[Show abstract][Hide abstract] ABSTRACT: Slanted lamellar gratings made of dielectric materials are considered, used in conical diffraction mounts. We extend the modal method for slanted lamellar gratings from classical to conical incidence, develop fully generalized Fresnel matrices, and derive energy conservation relations for these matrices. Using the method, we verified a uniaxial crystal model for slanted lamellar gratings in a homogenization regime, examined the effects of grating symmetry on the maximum reflectance of Fano resonances, and showed that slanted lamellar gratings support Fano resonances despite the homogenization of their other optical properties.
Journal of the Optical Society of America A 05/2009; 26(4):938-48. DOI:10.1364/JOSAA.26.000938 · 1.56 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: A formulation of the modal method for multi-element dielectric lamellar diffraction gratings is presented. It combines the conventional semi-analytic Kronig-Penny formulation with a Fresnel scattering matrix approach to the solution of the diffraction problem. The theory is intuitive, applicable to complex geometries, and provides insight into diffraction grating physics. With the Fresnel matrix extensions the method potentially has greater generality than other formulations, and is applicable to non-trivial waveguide problems, such as characterizing the coupling between 1D photonic crystal waveguides. A numerically stable way of using the modal method for multilayer stacks of lamellar gratings is described.
Waves in Random and Complex Media 10/2007; 17(4). DOI:10.1080/17455030701466428 · 0.95 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We describe the differential multipole method, an extended multipole method used to calculate the modes of microstructured optical fibers with noncircular inclusions. We use a multipole expansion centered on each inclusion and a differential method to calculate the scattering properties of the individual inclusions. Representative results for a fiber with one ring of elliptical inclusions are presented, and a direct comparison is made with an existing method. The new method is also applied to a microstructured optical fiber with seven rings of elliptical inclusions, which is found, in effect, to support a single polarization of the fundamental mode.
Journal of the Optical Society of America B 10/2004; 21(11):1919-1928. DOI:10.1364/JOSAB.21.001919 · 1.97 Impact Factor