Slow convergence to effective medium in finite discrete metamaterials

© 2016 American Physical Society. It is known that metamaterial properties may differ significantly from the predictions of effective-medium theory. In many cases this is due to the finite size and discrete structure, which cannot be neglected in practical samples with a relatively small amount of elements. We analyze the response of finite discrete metamaterial objects of a spherical shape and demonstrate the role of boundary effects in these structures, pointing out an interplay between the size of the structure and the dissipation. We conclude that the discrepancy between the actual resonance frequency of a sphere and the effective-medium prediction is inversely proportional to the size of the sphere

On the deviation of metamaterial spheres from effective medium

© 2016 IEEE. We analyse the convergence of the actual properties of finite subwavelength metamaterial samples where all the prerequisites for a reliable effective medium description, except for the finite size, are fulfilled, towards the effective medium predictions. We show that the convergence is rather slow and it is likely that hundreds of thousands of individual meta-atoms must be assembled together before the properties of the resulting structure can be claimed to correspond to those a bulk material. These observations are directly relevant for practical design of metamaterials and their future development

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

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

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

Efficient slow-light coupling in a photonic crystal waveguide without transition region

We consider the coupling into a slow mode that appears near an inflection point in the band structure of a photonic crystal waveguide. Remarkably, the coupling into this slow mode, which has a group index ng > 1000, can be essentially perfect without any transition region. We show that this efficient coupling occurs thanks to an evanescent mode in the slow medium, which has appreciable amplitude and helps satisfy the boundary conditions but does not transport any energy. © 2008 Optical Society of America