The usual photonic crystal is a periodic array of dielectric materials ordered such that the dielectric constant varies regularly.  Wave reflection at the impedance mismatch results in heavily diminished transmission at wavelengths corresponding to the periodicity of the structure.  If the waves are transverse polarized in the plane of the impedance interface, the transmission is completely suppressed in certain frequency ranges and the forbidden frequencies are referred to as "bandgaps".

Photonic crystals can also be formed by a conducting microstrip with periodic variations in the impedance.  At the impedance boundaries wave reflections occur, resulting in forbidden frequencies. 

The electromagnetic wave dispersion characteristics in 1-, 2- and 3- dimensions are constructed in a similar manner as electron dispersion in a crystal lattice.  I am interested in exploring ways to use photonic bandgap structures as a tool for teaching band theory in solid state physics.  Most students struggle with the theory of electronic band structures.  While waiting to find a faculty position, I am working on experiments in photonic crystals that will give the student a tangible device with which to study band theory.  Microwave photonic crystals have a periodic structure with a length scale familiar to the student (millimeters instead of Angstroms).  The student can change the structure by hand and see how this affects the dispersion characteristics.  With this, it’s possible to study a periodic lattice in 1-, 2-, or 3- dimensions.

To highlight the pedagogical invention, the periodic impedence mismatches cause a coupling between electromagnetic modes at the interfaces.  This causes a split between modes at the edge of the first Brillouin zone, which then causes a bandgap in the dispersion characteristic of the tranmission line.  This serves the same spectral purpose as a bandgap in electronic states.  The spectrum between the two split electromagnetic frequencies is the forbidden band.

To develop a pedagogical approach, I am using IE3D to simulate microstrip photonic crystals, fashioning them out of RT Duroid^Ò, and measuring their dispersion with a microwave vector network analyzer.  I have only gotten started on this work, but here is a summary so far.