Regular Averaging and Regular Extension Operators in Weakly Compact Subsets of Hilbert Spaces

2000 Mathematics Subject Classification: Primary 46E15, 54C55; Secondary 28B20.For weakly compact subsets of Hilbert spaces K, we study the existence of totally disconnected spaces L, such that C(K) is isomorphic to C(L). We prove that the space C(BH ) admits a Pełczyński decomposition and we provide a starshaped weakly compact K, subset of BH with non-empty interior in the norm topology, and such that C(K) ~= C(L) with L totally disconnected.Research partially supported by EPEAEK program “Pythagoras”

Hybrid Optical Fibers – An Innovative Platform for In‐Fiber Photonic Devices

The field of hybrid optical fibers is one of the most active research areas in current fiber optics and has the vision of integrating sophisticated materials inside fibers, which are not traditionally used in fiber optics. Novel in-fiber devices with unique properties have been developed, opening up new directions for fiber optics in fields of critical interest in modern research, such as biophotonics, environmental science, optoelectronics, metamaterials, remote sensing, medicine, or quantum optics. Here the recent progress in the field of hybrid optical fibers is reviewed from an application perspective, focusing on fiber-integrated devices enabled by including novel materials inside polymer and glass fibers. The topics discussed range from nanowire-based plasmonics and hyperlenses, to integrated semiconductor devices such as optoelectronic detectors, and intense light generation unlocked by highly nonlinear hybrid waveguides

Saturated extensions, the attractors method and Hereditarily James Tree Space

In the present work we provide a variety of examples of HI Banach spaces containing no reflexive subspace and we study the structure of their duals as well as the spaces of their linear bounded operators. Our approach is based on saturated extensions of ground sets and the method of attractors

Multiplexed FBG sensor recorded in multimode microstructured polymer optical fibre

Fibre Bragg gratings have been inscribed in multimode microstructured polymer optical fibre (POF), with a core size of 50μm. The microstructured POF (mPOF) consists of a three ring hole structure and is made purely from poly(methyl methacrylate) (PMMA). In comparison to silica fibre, POF has a much smaller Young's modulus and a much greater breaking strain; additionally multimode fibre holds advantages of ease of handling and launching conditions. A linear strain sensitivity of 1.32 ± 0.01pm/με has been measured in the range 0 to 2% strain. The fibre drawing process leads to a degree of molecular alignment along the fibre axis. This alignment can be thermally annealed out; this can induce a permanent blue shift in the Bragg wavelength of a grating fabricated prior to annealing by up to 20 nm. Utilising this, wavelength demultiplexed gratings can be fabricated using a single phase mask. As an illustration of this we present for the first time wavelength division multiplexing of the spectral response of three Bragg gratings in POF within the C-band region. Complementing this work, a technique of splicing mPOF to step index silica fibre is described using UV curing optical adhesive, allowing characterisation of Bragg gratings fabricated in this fibre

Tunable metamaterials fabricated by fiber drawing

We demonstrate a practical scalable approach to the fabrication of tunable metamaterials. Designed for THz wavelengths, the metamaterial is comprised of polyurethane filled with an array of indium wires using the well-established fiber drawing technique. Modification of the dimensions of the metamaterial provides tunability: by compressing the metamaterial we demonstrated a 50% plasma frequency shift using THz time domain spectroscopy. Releasing the compression allowed the metamaterial to return to its original dimensions and plasma frequency, demonstrating dynamic reversible tunability

Thermal response of Bragg gratings in PMMA microstructured optical fibers

We report on the thermal characteristics or Bragg gratings fabricated in polymer optical fibers. We have observed a permanent shift in the grating wavelength at room temperature which occurs when the grating has been heated above a threshold temperature. This threshold temperature is dependent on the thermal history of the grating, and we attribute the effect to a shrinking of the fiber. This effect can be avoided by annealing the fiber before grating inscription, resulting in a linear response with temperature and an increased linear operating temperature range of the grating. © 2007 Optical Society of America