Hope College Physics Department
Research Experiences for Undergraduates
Summer 2009
Project Summary


Project Title: Experimental Observation and Control of Wave Dispersion
Student Name: Kyle McLellan
Student's Home Institution: Hope College
Research Advisor: Dr. Stephen Remillard
Source of Support: This material is based upon work supported by the National Science Foundation under NSF-REU Grant No. PHY-0452206, by an R&D contract from Mesaplexx, pty ltd., and by the Hope College Division of Natural and Applied Science.

Deviations from the simple model of constant phase velocity, called dispersion, are common, with well known examples including electron propagation through a crystal lattice, electromagnetic wave propagation near the plasma frequency, and sound wave propagation through elastic media. The motivation of this work was twofold: to find a hands-on way to investigate the dispersion of electron waves in a crystal lattice, and to introduce defects into the crystal which result in controllable states in the band gap. In this experiment, crystals were simulated using transmission lines with periodic variations which were hand-carved from copper tape on an alumina substrate or fabricated using photolithography. The transmission and reflection coefficients, measured by a vector network analyzer, were turned into a complex propagation constant, which when plotted as a dispersion curve revealed a band structure which agrees with the textbook transcendental formulation of dispersive wave propagation. This approach provides an experimental way to discover, to study and to understand the band theory of solids. Defects were then introduced into the lattice, which resulted in states in the band gap. It was found that adjustments to the length of the defect altered the location of the state, which yielded both p-type and n-type defects.

_________________________________________________________________________________________________________________________________________________________ Publications and Presentations:
"Experimental Observation and Control of Wave Dispersion", K.R. McLellan, C.I. Angert, and S.K. Remillard, AAPT Advanced Labs Topical Conference, Ann Arbor, MI, July 23-25, 2009.

"Comparison of network analysis methods for computing complex propagation coefficients of dispersive transmission lines," S.K. Remillard, Caitlin Ploch*, Kyle McLellan*, and V. Andrew Bunnell, Microwave and Optical Technology Letters, 56, no. 3, 758-761, (2014).