Date of Graduation


Document Type


Degree Name

Doctor of Philosophy in Physics (PhD)

Degree Level





Surendra Singh

Committee Member

Reeta Vyas

Second Committee Member

Huaxiang Fu

Third Committee Member

Salvador Barraza-Lopez

Fourth Committee Member

Mark Arnold


Airy beams, Ince-Gauss beams, lasers, Maxwells equations, polarization


The description of polarization states of laser light as linear, circular polarization within the paraxial scalar wave approximation is adequate for most applications. However, this description falls short when considering laser light as an electromagnetic wave satisfying Maxwell's equations. An electric field with a constant unit vector for direction of the field and a space dependent complex scalar amplitude in the paraxial wave approximation does not satisfy Maxwell equations which, in general, requires all three Cartesian components of electric and magnetic fields associated for a nonzero laser beam to be nonzero.

Physical observation of passing a linearly polarized laser through a pair of polarizers with their transmission axes perpendicular to one another (crossed polarizers) shows that the beam cannot be completely extinguished. Some intensity is always transmitted through the polarizers. In this case, the transmitted intensity exhibits a unique spatial pattern corresponding to a polarization component that is orthogonal (cross component) to the original polarization (dominant component) of the beam incident. These unique spatial patterns of the cross component have been studied for Hermite and Laguerre Gaussian beams (HG and LG beams). In this work, the investigation is extended to Ince Gauss (IG) and Airy beams. Both types of beams were produced by shining a collimated fundamental Gaussian beam onto a spatial light modulator (SLM). IG beams are more general solutions of the paraxial wave equation, which reduce to HG or LG type of solutions in two opposite limits. Using this method, IG beams up to order p = 5 with ellipticity variation from 0.01 to 2.0 and Airy beams truncated to have finite transverse extent were produced. These beams were produced to have a dominant linear polarization. Each beam produced was then passed through a pair of crossed linear polarizers. The irradiance of the resulting cross component after the polarizers was recorded via a CCD. In all cases, the observed cross components follow a general trend such that the positions of inflection in the dominant component become maxima in the cross components and the extrema positions become minima (positions with no irradiance) in the cross component.