Strengths and applications of semi-analytic techniques for photonic crystal modelling

Semi-analytic modelling techniques offer a significant alternative to purely computational techniques for modelling photonic crystal structures, allowing us to capture the essential physics of complex photonic systems in a manner that generalises, in a straightforward manner, familiar concepts from other areas of optics. Though such methods may lack some of the generality of purely numerical techniques, the up-side of their use is excellent computational efficiency, very high accuracy and, above all, outstanding physical insight into the scattering and diffraction processes involved, together with the capacity to answer difficult questions, not otherwise accessible. This paper surveys the origin and implementation of semi-analytic methods and goes on to demonstrate their utility with a range of modelling and theoretical applications