Broadband high-reflection multilayer coatings at oblique angles of incidence

The angular properties of various wideband high reflectors are investigated. The theory is developed for the design of high reflectors based on contiguous quarter-wave stacks for use at one oblique angle or for a range of angles of incidence. Numerical results are presented for several high reflectors designed to have a high reflectance in the 0.4-0.8-mum spectral region for use at 50 degrees and with angles of incidence ranging between 0 degrees and 50 degrees . A random error perturbation analysis shows that such layer systems can be produced experimentally.     

Characterization of thin films based on reflectance and transmittance measurements at oblique angles of incidence

The optical parameters of a SiO2 thin-film coating determined from the spectral reflectance and transmittance measurements at various incidence angles, including the normal incidence and the Brewster's angle, are compared in this paper. The high-accuracy measurements were carried out through visible-near-infrared spectral regions by using our purpose-built instruments. The optical parameters obtained from the reflectance and the transmittance data are consistent over the angles of incidence and agree within 0.2%. The effect of important systematic factors in the oblique-incidence spectrophotometric measurements is also discussed.     

Microwave heating of laminate panels

The use of microwaves to heat laminate panels occurs in a variety of industrial processes, from chemical vapor infiltration (CVI) systems to the curing of adhesives in laminate panels. The electrical conductivity of the materials used in these systems is typically temperature-dependent. Characteristically, the thickness of the laminate panel is on the order of wavelength of the incident microwave, but the thickness of the laminate sheet is much smaller. This allows us to apply asymptotic techniques to find averaged wave and heat equations when the direction of the incident microwave is normal to, or tangent to, the laminates. These equations are analyzed in the small-Biot-number limit and are numerically approximated using finite differences. The results are in excellent agreement for small Biot numbers. More importantly, heating trends are observed for a wide variety of volume fractions for two particular CVI applications. In addition, the effect of the incident polarization on the heating process are also established. In particular, the use of a TE polarized incident microwave is shown to be inefficient in certain CVI applications, but produces a more favorable temperature gradient.     

On-machine interlocking of 3D laminate structures for composites

By using an adjacent-layer interlocking method on a weaving machine, multi-layer preform structures are developed. The on-loom interlocking method eliminates the yarn breakage resulting from needle penetration which is the case for off-loom interlocking of fabric layers. The concept of this three-dimensional (3D) fabric design is to bind each pair of adjacent layers at one connecting point in every other plain-weave repeat within each layer. The mechanical properties of the resulting composites are investigated by means of impact, short-beam shear and the long-beam flexural testing. The failure mechanisms found in 3D on-loom interlocked composites include fiber breakage, fiber debonding and fiber pull-out.     

Classical laminate theory model for twill weave fabric composites

The present paper is concerned with the development of an analytical model, based on Classical Lamination Theory, to predict the stiffness of twill in composites. A very simple yet quite general model is developed to obtain the elastic properties, i.e. extensional stiffness (A), extension–bending coupling stiffness (B) and bending stiffness (D). The model takes into account effects of the fabric structure by considering tow undulations and continuity along both the fill and warp directions. Various tow cross sections are possible and can be easily incorporated for a particular application. The model results in simple formulae for calculating in-plane and bending elastic constants, which can be used further in structural analysis.     

Nonpolarizing guided-mode resonant grating filter for oblique incidence

A new type of guided-mode resonant grating filter is described. The filter is independent of polarization state for oblique incidence. The filter has a crossed grating structure, and the plane of incidence on the filter contains the symmetric axis of the grating structure. Theoretical considerations and numerical calculations using two-dimensional rigorous coupled-wave analysis show that a rhombic lattice structure is suitable to such filters. In this configuration an incident light wave is diffracted into the waveguide and is divided into two propagation modes whose directions are symmetric with respect to the plane of incidence. In particular, when the propagation directions of the two modes are perpendicular to each other, the fill factor of grating structure can be approximately 50%. The filter was designed for an incident angle of 45 degrees. Tolerances of setting errors and fabrication errors for this filter were estimated by numerical calculations.     

A scatter search algorithm for stacking sequence optimisation of laminate composites

This paper explores the metaheuristic approach called scatter search for lay-up sequence optimisation of laminate composite panels. Scatter search is an evolutionary method that has recently been found to be promising for solving combinatorial optimisation problems. The scatter search framework is flexible and allows the development of alternative implementations with varying degree of sophistication. The main objective of this paper is to demonstrate the effectiveness of the proposed scatter search algorithm for the combinatorial problem like stacking sequence optimisation of laminate composite panels. Preliminary investigations have been carried out to compare the optimal stacking sequences obtained using scatter search algorithm for buckling load maximisation with the best known published results. Studies indicate that the optimal buckling load factors obtained using the proposed scatter search algorithm found to be either superior or comparable to the best known published results.

Later, two case studies have been considered in this paper. Thermal buckling optimisation of laminated composite plates subjected to temperature rise is considered as the first case study. The results obtained are compared with an exact enumerative study conducted on the problem to demonstrate the effectiveness and performance of the proposed scatter search algorithm. The second case study is optimisation of hybrid laminate composite panels for weight and cost with frequency and buckling constraints. The two objectives are considered individually and also collectively to solve as multi-objective optimisation problem. Finally the computational efficiency of the proposed scatter search algorithm has been investigated by comparing the results with various implementations of genetic algorithm customised for laminate composites. It was shown in this paper through numerical experiments that the scatter search is capable of finding practical solutions for optimal lay-up sequence optimisation of composite laminates and results are comparable and sometimes even superior to genetic algorithms.     

