Two-dimensional Green's tensor for gyrotropic clusters composed of circular cylinders.

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.

Mode-based analysis of silicon nanohole arrays for photovoltaic applications.

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.

Absorption enhancing proximity effects in aperiodic nanowire arrays.

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.

Modal formulation for diffraction by absorbing photonic crystal slabs.

A finite element-based modal formulation of diffraction of a plane wave by an absorbing photonic crystal slab of arbitrary geometry is developed for photovoltaic applications. The semianalytic approach allows efficient and accurate calculation of the absorption of an array with a complex unit cell. This approach gives direct physical insight into the absorption mechanism in such structures, which can be used to enhance the absorption.

Modal analysis of enhanced absorption in silicon nanowire arrays.

We analyze the absorption of solar radiation by silicon nanowire arrays, which are being considered for photovoltaic applications. These structures have been shown to have enhanced absorption compared with thin films, however the mechanism responsible for this is not understood. Using a new, semi-analytic model, we show that the enhanced absorption can be attributed to a few modes of the array, which couple well to incident light, overlap well with the nanowires, and exhibit strong Fabry-Pérot resonances.

Local observation of modes from three-dimensional woodpile photonic crystals with near-field microspectroscopy under supercontinuum illumination.

A near-field microscope coupled with a near-infrared (NIR) supercontinuum source is developed and applied to characterize optical modes in a three-dimensional (3D) woodpile photonic crystal (PC) possessing a NIR partial bandgap. Spatially resolved near-field intensity distributions under different illumination wavelengths demonstrate that the electric fields preferentially dwell in the polymer rods or in the gaps between rods, respectively, for frequencies below or above the stop gap, as predicted by the 3D finite-difference time-domain modeling. Near-field microspectroscopy further reveals that the position-dependent band-edge effect plays an important role in PC-based all-optical integrated devices.

Suppression of Anderson localization in disordered metamaterials.

We study wave propagation in mixed, 1D disordered stacks of alternating right- and left-handed layers and reveal that the introduction of metamaterials substantially suppresses Anderson localization. At long wavelengths, the localization length in mixed stacks is orders of magnitude larger than for normal structures, proportional to the sixth power of the wavelength, in contrast to the usual quadratic wavelength dependence of normal systems. Suppression of localization is also exemplified in long-wavelength resonances which largely disappear when left-handed materials are introduced.

Transverse coupling to the core of a photonic crystal fiber: the photo-inscription of gratings.

The effect of the microstructure on transversely coupled laser light into the core of a photonic crystal fiber is investigated. Computational two-dimensional modeling and direct experimental measurements indicate that there exist angles and positions of the fiber microstructure, relative to a transversely launched laser beam, that preferentially couple laser light into the fiber core. The implications of these observations on long period and fiber-Bragg grating fabrication in photonic crystal fibers are discussed.

Gap-edge Asymptotics of defect modes in 2D Photonic Crystals.

We consider defect modes created in complete gaps of 2D photonic crystals by perturbing the dielectric constant in some region. We study their evolution from a band edge with increasing perturbation using an asymptotic method that approximates the Green function by its dominant component which is associated with the bulk mode at the band edge. From this, we derive a simple exponential law which links the frequency difference between the defect mode and the band edge to the relative change in the electric energy.

Evidence of a mobility edge for photons in two dimensions.

A scaling analysis of conductance for photons in two dimensions is carried out and, contrary to widely held belief, we find strong evidence of a mobility edge. Such behavior is compatible with the existence of an Anderson transition for electronic systems under symplectic symmetry, and indeed we show that the transfer matrix in the photonic system we have modelled has such a symmetry. We verify single parameter scaling of the conductance and demonstrate the transition from the metallic phase to localization.

Conductance of photons in disordered photonic crystals.

The conductance of photons in two-dimensional disordered photonic crystals is calculated using an exact multipole-plane wave method that includes all multiple scattering processes. Conductance fluctuations, the universal nature of which has been established for electrons in the diffusive regime, are studied for photons, in both principal polarizations and for varying disorder. Our simulations show that universal conductance fluctuations can be observed in H(||) (TE) polarization for weak and intermediate disorder while, for E(||) (TM) polarization, we show that the conductance variance is essentially independent of sample size but strongly dependent on disorder.

Bloch mode scattering matrix methods for modeling extended photonic crystal structures. II. Applications.

The Bloch mode scattering matrix method is applied to several photonic crystal waveguide structures and devices, including waveguide dislocations, a Fabry-Pérot resonator, a folded directional coupler, and a Y-junction design. The method is an efficient tool for calculating the properties of extended photonic crystal (PC) devices, in particular when the device consists of a small number of distinct photonic crystal structures, or for long propagation lengths through uniform PC waveguides. The physical insight provided by the method is used to derive simple, semianalytic models that allow fast and efficient calculations of complex photonic crystal structures.

Bloch mode scattering matrix methods for modeling extended photonic crystal structures. I. Theory.

We present a rigorous Bloch mode scattering matrix method for modeling two-dimensional photonic crystal structures and discuss the formal properties of the formulation. Reciprocity and energy conservation considerations lead to modal orthogonality relations and normalization, both of which are required for mode calculations in inhomogeneous media. Relations are derived for studying the propagation of Bloch modes through photonic crystal structures, and for the reflection and transmission of these modes at interfaces with other photonic crystal structures.

