Theoretical investigation of one-dimensional cavities in two-dimensional photonic crystals

We study numerically the features of the resonant peak of one-dimensional (1-D) dielectric cavities in a two-dimensional (2-D) hexagonal lattice. We use both the transfer matrix method and the finite difference time-domain (FDTD) method to calculate the transmission coefficient. We compare the two methods and discuss their results for the transmission and quality factor Q of the resonant peak. We also examine the dependence of Q on absorption and losses, the thickness of the sample and the lateral width of the cavity. The Q- factor dependence on the width of the source in the FDTD calculations is also given.Comment: 25 pages, 8 figure

Topological analysis of polymeric melts: Chain length effects and fast-converging estimators for entanglement length

Primitive path analyses of entanglements are performed over a wide range of chain lengths for both bead spring and atomistic polyethylene polymer melts. Estimators for the entanglement length N_e which operate on results for a single chain length N are shown to produce systematic O(1/N) errors. The mathematical roots of these errors are identified as (a) treating chain ends as entanglements and (b) neglecting non-Gaussian corrections to chain and primitive path dimensions. The prefactors for the O(1/N) errors may be large; in general their magnitude depends both on the polymer model and the method used to obtain primitive paths. We propose, derive and test new estimators which eliminate these systematic errors using information obtainable from the variation of entanglement characteristics with chain length. The new estimators produce accurate results for N_e from marginally entangled systems. Formulas based on direct enumeration of entanglements appear to converge faster and are simpler to apply.Comment: Major revisions. Developed near-ideal estimators which operate on multiple chain lengths. Now test these on two very different model polymers

Refraction at Media with Negative Refractive Index

We show that an electromagnetic (EM) wave undergoes negative refraction at the interface between a positive and negative refractive index material. Finite difference time domain (FDTD) simulations are used to study the time evolution of an EM wave as it hits the interface. The wave is trapped temporarily at the interface and after a long time, the wave front moves eventually in the negative direction. This explains why causality and speed of light are not violated in spite of the negative refraction always present in a negative index material.Comment: 5 pages, 4 figures, submitted to Phys. Rev. Let

Broadband Mid-IR superabsorption with aperiodic polaritonic photonic crystals

We propose an approach for broadband near-perfect absorption with aperiodic-polaritonic photonic crystals (PCs) operating in the phononpolariton gap of the constituent material. In this frequency regime the bulk polaritonic materials are highly reflective due to the extreme permittivity values, and so their absorption capabilities are limited. However, we are able to achieve absorptance of more than 90%  almost across the entire phonon-polariton gap of SiC with a SiC-air aperiodic one-dimensional(1D)-PC with angular bandwidth that covers the range of realistic diffraction-limited sources. We explore two types of aperiodic PC schemes, one in which the thickness of the SiC layer increases linearly, and one in which the filling ratio increases linearly throughout the structure. We find that the former scheme performs better in terms of exhibiting smoother spectra and employing less SiC material. On the other hand, the second scheme performs better in terms of the required total structure size. We analyze the principles underpinning the broadband absorption merit of our proposed designs, and determine that the key protagonists are the properties of the entry building block and the adiabaticity of the aperiodic sequencing scheme. Further investigation with derivative lamellar sequences,–resulting by interchanging or random positioning of the original building blocks–, underline the crucial importance of the building block arrangement in an increasing order of thickness. If we relax the requirement of near-perfect absorption, we show that an averaged absorption enhancement across the SiC phonon-polariton gap of ~10 can be achieved with much shorter designs of the order of two free-space wavelengths. Our findings suggest that our aperiodic polaritonic PC route can be promising to design broadband electromagnetic absorbers across the spectrum

Compact photonic-crystal superabsorbers from strongly absorbing media

Copyright © 2013 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in Journal of Applied Physics, Volume 114 (3), article 033504, and may be found at http://dx.doi.org/10.1063/1.4811521We present a route to near-perfect absorption in compact photonic-crystal (PC) structures constructed from strongly absorbing media that are typically highly reflective in bulk form. Our analysis suggests that the key underlying mechanism in such PC superabsorbers is the existence of a PC-band-edge reflectionless condition. Although the latter is by default uncharacteristic in photonic crystals, we propose here a clear recipe on how such condition can be met by tuning the structural characteristics of one-dimensional lossy PC structures. Based on this recipe, we constructed a realizable three-layer SiC- BaF2 -SiC PC operating within the Reststrahlen band of SiC. We demonstrate near-perfect absorption in this prototype of total thickness smaller than λ/3 , where more than 90% of the impinging light is absorbed by the top deep-subwavelength layer of thickness ∼λ/1100 . We believe our study will inspire new photonic-crystal-based designs for extreme absorption harnessing across the electromagnetic spectrum.University of Exete

EM wave propagation in two-dimensional photonic crystals: a study of anomalous refractive effects

We systematically study a collection of refractive phenomena that can possibly occur at the interface of a two-dimensional photonic crystal, with the use of the wave vector diagram formalism. Cases with a single propagating beam (in the positive or the negative direction) as well as cases with birefringence were observed. We examine carefully the conditions to obtain a single propagating beam inside the photonic crystal lattice. Our results indicate, that the presence of multiple reflected beams in the medium of incidence is neither a prerequisite nor does it imply multiple refracted beams. We characterize our results in respect to the origin of the propagating beam and the nature of propagation (left-handed or not). We identified four distinct cases that lead to a negatively refracted beam. Under these findings, the definition of phase velocity in a periodic medium is revisited and its physical interpretation discussed. To determine the ``rightness'' of propagation, we propose a wedge-type experiment. We discuss the intricate details for an appropriate wedge design for different types of cases in triangular and square structures. We extend our theoretical analysis, and examine our conclusions as one moves from the limit of photonic crystals with high index contrast between the constituent dielectrics to photonic crystals with low modulation of the refractive index. Finally, we examine the ``rightness'' of propagation in the one-dimensional multilayer medium, and obtain conditions that are different from those of two-dimensional systems.Comment: 65 pages, 17 figures, submitted to Phys. Rev.