MY4710/PH5520

Homework #4 – Photonic Crystals

Spring 2008

This Homework is due Friday, April 25th

 

 

1)      Given the wave equation and, show that there is a bandgap at the band edge and that near the band edge , where.  (Note:  There might be a small mistake in this expression).

2)      Show that the 3-dimensional matrix representation of the group of rotations about the z-axis constitutes a group with respect to matrix multiplication.  You should also indicate what the identity element and the inverse of any rotation are.

3)      Show that the dielectric tensorfor Faraday rotations for cubic magnetic crystals magnetized in the z-directions is invariant upon rotations about the z-axis.

4)      Given any group G, the class of an element AG is the set of all group elements BAB-1, for all BG.  List all the classes of the point group.