Hope
College Physics Department Research Experiences for Undergraduates Summer 2009Project 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).

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