We have applied the Lippman Schwinger techniques to analyze phenom-ena in photonic crystals which have analogies of narrow resonance scatteringof a discrete state in Quantum Mechanics.
We have extended and adoptedthe appropriate quantum mechanical modeling in order to describe such phe-nomena and predict classes of similar ones. This has important consequencesin applications of photonic crystals in optical communications. Path integration for photons in dielectric media.
This work has just began. The goal is to write solutions of the fullvectorial Maxwell equations in an arbitrary dielectric media via a suitablepath integral.