## Vector Helmholz-Gauss Beams

One of the main areas of my research is related to the study of vector beam solutions to the Maxwell equations. The existence of the vector Helmholtz-Gauss (vHzG) beams, which constitute a general family of localized electromagnetic beams, was demonstrated theoretically in a recent paper by our group. Special cases of the vHzG beams are the transverse electric (TE) and transverse magnetic (TM) Gaussian vector beams, nondiffracting vector Bessel beams, polarized Bessel–Gauss, Mathieu-Gauss, and Parabolic-Gauss beams, modes in cylindrical waveguides and cavities, and scalar Helmholtz-Gauss beams.

We have studied the paraxial propagation of a generalized form of VHzG beams,
in free space and through more general types of paraxial optical systems characterized by complex ABCD matrices, including lenses, Gaussian apertures, cascaded paraxial systems, and systems having quadratic amplitude as well as phase variations about the axis.

(a) Vector Mathieu-Gauss beam of order 2, and its (b) angular spectrum.

## Optical Vortices

The study of optical vortices is an important part of my research. An optical vortex (OV) is a point in an optical field where there exists a phase singularity, in other words the phase is not well defined and the intensity is zero. The study of OVs using coherent light sources is well established, and their properties are also well understood. For instance, a Laguerre-Gaussian beam carries an OV in its center and around this point the phase of the beam circulates spirally. The beam carries orbital angular momentum, and therefore it is possible to use this property for different applications.

Until very recently, vortices in spatially incoherent light had not received much attention, thus it is an emerging area of study. Perfect spatial coherence (and incoherence) is not physical, and thus a lack of understanding is a fundamental problem. In collaboration with Prof. Grover Swartzlander from the College of Optical Sciences, at the University of Arizona, we have studied the fundamental properties of vortices in spatially incoherent light, and have described how the spatial coherence properties of optical vortices require them to exhibit Rankine Vortex characteristics.

Spatially incoherent source carrying an optical vortex. The presence of the vortex can be observed in the form of a ring dislocation in the cross correlation function of the beam.