Hope College Physics Department
Research Experiences for Undergraduates
|Project Title:||Electromagnetic Dispersion in Periodic Structures|
|Student Name:||Caitlin Ploch|
|Student's Home Institution:||Hope College|
|Research Advisor:||Dr. Stephen Remillard|
|Source of Support:||
This material is based upon work supported by the Hope College Division of Natural and Applied Sciences Bultman Summer Research Award and by the L.T. Guess Physics Research Fund.
Photonic crystals are electromagnetic structures that affect the propagation
of microwaves, clearly demonstrating nonlinear, band gap dispersion in the
band theory of solids. Motivated partly by the development of an advanced physics
lab in dispersion, we have compared the dispersion of microwaves in photonic
crystals to the dispersion of electrons in semiconducting crystals. The transmission
lines were fabricated to achieve periodicity with alternating widths of adjacent
copper segments using photolithography. Three identical dispersion diagrams
were constructed using different sets of values: the S-parameters measured
by the vector network analyzer (V.N.A.), the S-parameters simulated using finite
element analysis software, and the delay values measured by the V.N.A. All
three methods showed close agreement in the dispersion with a band gap at the
Brillioun zone edge. The values from the network analyzer were then used to
examine the group velocity of the wave near the band gap. Near the edges of
the band gap, the group velocity approached zero; inside the band gap, the
evanescent waves tunneled through the crystal with superluminal group velocities.
Periodic transmission lines with defects were also constructed; the defects
engineered into the photonic crystals produced donor and acceptor states in
the band gap. These results indicate that the microwave transmission lines
successfully modeled the dispersion from band gaps in photonic crystals.
Publications and Presentations:
"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).