Joseph Park

Joseph Park 
Mentor: Dr. Sergei Shabanov
College of Liberal Arts and Sciences
 
"I want to make a career of research."

Major

Mathematics; Physics

Minor

Philosophy

Research Interests

  • Mathematical Physics
  • Particle Physics
  • Biological Physics

Academic Awards

  • UF University Scholars Program
  • Biophysical Society Fellowship
  • Johnson Scholarship
  • Trottman Scholarship
  • AP Scholar

Organizations

  • Sigma Pi Sigma
  • University Math Society
  • Golden Key International Honour Society

Volunteer

  • Editing for Math Competitions
  • City Litter Cleanup
  • Programming Simulations for a Research Project

Hobbies and Interests

  • Scientific Literature
  • History of Science and Math
  • Wrestling and General Fitness
  • Health Literature

Research Description

Electromagnetic Bound States in the Radiation Continuum and Subwavelength Structures
In 2008, Professor Shabanov proved that the interaction between trapped electromagnetic modes can lead to scattering resonances of negligible width, which are the bound states in the radiation continuum first discovered in quantum systems by von Neumann and Wigner. In 2010, Professor Shabanov and his graduate student, Remy Ndangali, showed in a specific example of appropriate subwavelength structure that by varying the spatial parameters toward the critical value, the near field can be amplified in certain regions. In 2011, they slightly generalized this mechanism to control and amplify the near fields in periodic planar structures with nonlinear dielectric susceptibility. In 2012, they made a step towards application in all-optical computing by showing that for a wide range of nonlinear susceptibilities, the conversion rate of the incident fundamental frequency into the second can be at most 40 percent when the distance between arrays of dielectric cylinders is at least half the incident wavelength. I will be slightly generalizing these results in application to a novel subwavelength structure that will be of greater utility to purpose of all-optical computing. Before I begin any problem solving, I need to be well versed with graduate level electrodynamics, mathemathical physics methods, and the papers written by Professor Shabanov thus far on the topic.