Knowledge of our gaps in photonic crystals

Ross McPhedran
U. of Sidney, Physics


We consider defect modes created in total gaps of 2D photonic
crystals by changing a property such as the dielectric constant or
radius of a single cylinder. Using an asymptotic method based on the
dominant contribution to the Green's function from the band edge, we
derive a simple exponential law which links the frequency difference
between the defect mode and the band edge to the change in
dielectric constant. We present numerical results which show the
accuracy of the exponential law, for TE and TM polarizations,
hexagonal and square arrays and for the first and second gaps. We
also discuss defects created by changing the properties of several
cylinders.