Propagation-invariant space-time supermodes in a multimode waveguide

Abstract

When an optical pulse is spatially localized in a highly multimoded waveguide, its energy is typically distributed among a multiplicity of modes, thus giving rise to a speckled transverse spatial profile that undergoes erratic changes with propagation. It has been suggested theoretically that pulsed multimode fields in which each wavelength is locked to an individual mode at a prescribed axial wavenumber will propagate invariantly along the waveguide at a tunable group velocity. In this conception, an initially localized field remains localized along the waveguide. Here, we provide proof-of-principle experimental confirmation for the existence of this class of pulsed guided fields, which we denote “space-time supermodes,” and verify their propagation invariance in a planar waveguide. By superposing up to 21 modes, each assigned to a prescribed wavelength, we construct space-time (ST) supermodes in a 170-µm-thick planar glass waveguide with group indices extending from <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mo>≈</mml:mo> <mml:mspace width="negativethinmathspace"/> <mml:mn>1</mml:mn> </mml:math> to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mo>≈</mml:mo> <mml:mspace width="negativethinmathspace"/> <mml:mn>2</mml:mn> </mml:math> . The initial transverse width of the field is 6 µm, and the waveguide length is 9.1 mm, which is <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mo>≈</mml:mo> <mml:mspace width="negativethinmathspace"/> <mml:mn>257</mml:mn> <mml:mo>×</mml:mo> </mml:math> the associated Rayleigh range. A variety of axially invariant transverse spatial profiles are produced by judicious selection of the modes contributing to the ST supermode, including single-peak and multi-peak fields, dark fields (containing a spatial dip), and even flat uniform intensity profiles.

Topics & Concepts