Abstract
We describe methods of investigating the behavior of photonic crystals. Our approach establishes a link between the dispersion relation of the Bloch modes for an infinite crystal (which describes the intrinsic properties of the photonic crystal in the absence of an incident field) and the diffraction problem of a grating (finite photonic crystal) illuminated by an incident field. We point out the relationship between the translation operator of the first problem and the transfer matrix of the second. The eigenvalues of the transfer matrix contain information about the dispersion relation. This approach enables us to answer questions such as When does ultrarefraction occur? Can the photonic crystal simulate a homogeneous and isotropic material with low effective index? This approach also enables us to determine suitable parameters to obtain ultrarefractive or negative refraction properties and to design optical devices such as highly dispersive microprisms and ultrarefractive microlenses. Rigorous computations add a quantitative aspect and demonstrate the relevance of our approach.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Journal of the Optical Society of America. A, Optics, image science, and vision
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
