Electromagnetic Dispersion in Periodic Structures
Dr. Stephen Remillard
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.
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