2009 Advanced Laboratories Conference Abstract Detail Page

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Abstract Title: Experimental Observation and Control of Wave Dispersion
Abstract: To refer to the relationship between wavelength and frequency, f=c/lambda, as "inverse" implies that the phase velocity, c, is a constant for all wavelengths.  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 to find a hands-on way to investigate the dispersion of, in particular, electron waves in a crystal lattice.  In this experiment, crystals are simulated using transmission lines with periodic variations which can be hand carved from copper tape on an alumina substrate or fabricated using photolithography.  Propagating microwaves along the periodic transmission line resemble nearly free electrons in the crystal lattice.  After measuring a hand-made periodic transmission line with a vector network analyzer, the student then writes a computer program to transform the measured transmission and reflection coefficients into a complex propagation constant, which when plotted as a dispersion curve (wave number versus frequency) reveals a band structure which agrees with the textbook transcendental formulation of dispersive wave propagation.  The student is then able to modify the location of the Brillouin zone edge in the reciprocal lattice space and to introduce defects in the crystal which result in states in the band gap.  This approach provides an experimental way to discover, to study and to understand the band theory of solids.
Abstract Type: Poster
Contributed Poster: Download the Contributed Poster
Session: Session IX - Effective Experiments Poster Session

Author/Organizer Information

Primary Contact: S.K. Remillard
Hope College
Physics Department
27 Graves Place
Holland, MI 49423
Phone: 616-395-7507
Fax: 616-395-7123
Co-Author(s)
and Co-Presenter(s)
K.R. McLellan and S.K. Remillard