Cold roll bonding of multi-layered bi-metal laminate composites

Multi-layered laminate composites of dissimilar metals have assumed importance industrially. Cold roll bonding can produce multi-layered sheet composites. Study of the effect of rolling and material variables on the bonding characteristics needs to be studied in order to predict the optimum bonding conditions and the final composition of the laminate sheets. In this work, cold roll bonding of multi-layered bimetals has been modeled using the slab method. The effect of anisotropy has been included. Effects of different process and material variables are analyzed. Novel experiments were performed on multilayered Ti–Al system and the numerical results from the model were compared with the experimental results. A good agreement was observed between the model and experimental results.     

Tunable, oblique incidence resonant grating filter for telecommunications

We have designed a tunable, oblique-incidence resonant grating filter that covers the C band as an add-drop device for incident TE-polarized light. We tune the filter by tilting a microelectromechanical systems platform onto which the filter is attached. The fabrication tolerances as well as the role of finite incident-beam size and limited device size were addressed. The maximum achievable efficiency of a finite-area device as well as a scaling law that relates the resonance peak width and the minimum device size is derived. In good agreement with simulations, measurements indicate a negligible change in shape of the resonance peak from 1526 nm at a 45 degrees angle of incidence to 1573 nm at a 53 degrees angle with a full width at half-maximum of 0.4 nm. In this range the shift of the peak wavelength is linear with respect to changes in the angle of incidence.     

Optical properties of a slightly absorbing film for oblique incidence

Approximate equations are derived for calculating the transmittance and reflectance of a slightly absorbing film when radiation is incident at an arbitrary angle. These formulas are compared with those derived from wave optics. Examination of the real and the imaginary parts of the complex phase change and the complex angle of refraction shows the simple equations to be consistent with the wave-optics formulation under the assumption that the imaginary part of the refractive index of the film is much smaller than its real counterpart.     

Modelling of thick composites using a layerwise laminate theory

The layerwise laminate theory of Reddy¹ is used to develop a layerwise, two-dimensional, displacement-based, finite element model of laminated composite plates that assumes a piecewise continuous distribution of the tranverse strains through the laminate thickness. The resulting layerwise finite element model is capable of computing interlaminar stresses and other localized effects with the same level of accuracy as a conventional 3-D finite element model. Although the total number of degrees of freedom are comparable in both models, the layerwise model maintains a 2-D-type data structure that provides several advantages over a conventional 3-D finite element model, e.g. simplified input data, ease of mesh alteration, and faster element stiffness matrix formulation. Two sample problems are provided to illustrate the accuracy of the present model in computing interlaminar stresses for laminates in bending and extension.     

Initial water impact of a wedge at vertical and oblique angles

This paper examines initial asymmetric wedge-impact flows with horizontal as well as vertical impact velocity. The method of two-dimensional vortex distributions is employed to model the initial-boundary-value problem. The numerical analysis involves discretization of the body surface and an iterative solution technique. Experimental drop tests of a prismatic wedge were performed to gain understanding and provide data for comparison of initial water impact when asymmetry and horizontal impact velocity are present. The experimental investigation of initial flow separation off the wedge vertex (i.e., keel) during impact is described. Initial separation-ventilation of the flow from the vertex due to asymmetric impact or horizontal-vertical impact velocity is examined in relation to the present theory. Agreement between the data and the numerical predictions was demonstrated for small degrees of asymmetry and small ratios of horizontal to vertical impact velocity. The initial flow detachment from the vertex also revealed interesting hydrodynamic characteristics.     

Minimax refining of wideband antireflection coatings for wide angular incidence

The design of antireflection coatings at any light incidence is a challenging task in optics. To this aim, a minimax method is presented: it minimizes the maximum deviation of the spectral reflectance from the desired specifications over the wavelength for a given set of incidence angles. Refining is limited to lossless coatings with assigned refractive indices and undetermined thicknesses; the algorithm consists of iterating appropriate linear optimization steps. In the examples some minimax-refined coatings are compared with coatings reported in the literature.     

Half-plane diffraction in a case of oblique incidence

Abstract

The classical problem of half-plane diffraction is examined in a particular case of oblique incidence. A scalar solution to the problem is proposed using boundary diffraction wave theory and some limitations of the solution are discussed.     

Impact response of woven composites with small weaving angles

This paper presents experimental investigations on impact response of woven composites with various weaving angles between interlacing yarns. A method for preparing novel woven composites with small weaving angles is presented. The effects of the weaving angle on the impact characteristics such as peak force, contact duration, maximum deflection and absorbed energy are also examined. An energy profiling method seems to be useful for identifying the penetration and perforation thresholds of the woven composites. The damage process of individual woven composites can be reconstructed from comparing the corresponding load–deflection curves, energy profile and images of damaged specimens. The study concludes that the energy absorption capability and perforation threshold of woven composites can be significantly improved by using a small weaving angle between interlacing yarns. For example, the perforation threshold of [0/20]₄ woven composite, which has a weaving angle of 20° between interlacing yarns, is about 40% higher than that of [0/90]₄ woven composite, which has a weaving angle of 90° between interlacing yarns. The higher energy absorption capability of [0/20]₄ over [0/90]₄ is attributed to a lower stiffness caused by a more polarized fiber orientation and a smaller fiber crimp, resulting in a larger maximum deflection, a more extended damage zone and a larger amount of fiber pullout.