#### Date of Graduation

8-2012

#### Document Type

Dissertation

#### Degree Name

Doctor of Philosophy in Physics (PhD)

#### Degree Level

Graduate

#### Department

Physics

#### Advisor

Surendra Singh

#### Committee Member

Reta Vyas

#### Second Committee Member

Min Xaio

#### Third Committee Member

Julia Kennefick

#### Fourth Committee Member

Hameed Naseem

#### Keywords

Pure sciences, Cross-polarization, Hermite-Gauss, Laguerre-Gauss, Laser beams, Polarization

#### Abstract

Laser beams are wave-like optical disturbances. They are characterized by a dominant direction of propagation and a finite extent transverse to the direction of propagation. Many characteristics of laser beams can be described in terms of a scalar function multiplied by a constant vector, which can be real (for linear polarization) or complex (for elliptical polarization). The scalar function is a solution to the paraxial scalar wave equation. This scalar description, however, fails to describe the polarization and focusing characteristics of laser beams correctly. For a correct accounting of these characteristics, the electric and magnetic fields associated with laser beams must satisfy not only the wave equation but also the Maxwell's equations. We show that, due to the finite transverse size of laser beams, Maxwell's equations require that the electric field (as well as the magnetic field) associated with laser beams will possess all three nonzero Cartesian components even in free space. Each component can be expressed in terms of the scalar solutions of the paraxial wave equation.

We construct three-component solutions giving expressions for the dominant, cross, and longitudinal-polarization components, for linearly polarized Hermite-Gauss and Laguerre-Gauss beams. Such a description correctly accounts for focusing as well as polarization properties of laser beams. We demonstrate the validity of this description experimentally by generating two families of laser beams and verify the existence of cross-polarization field components and their evolution in propagation. We generate experimental higher-order Hermite-Gauss laser beams intracavity via a pair of crossed fibers. Laguerre-Gauss laser beams were generated by converting Hermite-Gauss beams into Laguerre-Gauss beams of the same order by using a pair of cylindrical lenses to manipulate Guoy phase of the beams. Intensity profiles of the dominant and cross-polarization components of linearly polarized Hermite-Gauss and Laguerre-Gauss beams are measured and their evolution as the beam propagates away from its focal region was studied. The transverse profiles of the cross-polarization components of these beams undergo an evolution with propagation. The theoretically expected and experimentally observed intensity profiles are in reasonable agreement confirming the field structure of laser beams derived in this thesis.

#### Recommended Citation

Conry, Jessica Patricia, "Polarization Properties of Maxwell-Gauss Laser Beams" (2012). *Theses and Dissertations*. 491.

https://scholarworks.uark.edu/etd/491