Theory of space-time supermodes in planar multimode waveguides

TL;DR

This paper develops a theoretical framework for space-time supermodes in planar multimode waveguides, enabling invariant propagation, tunable group velocity, and customizable intensity profiles, with potential applications in optical beam delivery.

Contribution

It introduces a novel theoretical approach to design and analyze space-time supermodes in planar waveguides, including modal engineering and incoherent light synthesis methods.

Findings

Space-time supermodes propagate invariantly with customizable profiles.

Group velocity of supermodes is independently tunable.

Incoherent light can be used to synthesize supermodes.

Abstract

When an optical pulse is focused into a multimode waveguide or fiber, the energy is divided among the available guided modes. Consequently, the initially localized intensity spreads transversely, the spatial profile undergoes rapid variations with axial propagation, and the pulse disperses temporally. Space-time (ST) supermodes are pulsed guided field configurations that propagate invariantly in multimode waveguides by assigning each mode to a prescribed wavelength. ST supermodes can be thus viewed as spectrally discrete, guided-wave counterpart of the recently demonstrated propagation-invariant ST wave packets in free space. The group velocity of an ST supermode is tunable independently -- in principle -- of the waveguide structure, group-velocity dispersion is eliminated or dramatically curtailed, and the time-averaged intensity profile is axially invariant along the waveguide in absence of mode-coupling. We establish here a theoretical framework for studying ST supermodes in planar waveguides. Modal engineering allows sculpting this axially invariant transverse intensity profile from an on-axis peak or dip (dark beam), to a multi-peak or flat distribution. Moreover, ST supermodes can be synthesized using spectrally incoherent light, thus paving the way to potential applications in optical beam delivery for lighting applications.