Effective impedance modeling of metamaterial structures

© 2016 Optical Society of America. We present methods for retrieving the effective impedance of metamaterials from the Fresnel reflection coefficients at the interface between two semi-infinite media. The derivation involves the projection of rigorous modal expansions onto the dominant modes of the two semi-infinite media. It is shown that the effective impedance can also be written as a ratio of averaged field quantities. Thus, a number of effective impedance formulas, previously obtained by field averaging techniques, can also be derived from the scattering-based formalism by an appropriate choice of projection. Within the effective medium limit, it is observed that a simple semianalytic modeling technique based on the effective impedance can be used to reliably compute the reflection coefficients of metamaterials over a wide range of incidence angles. We use this technique to model planar metamaterial waveguides or surface modes

Modeling waveguides in photonic woodpiles using the fictitious source superposition method

We extend the fictitious source superposition method in order to model linear defects in photonic woodpiles, and we use the method to model a waveguide that is created by changing either the radius or refractive index of a single rod of an infinite woodpile composed of chalcogenide glass cylinders. In one instance, a nearly constant dispersion was observed over a sizable kx interval, where kx is the Bloch vector in the waveguiding direction, making this a compelling geometry for slow-light waveguides. The principal advantage of the method is that it does not rely on a supercell, thus avoiding what is possibly the greatest source of inefficiency present in most of the other methods that are used for modeling these structures. Instead, the method proceeds by placing an artificial source inside each rod of the defect layer and then subsequently taking an appropriate field superposition to remove all but one of these sources. The remaining source can then be used to mimic the fields that would be produced by a defect rod. © 2011 Optical Society of America

Localisation and disorder in the design of 2D photonic crystal devices

Photonic crystals are meta-materials that can inhibit the propagation of light in all directions for specific wavelength ranges. Material or structural defects can be introduced into the crystal to cause localised modes, providing the ability to mould the flow of light on the wavelength scale and allowing the development of miniaturised, integrated photonic devices. For this reason, photonic crystals will likely be key building blocks for future micro-optical and communication technology. In this paper, we examine the Bloch mode modelling of 2D photonic crystal structures with application to the analysis of photonic crystal waveguides and their susceptibility to disorder, which provides a framework for studying fabrication tolerances in realistic devices

Confinement losses in microstructured optical fibers

We describe a multipole formulation that can be used for high-accuracy calculations of the full complex propagation constant of a microstructured optical fiber with a finite number of holes. We show how the imaginary part of the microstructure, which describes confinement losses not associated with absorption, varies with hole size, the number of rings of holes, and wavelength, and give the minimum number of rings of holes required for a specific loss for given parameters. © 2001 Optical Society of America

Symmetry and degeneracy in microstructured optical fibers

The symmetry of an optical waveguide determines its modal degeneracies. A fiber with rotational symmetry of order higher than 2 has modes that either are nondegenerate and support the complete fiber symmetry or are twofold degenerate pairs of lower symmetry. The latter case applies to the fundamental modes of perfect microstructured optical fibers, guaranteeing that such fibers are not birefringent. We explore two numerical methods and demonstrate their agreement with these symmetry constraints. © 2001 Optical Society of America

Photonic-crystal surface modes found from impedances

We present a method for finding surface modes at interfaces between two-dimensional photonic crystals (PCs), in which the surface modes are represented as superpositions of the PCs' propagating and evanescent Bloch modes. We derive an existence condition for surface modes at an air-PC interface in terms of numerically calculated PC impedance matrices, and use the condition to find surface modes in the partial band gap of a PC. We also derive a condition for modes of a three-layer structure with two interfaces, and find both coupled surface modes and waveguide modes. We show that some waveguide modes cross the band edge and become coupled surface modes. © 2010 The American Physical Society

Efficient coupling into slow light photonic crystal waveguide without transition region: Role of evanescent modes

We show that efficient coupling between fast and slow photonic crystal waveguide modes is possible, provided that there exist strong evanescent modes to match the waveguide fields across the interface. Evanescent modes are required when the propagating modes have substantially different modal fields, which occurs, for example, when coupling an index-guided mode and a gap-guided mode. ©2009 Optical Society of America