
184 Biosensors Based on Nanomaterials and Nanodevices
minimization technique for each value of k. The electromagnetic variational theorem
states that “the lowest frequency mode of a system is the eld pattern that minimizes
the electromagnetic energy functional,” (Nightingale 2008) and this is accomplished by
concentrating electric eld energy in the high dielectric regions. Therefore, the denition
of a PhC’s dielectric and air bands is analogous to a semiconductor’s valence and conduc-
tion bands. A band diagram of a 2D innitely long PhC of triangular lattice of air holes
in silicon is shown in Figure 8.3. In this gure, the lower frequency ...