## Physics & Astronomy ETDs

#### Publication Date

Summer 8-1-2023

#### Abstract

The focus of this dissertation is on the application of supersymmetric quantum mechanics to the problem of microbending in optical waveguides and on the analysis of soliton decay due solely to quantum mechanical effects.

The techniques of supersymmetric quantum mechanics are applied to the equation of motion describing light propagation in an optical waveguide which is undergoing microbending. Based on these supersymmetric techniques, given a particular refractive index profile, one may derive a new refractive index profile which results in less loss due to the microbending -- the particular example of the monomial index profile is analyzed in detail. An equivalence class of refractive indices which possess equivalent loss due to microbending is generated from an initial refractive index profile.

An analysis of quantum soliton decay is performed using a perturbative method on the linearized nonlinear Schr\"{o}dinger equation. It is shown that a classical optical soliton decays proportionally to the square of the soliton's period and hence is only a classically stable object. An analysis of the continuum radiation generated by the decay is performed and is found to be suppressed by a factor which is inversely proportional to the initial photon number of the soliton. Furthermore, the power spectrum of the continuum radiation is computed and is found to lie in a narrow band centered about the initial soliton momentum and having a width which is inversely proportional to the initial soliton width.

#### Degree Name

Physics

#### Level of Degree

Doctoral

#### Department Name

Physics & Astronomy

#### First Committee Member (Chair)

Arash Mafi

#### Second Committee Member

Rouzbeh Allahverdi

#### Third Committee Member

David Dunlap

#### Fourth Committee Member

Ganesh Balakrishnan

#### Document Type

Dissertation

#### Recommended Citation

Ward, Stuart. "Application of Quantum Mechanical Techniques to Optical Waveguide Structures." (2023). https://digitalrepository.unm.edu/phyc_etds/283