The scattering of waves of all types is one of the fundamental problems of physics. The essential feature of any multipole method is the application of an ingenious field identity that relates the regular field in the vicinity of any scatterer to fields radiated by other scatterers and external sources. This chapter discusses cylindrical structures. It provides an integrated tutorial on the multipole method, commencing with the analysis of a single scatterer and its extension to a finite cluster. Before commencing the detailed derivation of the theory, the chapter shows that some of the key nomenclature. It considers global array sums and discusses the difficulties in their evaluation caused by convergence problems in the defining series, the terms of which are summed over the direct lattice. The chapter describes some typical applications of the multipole method to studying both index guiding and photonic bandgap guiding microstructured optical fibers.

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 modal expansions onto the dominant modes of the two semi-infinite media. It is shown that 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.

The perfect absorption of light in subwavelength thickness layers generally relies on exotic materials, metamaterials or thick metallic gratings. Here we demonstrate that total light absorption can be achieved in ultra-thin gratings composed of conventional materials, including relatively weakly-absorbing semiconductors, which are compatible with optoelectronic applications such as photodetectors and optical modulators. We fabricate a 41 nm thick antimony sulphide grating structure that has a measured absorptance of A = 99.3% at a visible wavelength of 591 nm, in excellent agreement with theory. We infer that the absorption within the grating is A = 98.7%, with only A = 0.6% within the silver mirror. A planar reference sample absorbs A = 7.7% at this wavelength.

We describe EMUstack, an open-source implementation of the Scattering Matrix Method (SMM) for solving field problems in layered media. The fields inside nanostructured layers are described in terms of Bloch modes that are found using the Finite Element Method (FEM). Direct access to these modes allows the physical intuition of thin film optics to be extended to complex structures. The combination of the SMM and the FEM makes EMUstack ideally suited for studying lossy, high-index contrast structures, which challenge conventional SMMs.Program summaryProgram title: EMUstack Catalogue identifier: AEZI_v1_0Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEZI_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: GNU General Public License, version 3No. of lines in distributed program, including test data, etc.: 154301No. of bytes in distributed program, including test data, etc.: 5308635Distribution format: tar.gzProgramming language: Python, Fortran.Computer: Any computer with a Unix-like system with Python, a Fortran compiler and F2Py [1]. Also required are the following free libraries LAPACK and BIAS [2], UMFPACK [3]. Developed on 1.6 GHz Intel Core i7.Operating system: Any Unix-like system; developed on Ubuntu 14.04 (using Linux kernel 3.16).RAM: Problem dependent; specifically on the resolution of the FEM mesh and the number of modes included. The given example uses approximately 100 MB.Classification: 10.External routines: Required are the following free libraries LAPACK and BIAS [2], UMFPACK [3]. Optionally exploits additional commercial software packages: Intel MKL [4], Gmsh [5].Nature of problem: Time-harmonic electrodynamics in layered media.Solution method: Finite element method and the scattering matrix method.Running time: Problem dependent (typically about 3 s per wavelength including plane wave orders <= 3).References:[1] P. Peterson, F2PY: A tool for connecting Fortran and Python programs, International Journal of Computational Science and Engineering 4 (4) (2009) 296.[2] LAPACK, http://www.netlib.org/Iapack[3] T.A. Davis, Algorithm 832: UMFPACK V4.3 - An Unsymmetric-Pattern Multifrontal Method, ACM Transactions on Mathematical Software 30,(2) (2004) 165-195.[4] Intel MKL, http://www.software.intel.com/intel-mkl[5] C. Geuzaine, J.-F. Remade, Gmsh: a three-dimensional finite element mesh generator with built-in pre- and post-processing facilities, International Journal for Numerical Methods in Engineering 79 (2009) 1309-1331. (C) 2016 Elsevier B.V. All rights reserved.

We show that essentially total absorption can be achieved in ultrathin layers of a modestly absorbing semiconductor using a grating geometry. Fabrication requires standard techniques and structured metal elements are not required.

We correct the errors made in the field-overlap derivation in Appendix A of J. Opt. Soc. Am. B33, 1044 (2016)JOBPDE0740-322410.1364/JOSAB.33.001044.

Butt-coupling of light into a surface plasmon is a simple and compact coupling method with a range of potential uses in photonic circuitry. Although butt-coupling has been successfully implemented in many coupling configurations, the coupling effectiveness is not fully understood. Here, we present a semi-analytical study which models the coupling efficiency of an incident beam into a surface plasmon on silver in the presence of loss using an projection method in one dimension. We find that the coupling efficiencies for silver between the wavelengths of 0:38 - 1:6 μm reach 77 - 88% with optimum incident beam parameters.

We consider the conditions for perfect absorption in uniform thin-films and in thin gratings. We find that perfect absorption of TE polarized light can occur in gratings composed of weakly absorbing materials.

We present a semi-analytical study exploring the end-fire coupling of an incident beam into a surface plasmon mode propagating on a metal-dielectric interface. An energy-conserving projection method is used to solve for the resultant reflected and transmitted fields for a given incident beam, thereby determining the efficiency of the surface plasmon coupling. The coupling efficiency is found to be periodic with waveguide width due to the presence of a coupled, transversely propagating surface plasmon. Optimization of the incident beam parameters, such as beam width, position, and wavelength, leads to numerically observed maximum efficiencies of approximately 80% when the beam width roughly matches the width of the surface plasmon. (C) 2015 Optical Society of America

The guided mode resonances (GMRs) of diffraction gratings surrounded by low index materials can be designed to produce broadband regions of near perfect reflection and near perfect transmission. These have many applications, including in optical isolators, in hybrid lasers cavities and in photovoltaics. The excitation of rapid GMRs occurs in a background of slowly varying Fabry-Perot oscillation, which produces Fano resonances. We demonstrate the critical role of the polarity of adjacent Fano resonances in the formation of the broadband features. We design gratings for photovoltaic applications that operate at wavelengths where material absorption must be considered and where light is incident at non-normal angles.

