Topological aberration of optical vortex beams and singularimetry of dielectric interfaces

Abstract

The splitting of a high-order optical vortex into a constellation of unit vortices, upon total reflection, is described and analyzed. The vortex constellation generalizes, in a local sense, the familiar longitudinal Goos-Hänchen and transverse Imbert-Federov shifts of the centroid of a reflected optical beam. The centroid shift is related to the centre of the constellation, whose geometry otherwise depends on higher-order terms in an expansion of the reflection matrix. We present an approximation of the field around the constellation of increasing order as an Appell sequence of complex polynomials whose roots are the vortices, and explain the results by an analogy with the theory of optical aberration.

5 pages, 3 figures, REVTeX 4.1

References in corpus (7)

• Role of beam propagation in Goos-Hänchen and Imbert-Fedorov shifts
• Goos-Hänchen and Imbert-Fedorov shifts of polarized vortex beams
• The analogy between optical beam shifts and quantum weak measurements
• Rows of optical vortices from elliptically perturbing a high-order beam
• Generalized shifts and weak values for polarization components of reflected light beams
• Observation of OAM sidebands due to optical reflection
• Spin and orbital Hall effects for diffracting optical beams in gradient-index media

Cited by in corpus (6)

• Goos-Hänchen and Imbert-Fedorov beam shifts: An overview
• Topological features of vector vortex beams perturbed with uniformly polarized light
• Hydrodynamics Explanation for the Splitting of Higher-charge Optical Vortices
• Generalized Matrix Transformation Formalism for Reflection and Transmission of Complex Optical Waves at a Plane Dielectric Interface
• Wigner time delays and Goos-Hänchen shifts of 2D quantum vortices scattered by potential barriers
• Transverse Shifts and Time Delays of Spatiotemporal Vortex Pulses Reflected and Refracted at a Planar Interface