Modes of coupled photonic crystal waveguides.

We consider the modes of coupled photonic crystal waveguides. We find that the fundamental modes of these structures can be either even or odd, in contrast with the behavior in coupled conventional waveguides, in which the fundamental mode is always even. We explain this finding using an asymptotic model that is valid for long wavelengths.

Density of states functions for photonic crystals.

We discuss density of states functions for photonic crystals, in the context of the two-dimensional problem for arrays of cylinders of arbitrary cross section. We introduce the mutual density of states (MDOS), and show that this function can be used to calculate both the local density of states (LDOS), which gives position information for emission of radiation from photonic crystals, and the spectral density of states (SDOS), which gives angular information. We establish the connection between MDOS, LDOS, SDOS and the conventional density of states, which depends only on frequency.

Effects of disorder in two-dimensional photonic crystal waveguides.

The effects of randomness on the guiding properties of waveguides embedded in disordered two-dimensional photonic crystals composed of a finite cluster of circular cylinders of infinite length are investigated for TM-polarized radiation. Different degrees of disorder in the radius, filling fraction, refractive index, and position are considered for both straight and 90 degrees bent guides. The crystals exhibit similar sensitivity to refractive index and radius disorder, with a degree of disorder from 15%-20% yielding little substantial change in the guiding properties.

Three-dimensional local density of states in a finite two-dimensional photonic crystal composed of cylinders.

The three-dimensional local density of states (LDOS), which determines the radiation dynamics of a point source, is presented here for a finite two-dimensional photonic crystal as a function of space and frequency. The LDOS is obtained from the dyadic Green's function, which is calculated exactly using the multipole method. Maximum suppression in the LDOS occurs at the high frequency edge of the complete two-dimensional band gap and varies smoothly about this frequency.

Semianalytic treatment for propagation in finite photonic crystal waveguides.

We present a semianalytic theory for the properties of two-dimensional photonic crystal waveguides of finite length. For single-mode guides, the transmission spectrum and field intensity can be accurately described by a simple two-parameter model. Analogies are drawn with Fabry-Perot interferometers, and generalized Fresnel coefficients for the interfaces are calculated.

Diffusion and anomalous diffusion of light in two-dimensional photonic crystals.

The transport properties of electromagnetic waves in disordered, finite, two-dimensional photonic crystals composed of circular cylinders are considered. Transport parameters such as the transport and scattering mean free paths and the transport velocity are calculated, for the case where the electromagnetic radiation has its electric field along the cylinder axes. The range of the parameters in which the diffusion process can take place is specified.

Calculation of electromagnetic properties of regular and random arrays of metallic and dielectric cylinders.

A method is developed to calculate electromagnetic properties of arrays of metallic and dielectric cylinders. It incorporates and exploits cylindrical boundary conditions and Rayleigh identities for efficient, high-accuracy calculation of scattering off individual layers that are stacked into arrays using scattering matrices. The method enables absorption, dispersion, and randomness to be incorporated efficiently, and reproduces known results with vastly improved speed and accuracy.

Effects of disorder on wave propagation in two-dimensional photonic crystals.

The electromagnetic transmittance of disordered two-dimensional photonic crystals composed of circular cylinders is investigated as a function of wavelength and polarization. At short wavelengths, the transmittance shows a band structure similar to that found in the optical absorption spectrum of amorphous semiconductors, with impurity states increasingly appearing on the long wavelength side of the band gaps as the degree of disorder is increased. In the long-wavelength limit, Anderson localization of waves is found, provided that the wavelength is not so large that the random photonic crystal can be viewed as homogeneous.

Photonic band structure calculations using scattering matrices.

We consider band structure calculations of two-dimensional photonic crystals treated as stacks of one-dimensional gratings. The gratings are characterized by their plane wave scattering matrices, the calculation of which is well established. These matrices are then used in combination with Bloch's theorem to determine the band structure of a photonic crystal from the solution of an eigenvalue problem.

Two-dimensional Green's function and local density of states in photonic crystals consisting of a finite number of cylinders of infinite length.

Using the exact theory of multipole expansions, we construct the two-dimensional Green's function for photonic crystals, consisting of a finite number of circular cylinders of infinite length. From this Green's function, we compute the local density of states (LDOS), showing how the photonic crystal affects the radiation properties of an infinite fluorescent line source embedded in it. For frequencies within the photonic band gap of the infinite crystal, the LDOS decreases exponentially inside the crystal; within the bands, we find "hot" and "cold" spots.

Formulation for electromagnetic scattering and propagation through grating stacks of metallic and dielectric cylinders for photonic crystal calculations. Part II. Properties and implementation.

A numerical implementation and generalized conservation properties of a formulation for calculating wave propagation through stacked gratings comprising metallic and dielectric cylinders are presented. The basic formulation of the method was given in a companion paper [J. Opt.

Formulation for electromagnetic scattering and propagation through grating stacks of metallic and dielectric cylinders for photonic crystal calculations. Part I. Method.

We present a formulation for wave propagation and scattering through stacked gratings comprising metallic and dielectric cylinders. By modeling a photonic crystal as a grating stack of this type, we thus formulate an efficient and accurate method for photonic crystal calculations that allows us to calculate reflection and transmission matrices. The stack may contain an arbitrary number of gratings, provided that each has a common period.