoretical predictions is provided in accompanying papers.

Abstract

Space-time (ST) wave packets are pulsed optical beams endowed with precise spatio-temporal structure by virtue of which they exhibit unique and useful characteristics, such as propagation invariance and tunable group velocity. We study in detail here, and in two accompanying papers, the refraction of ST wave packets at planar interfaces between non-dispersive, homogeneous, isotropic dielectrics. We formulate a law of refraction that determines the change in the ST wave-packet group velocity across such an interface as a consequence of a newly identified optical refractive invariant that we call 'the spectral curvature'. Because the spectral curvature vanishes in conventional optical fields where the spatial and temporal degrees of freedom are separable, these phenomena have not been observed to date. We derive the laws of refraction for baseband, X-wave, and sideband ST wave packets that reveal fascinating refractive phenomena, especially for the former class of wave packets. We predict theoretically, and confirm experimentally in the accompanying papers, refractive phenomena such as group-velocity invariance (ST wave packets whose group velocity does not change across the interface), anomalous refraction (group-velocity increase in higher-index media), group-velocity inversion (change in the sign of the group velocity upon refraction but not its magnitude), and the dependence of the group velocity of the refracted ST wave packet on the angle of incidence.