We show here, with three examples, that a simple perturbative approach is very useful to understand certain photonic band gap problems. In the first example, we will demonstrate that the perturbation analysis can provide us a simple, systematic and efficient way to engineer a photonic band gap. The change of a gap size caused by the variation in the microstructure can be easily determined from the knowledge of eigenfield distribution at two band edge states. Thus, by knowing the field distribution at some symmetry points, one should be able to manipulate an existing gap by changing its microstructure. Explicit examples are given for certain 2D photonic crystals where full/absolute gaps are enlarged significantly. By extending this perturbation analysis to a disordered photonic crystal, in the second example, we explain why a gap is more robust against positional disorder of the scatterers and more sensitive to the randomness in the size of the scatterers. Specific examples are presented for some 2D and 3D photonic crystals. In the final example, we will use the various eigenfield distributions to explain why an incomplete infiltration has a larger photonic gap in an inverse opal photonic crystal. By careful mode analysis, we see that the enlargement of the photonic band gap due to incomplete infiltration in
inverse opal is the result of subtle changes in the photonic bands at two particular k-points in the Brillouzin zone due to the depletion of high dielectric material.