In case of semi conductors the bandgap shrinks due to excess doping. Is the same applicable to photonic bandgap as well? or either it shrink or expand? please explain.
Geometrical defects in photonic band gaps can trap photons (http://www.nature.com/nature/journal/v407/n6804/full/407608a0.html) and even be used as laser cavities (http://copilot.caltech.edu/publications/Painter_Science_06_11_99_1819.pdf).
Doping the material used in a photonic band gap can either shrink or expand the band gap, depending on the sign of the refractive index change due to doping.
By definition, the complete photonic band gap prevents propagation of light of a certain frequency and any polarization in any direction in the material. There are also non-complete photonic band gaps, also known as stop-bands. They prevent propagation of light only in specific direction(s). It's informative to think about the reciprocal lattice when considering such directions of propagation.
Since light can't propagate in any direction (for the complete 3D band gap), it becomes trapped in the material when for example a point light source is embedded in such a material. If the degree confinement is less than 3, one can get photonic guiding effect in the certain direction. The example is the photonic band gap fiber where there is a large hollow tube (air defect) surrounded by PBG structure. Light is guided in air by being confined with PBG material that has 2D degree of confinement.
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