We show that perfect absorption can be achieved in ultra-thin gratings composed of weakly absorbing dielectric materials combined with a mirror. The structures can be fabricated using standard processing techniques.

Nanowire arrays exhibit efficient light coupling and strong light trapping, making them well suited to solar cell applications. The processes that contribute to their absorption are interrelated and highly dispersive, so the only current method of optimizing the absorption is by intensive numerical calculations. We present an efficient alternative which depends solely on the wavelength-dependent refractive indices of the constituent materials. We choose each array parameter such that the number of modes propagating away from the absorber is minimized while the number of resonant modes within the absorber is maximized. From this we develop a semi-analytic method that quantitatively identifies the small range of parameters where arrays achieve maximum short circuit currents. This provides a fast route to optimizing NW array cell efficiencies by greatly reducing the geometries to study with full device models. Our approach is general and applies to a variety of materials and to a large range of array thicknesses.

We investigate how a dielectric grating positioned on top of a thin absorber can enhance the absorption of the photovoltaic cell. We observe absorption peaks from electric field enhancement within the absorber due to Fabry-Perot resonances.

We investigate the optical properties of silicon nanohole arrays for application in photovoltaic cells in terms of the modes within the structure. We highlight three types of modes: fundamental modes, important at long wavelengths; guided resonance modes, which enhance absorption for wavelengths where the intrinsic absorption of silicon is low; and channeling modes, which suppress front-surface reflection. We use this understanding to explain why the parameters of optimized nanohole arrays occur in specific ranges even as the thickness is varied.

The construction of Green's tensor for two-dimensional gyrotropic photonic clusters composed of cylinders with circular cross sections using the semi-analytic multipole method is presented. The high efficiency and accuracy of the method is demonstrated. The developed method is applied to gyrotropic clusters that support topological chiral Hall edge states. The remarkable tolerance of chiral Hall edge modes toward substantial cluster separation is revealed. The transformation of chiral Hall edge states as the cluster separation increases is also presented. The excitation of chiral Hall edge modes for different source orientations is considered. Both gyroelectric and gyromagnetic (ferrite) clusters are treated.

Nanowire and Nanohole arrays exhibit strong absorption driven by competing nanophotonic effects. We present a semi-analytic approach to optimizing the absorption of these structures that is based on simple physical arguments.

Get PDF Email Share Share with Facebook Tweet This Post on reddit Share with LinkedIn Add to CiteULike Add to Mendeley Add to BibSonomy Get Citation Copy Citation Text C. M. de Sterke, H. Moore, J. S. Brownless, F. Lawrence, S. Mahmoodian, K. Dossou, and L. Botten, "Waveguides arrays in hexagonal photonic crystals," in Frontiers in Optics 2014, OSA Technical Digest (online) (Optical Society of America, 2014), paper LTu4H.2. Export Citation BibTex Endnote (RIS) HTML Plain Text Citation alert Save article

Aperiodic Nanowire (NW) arrays have higher absorption than equivalent periodic arrays, making them of interest for photovoltaic applications. An inevitable property of aperiodic arrays is the clustering of some NWs into closer proximity than in the equivalent periodic array. We focus on the modes of such clusters and show that the reduced symmetry associated with cluster formation allows external coupling into modes which are dark in periodic arrays, thus increasing absorption. To exploit such modes fully, arrays must include tightly clustered NWs that are unlikely to arise from fabrication variations but must be created intentionally.

We define the concept of an impedance matrix for three-dimensional (3D) photonic and metamaterial structures relative to a reference medium and show that it satisfies a matrix generalization of the basic algebraic properties of the wave impedance between homogeneous media. This definition of the impedance matrix is motivated by the structure of the Fresnel reflection and transmission matrices at the interface between the media. In the derivation of the Fresnel scattering matrices, the field in each medium is expressed by a Bloch mode expansion, with field matching at the interface being undertaken in a least-squares manner by exploiting a biorthogonality relation between primal and adjoint Bloch modes. A semi-analytic technique, based on the impedance matrix, is developed for modeling the scattering of light by 3D periodic photonic and metamaterial structures. The advantages (in design and intuition) of the formalism are demonstrated through two applications.

We have constructed the Green's tensor for two-dimensional gyrotropic photonic clusters and have calculated their optical local density of states (LDOS). For clusters that support the chiral Hall edge states we calculate the LDOS as a function of wavelength, position, size, and shape of the cluster. It is shown that the LDOS of Hall edge states is a strong function of the cluster shape and position. The LDOS can be orders of magnitude higher at the edges of the cluster compared to the free space value while it vanishes towards the cluster center. It is shown that the LDOS in such photonic clusters can withstand a very strong disorder due to their topological protection. The spatial profiles of chiral Hall edge modes, their quality factors, and their excitations have been calculated. Both gyroelectric and gyromagnetic (ferrite) clusters have been treated.