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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 equiv

We derive a frequency-domain-based approach for radiation from double-heterostructure cavity (DHC) modes. We use this to compute the quality factors and radiation patterns of DHC modes. The semianalytic nature of our method enables us to provide a general relationship between the radiation pattern of the cavity and its geometry. We use this to provide general designs for ultrahigh-quality-factor DHCs with radiation patterns that are engineered to emit vertically.

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-Perot resonances. For some wavelengths the absorption is further enhanced by slow light effects. We study the evolution of these modes with wavelength to explain the various features of the absorption spectra, focusing first on a dilute array at normal incidence, before generalizing to a dense array and off-normal angles of incidence. The understanding developed will allow for optimization of simple SiNW arrays, as well as the development of more advanced designs.

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.

We consider the modal fields and resonance frequencies of composite defects in two-dimensional photonic crystals (PCs). Using an asymptotic method based on Green's functions, we show that the coupling matrices for the composite defect can be represented as circulant or block-circulant matrices. Using the properties of these matrices, specifically that their eigenvectors are independent of the values of the matrix elements, we obtain modal properties such as dispersion relations, modal cutoff, degeneracy, and symmetry of the mode fields. Using our formulation, we investigate defects arranged on the vertices of regular polygons as well as PC ring resonators with defects arranged on the edges of polygons. Finally, we discuss the impact of band-edge degeneracies on composite-defect modes.

We investigate the formation and coupling of defect modes in two-dimensional photonic crystal (PC) band gaps associated with degenerate edges. Using a method based on Green's functions and perturbation theory, we derive a condition for the degeneracy of a defect mode in a PC band gap. We show that the interaction between multiple degenerate defects splits this degeneracy and provide a semi-analytic model for the splitting using a 4??4 tight-binding matrix. We observe that the structure of this tight-binding matrix is related to the overlap and corresponding symmetry of the defect modes. We confirm our analysis by comparing with numerical results.

We give a rigorous semianalytical definition of impedance for square and triangular (hexagonal) lattice two-dimensional photonic crystals (PCs). Our impedance is a small matrix, derived from transfer matrices, which stores the information required to calculate the reflection and the transmission between PCs. We apply our definition to design PC antireflection coatings efficiently. This task is O(n) with the number of candidate PCs as only one simulation per PC is required to find the impedances; the reflection and the transmission properties of a large number of coatings may then be evaluated quickly using the impedances in a simple matrix equation, in a way similar to the design of thin-film coatings. This is much faster than directly finding the reflections and the transmissions between pairs of candidate PCs, which requires one simulation per pair, a task that is O(n^2).

This paper discusses the importance of stress-induced contributions to the photo-induced birefringence observed in fiber Bragg gratings. Optical tomography measurements are performed in exposed and unexposed fibers to extract the stress profiles induced by UV-writing of fiber Bragg gratings for various exposure levels. A photoelastic analysis and a high-order isoparametric finite elements method are then used to calculate the birefringence caused by stress profile modifications. The results are compared to the birefringence directly measured by spectral analysis of a chirped fiber grating with multiple phase-shifts. We can therefore estimate the fraction of the photo-induced birefringence due to stress-induced anisotropy following UV exposure. © 2008 Optical Society of America.

We consider the calculation of the band structure and Bloch mode basis of two-dimensional photonic crystals, modelled as stacks of one-dimensional diffraction gratings. The scattering properties of each grating are calculated using an efficient finite element method (FEM) and allow the complete mode structure to be derived from a transfer matrix method. A range of numerical examples showing the accuracy, flexibility and utility of the method is presented. © 2006 Elsevier Inc. All rights reserved.

We use two-dimensional simulations to study the design of tapers to provide efficient, low reflection coupling between a waveguide in a two-dimensional photonic crystal (PC) and free space. We find that, largely independent of the PC parameters, or of the length and width of the tapered region, the same type of concave, horn-shaped tapering profile is optimal for coupling from the waveguide into free space, and significantly out-performs the widely used linear taper. We also find that optimal tapers can radiate nearly Gaussian beams, and therefore they can also provide efficient coupling of Gaussian beams from free space into the PC waveguide. These properties are better exhibited by rod-type PCs with Ez polarization than by hole-type PCs with Hz polarization. This study of taper couplers exemplifies a design strategy for photonic circuits which optimizes positioning of the cylinders immediately surrounding the light path, and then builds the rest of the crystal structure around these cylinders. © 2006 Elsevier B.V. All rights reserved.

We have studied the approximation of optical waveguide eigenvalues by a high order isoparametric vector finite element method. Isoparametric mappings are used for the approximation of domains with curved boundaries or curved material interfaces. Eigenvalue convergence for curved elements is investigated. Numerical results verify the predicted order of convergence and show the remarkable accuracy of the method. © 2004 Elsevier B.V. All rights reserved.

Typically the grating problem is formulated for TE and TM polarizations by using, respectively, the electric and magnetic fields aligned with the grating wall and perpendicular to the plane of incidence, and this leads to a one-field-component problem. For some grating profiles such as metallic gratings with a triangular profile, the prediction of TM polarization by using a standard finite-element method experiences a slower convergence rate, and this reduces the accuracy of the computed results and also introduces a numerical polarization effect. This discrepancy cannot be seen as a simple numerical issue, since it has been observed for different types of numerical methods based on the classical formulation. Hence an alternative formulation is proposed, where the grating problem is modeled by taking the electric field as unknown for TM polarization. The application of this idea to both TE and TM polarizations leads to a two-field-component problem. The purpose of the paper is to propose an edge finite-element method to solve this wave problem. A comparison of the results of the proposed formulation and the classical formulation shows improvement and robustness in the new approach. © 2005 Optical Society of America.

We describe a numerical method to compute the reflectivity of a metallised integrated echelle grating. The modelling is based on a combination of a finite element method in the region inside the grating teeth and the Rayleigh field expansion outside. Results show a net dependence of the efficiency on the polarisation state (directly related to PDL), as a function of the wavelength, due to two factors: a lower reflectivity for the TM light in the operating order and a shift in the maximum of the response curve.

Silica planar waveguide echelle grating demultiplexers with 48 channels and 256 channels are described and demonstrated. Polarization effects due to stress birefringence and polarization-dependent grating efficiency have been eliminated using a modified polarization compensator and grating design. The devices have a polarization-dependent wavelength shift of less than 10 pm, and a polarization-dependent loss below 0.2 dB. The 48-channel device has a measured crosstalk of -35 dB, an insertion loss better than 4 dB, and a uniformity of 1 dB across the C-band.

The effective index change and form birefringence are calculated in UV-exposed fibers using a high-order vectorial finite element method. The birefringence is compared in optical fibers with and without photosensitive inner cladding. © 2004 Optical Society of America.

We propose a Newton-GMRES-type algorithm to solve the discrete von Kármán problem. We show that this algorithm is efficient both in memory and computation time and robust in the neighborhood of the singular points of the bifurcation diagrams. Placing ourselves in the context of the Schaeffer and Golubitsky theory, we use this algorithm to study the postbuckling behavior of a rectangular plate clamped and compressed along its four sides.