Effective impedance modeling of metamaterial structures.

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.

Fano resonances of dielectric gratings: symmetries and broadband filtering.

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.

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.

Semi-analytic impedance modeling of three-dimensional photonic and metamaterial structures.

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.

First-principles method for high-Q photonic crystal cavity mode calculations.

We present a first-principles method to compute radiation properties of ultra-high quality factor photonic crystal cavities. Our Frequency-domain Approach for Radiation (FAR) can compute the far-field radiation pattern and quality factor of cavity modes ~ 100 times more rapidly than conventional finite-difference time domain calculations. We explain how the radiation pattern depends on the perturbation used to create the cavity and on the Bloch modes of the photonic crystal.

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.

Degenerate band edges in optical fiber with multiple grating: efficient coupling to slow light.

Degenerate band edges (DBEs) of a photonic bandgap have the form (ω-ω(D)) ∝k(2m) for integers m>1, with ω(D) the frequency at the band edge. We show theoretically that DBEs lead to efficient coupling into slow-light modes without a transition region, and that the field strength in the slow mode can far exceed that in the incoming medium. A method is proposed to create a DBE of arbitrary order m by coupling m optical modes with multiple superimposed gratings.

Paired modes of heterostructure cavities in photonic crystal waveguides with split band edges.

We investigate the modes of double heterostructure cavities where the underlying photonic crystal waveguide has been dispersion engineered to have two band-edges inside the Brillouin zone. By deriving and using a perturbative method, we show that these structures possess two modes. For unapodized cavities, the relative detuning of the two modes can be controlled by changing the cavity length, and for particular lengths, a resonant-like effect makes the modes degenerate.

Coupled waveguide modes in hexagonal photonic crystals.

We investigate the modes of coupled waveguides in a hexagonal photonic crystal. We find that for a substantial parameter range the coupled waveguide modes have dispersion relations exhibiting multiple intersections, which we explain both intuitively and using a rigorous tight-binding argument.

Bloch-mode extraction from near-field data in periodic waveguides.

We demonstrate that the spatial profiles of both propagating and evanescent Bloch modes in a periodic structure can be extracted from a single measurement of an electric field at the specified optical wavelength. We develop a systematic extraction procedure by extending the concepts of high-resolution spectral methods previously developed for temporal data series to take into account the symmetry properties of Bloch modes simultaneously at all spatial locations. We illustrate the application of our method to a photonic crystal waveguide interface and confirm its robustness in the presence of noise.

Modal method for classical diffraction by slanted lamellar gratings.

We consider lamellar gratings made of dielectric or lossy materials used in classical diffraction mounts. We show how the modal diffraction formulation may be generalized to deal with slanted lamellar gratings and illustrate the accuracy and versatility of the new method through study of highly slanted gratings in a homogenization limit. We also comment on the completeness of the eigenmode basis and present tests enabling this completeness to be verified numerically.

Dispersionless tunneling of slow light in antisymmetric photonic crystal couplers.

We suggest a novel and general approach to the design of photonic-crystal directional couplers operating in the slow-light regime. We predict, based on a general symmetry analysis, that robust tunneling of slow-light pulses is possible between antisymmetrically coupled photonic crystal waveguides. We demonstrate, through Bloch mode frequency-domain and finite-difference time-domain (FDTD) simulations that, for all pulses with strongly reduced group velocities at the photonic band-gap edge, complete switching occurs at a fixed coupling length of just a few unit cells of the photonic crystal.

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.

Efficient slow light coupling into photonic crystals.

We study light coupling between two photonic crystal wave-guides, one of which supports slow light. We show theoretically that a short photonic crystal waveguide between the two that need to be coupled, can lead to a vanishingly small reflectivity. The design relies on the analogy with a lambda/4 anti-reflection layer in thin-film optics.

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.