Higher-order Poincaré sphere, stokes parameters, and the angular momentum of light.

A higher-order Poincaré sphere and Stokes parameter representation of the higher-order states of polarization of vector vortex beams that includes radial and azimuthal polarized cylindrical vector beams is presented. The higher-order Poincaré sphere is constructed by naturally extending the Jones vector basis of plane wave polarization in terms of optical spin angular momentum to the total optical angular momentum that includes higher dimensional orbital angular momentum. The salient properties of this representation are illustrated by its ability to describe the higher-order modes of optical fiber waveguides, more exotic vector beams, and a higher-order Pancharatnam-Berry geometric phase.

The Poynting vector and angular momentum of Airy beams.

We analyze and describe the evolution of the Poynting vector and angular momentum of the Airy beam as it propagates through space. A numerical approach is used to show the Poynting vector follows the tangent line of the direction of propagation. A similar approach is used to show that while the total angular momentum of the Airy beam is zero, the angular momentum of the main intensity peak and the Airy "tail" are non-zero.

Ultrashort Laguerre-Gaussian pulses with angular and group velocity dispersion compensation.

Coherent optical vortices are generated from ultrashort 6.4 fs pulses. Our results demonstrate angular dispersion compensation of ultrashort 6.

Laguerre-Gaussian supercontinuum.

We show what is believed to be the first coherent white-light optical vortices generated from supercontinuum that have the azimuthally varying phase structure consistent with a monochromatic Laguerre-Gaussian beam. Two methods of Laguerre-Gaussian supercontinuum generation are discussed and contrasted. We use a computer-generated hologram to convert a Gaussian white-light supercontinuum source into Laguerre-Gaussian supercontinuum.

Double-slit interference with Laguerre-Gaussian beams.

The interference of Laguerre-Gaussian beams carrying orbital angular momentum was demonstrated in Young's double-slit geometry. Double-slit interference is shown to be affected by the azimuthal phase dependence of a Laguerre-Gaussian beam. This interference provides new insight into the helical phase structure of the Laguerre-Gaussian beam and has potential applications for measuring the orbital angular momentum of an arbitrary wavefront.