Perturbation theory permits the analytic study of small changes on known solutions, and is especially useful in electromagnetism for understanding weak interactions and imperfections. Standard perturbation-theory techniques, however, have difficulties when applied to Maxwell's equations for small shifts in dielectric interfaces (especially in high-index-contrast, three-dimensional systems) due to the discontinuous field boundary conditions--in fact, the usual methods fail even to predict the lowest-order behavior. By considering a sharp boundary as a limit of anisotropically smoothed systems, we are able to derive a correct first-order perturbation theory and mode-coupling constants, involving only surface integrals of the unperturbed fields over the perturbed interface. In addition, we discuss further considerations that arise for higher-order perturbative methods in electromagnetism.

Increasing customer demand for durable and functional apparel manufactured in a sustainable manner has created an opportunity for nanomaterials to be integrated into textile substrates. Nanomoieties can induce stain repellence, wrinkle-freeness, static elimination, and electrical conductivity to fibers without compromising their comfort and flexibility. Nanomaterials also offer a wider application potential to create connected garments that can sense and respond to external stimuli via electrical, color, or physiological signals. This review discusses electronic and photonic nanotechnologies that are integrated with textiles and shows their applications in displays, sensing, and drug release within the context of performance, durability, and connectivity. Risk factors including nanotoxicity, nanomaterial release during washing, and environmental impact of nanotextiles based on life cycle assessments have been evaluated. This review also provides an analysis of nanotechnology consolidation in the textiles market to evaluate global trends and patent coverage, supplemented by case studies of commercial products. Perceived limitations of nanotechnology in the textile industry and future directions are identified.

We prove that an adiabatic theorem generally holds for slow tapers in photonic crystals and other strongly grated waveguides with arbitrary index modulation, exactly as in conventional waveguides. This provides a guaranteed pathway to efficient and broad-bandwidth couplers with, e.g., uniform waveguides. We show that adiabatic transmission can only occur, however, if the operating mode is propagating (nonevanescent) and guided at every point in the taper. Moreover, we demonstrate how straightforward taper designs in photonic crystals can violate these conditions, but that adiabaticity is restored by simple design principles involving only the independent band structures of the intermediate gratings. For these and other analyses, we develop a generalization of the standard coupled-mode theory to handle arbitrary nonuniform gratings via an instantaneous Bloch-mode basis, yielding a continuous set of differential equations for the basis coefficients. We show how one can thereby compute semianalytical reflection and transmission through crystal tapers of almost any length, using only a single pair of modes in the unit cells of uniform gratings. Unlike other numerical methods, our technique becomes more accurate as the taper becomes more gradual, with no significant increase in the computation time or memory. We also include numerical examples comparing to a well-established scattering-matrix method in two dimensions.

We present the light-propagation characteristics of OmniGuide fibers, which guide light by concentric multi-layer dielectric mirrors having the property of omnidirectional reflection. We show how the lowest-loss TE_01 mode can propagate in a single-mode fashion through even large-core fibers, with other modes eliminated asymptotically by their higher losses and poor coupling, analogous to hollow metallic microwave waveguides. Dispersion, radiation leakage, material absorption, nonlinearities, bending, acircularity, and interface roughness are considered with the help of leaky modes and perturbation theory, and both numerical results and general scaling relations are presented. We show that cladding properties such as absorption and nonlinearity are suppressed by many orders of magnitude due to the strong confinement in a hollow core, and other imperfections are tolerable, promising that the properties of silica fibers may be surpassed even when nominally poor materials are employed.

The concept of a Microstructured Optical Fiber-based Surface Plasmon Resonance sensor with optimized microfluidics is proposed. In such a sensor plasmons on the inner surface of large metallized channels containing analyte can be excited by a fundamental mode of a single mode microstructured fiber. Phase matching between plasmon and a core mode can be enforced by introducing air filled microstructure into the fiber core, thus allowing tuning of the modal refractive index and its matching with that of a plasmon. Integration of large size microfluidic channels for efficient analyte flow together with a single mode waveguide of designable effective refractive index is attractive for the development of integrated highly sensitive MOF-SPR sensors operating at any designable wavelength.