Evaluating zero error noise thresholds by replica method for Gallager code ensembles

The replica method, developed in statistical physics, is employed in conjunction with Gallager's methodology to accurately evaluate zero error noise thresholds for Gallager code ensembles. Our approach generally provides more optimistic evaluations than those reported in the information theory literature for sparse matrices; the difference vanishes as the parity check matrix becomes dense.

Structure of dysprosium and holmium phosphate glasses by the method of isomorphic substitution in neutron diffraction

The relative distribution of rare-earth ions R3+ (Dy3+ or Ho3+) in the phosphate glass RAl0.30P3.05O9.62 was measured by employing the method of isomorphic substitution in neutron diffraction and, by taking the role of Al into explicit account, a self-consistent model of the glass structure was developed. The glass network is found to be made from corner sharing PO4 tetrahedra in which there are, on average, 2.32(9) terminal oxygen atoms, OT, at 1.50(1) Å and 1.68(9) bridging oxygen atoms, OB, at 1.60(1) Å. The network modifying R3+ ions bind to an average of 6.7(1) OT and are distributed such that 7.9(7) R–R nearest neighbours reside at 5.62(6) Å. The Al3+ ion also has a network modifying role in which it helps to strengthen the glass through the formation of OT–Al–OT linkages. The connectivity of the R-centred coordination polyhedra in (M2O3)x(P2O5)1−x glasses, where M3+ denotes a network modifying cation (R3+ or Al3+), is quantified in terms of a parameter fs. Methods for reducing the clustering of rare-earth ions in these materials are then discussed, based on a reduction of fs via the replacement of R3+ by Al3+ at fixed total modifier content or via a change of x to increase the number of OT available per network modifying M3+ cation.

Structure of lanthanum and cerium phosphate glasses by the method of isomorphic substitution in neutron diffraction

Neutron diffraction was used to measure the total structure factors for several rare-earth ion R3+ (La3+ or Ce3+) phosphate glasses with composition close to RAl0.35P3.24O10.12. By assuming isomorphic structures, difference function methods were employed to separate, essentially, those correlations involving R3+ from the remainder. A self-consistent model of the glass structure was thereby developed in which the Al correlations were taken into explicit account. The glass network was found to be made from interlinked PO4 tetrahedra having 2.2(1) terminal oxygen atoms, OT, at 1.51(1) Angstrom, and 1.8(1) bridging oxygen atoms, OB, at 1.60(1) Angstrom. Rare-earth cations bonded to an average of 7.5(2) OT nearest neighbors in a broad and asymmetric distribution. The Al3+ ion acted as a network modifier and formed OT-A1-OT linkages that helped strengthen the glass. The connectivity of the R-centered coordination polyhedra was quantified in terms of a parameter f(s) and used to develop a model for the dependence on composition of the A1-OT coordination number in R-A1-P-O glasses. By using recent 17 A1 nuclear-magnetic-resonance data, it was shown that this connectivity decreases monotonically with increasing Al content. The chemical durability of the glasses appeared to be at a maximum when the connectivity of the R-centered coordination polyhedra was at a minimum. The relation of f(s) to the glass transition temperature, Tg, was discussed.

Direct femtosecond laser inscription in transparent dielectrics

Since 1996 direct femtosecond inscription in transparent dielectrics has become the subject of intensive research. This enabling technology significantly expands the technological boundaries for direct fabrication of 3D structures in a wide variety of materials. It allows modification of non-photosensitive materials, which opens the door to numerous practical applications. In this work we explored the direct femtosecond inscription of waveguides and demonstrated at least one order of magnitude enhancement in the most critical parameter - the induced contrast of the refractive index in a standard borosilicate optical glass. A record high induced refractive contrast of 2.5×10-2 is demonstrated. The waveguides fabricated possess one of the lowest losses, approaching level of Fresnel reflection losses at the glassair interface. High refractive index contrast allows the fabrication of curvilinear waveguides with low bend losses. We also demonstrated the optimisation of the inscription regimes in BK7 glass over a broad range of experimental parameters and observed a counter-intuitive increase of the induced refractive index contrast with increasing translation speed of a sample. Examples of inscription in a number of transparent dielectrics hosts using high repetition rate fs laser system (both glasses and crystals) are also presented. Sub-wavelength scale periodic inscription inside any material often demands supercritical propagation regimes, when pulse peak power is more than the critical power for selffocusing, sometimes several times higher than the critical power. For a sub-critical regime, when the pulse peak power is less than the critical power for self-focusing, we derive analytic expressions for Gaussian beam focusing in the presence of Kerr non-linearity as well as for a number of other beam shapes commonly used in experiments, including astigmatic and ring-shaped ones. In the part devoted to the fabrication of periodic structures, we report on recent development of our point-by-point method, demonstrating the shortest periodic perturbation created in the bulk of a pure fused silica sample, by using third harmonics (? =267 nm) of fundamental laser frequency (? =800 nm) and 1 kHz femtosecond laser system. To overcome the fundamental limitations of the point-by-point method we suggested and experimentally demonstrated the micro-holographic inscription method, which is based on using the combination of a diffractive optical element and standard micro-objectives. Sub-500 nm periodic structures with a much higher aspect ratio were demonstrated. From the applications point of view, we demonstrate examples of photonics devices by direct femtosecond fabrication method, including various vectorial bend-sensors fabricated in standard optical fibres, as well as a highly birefringent long-period gratings by direct modulation method. To address the intrinsic limitations of femtosecond inscription at very shallow depths we suggested the hybrid mask-less lithography method. The method is based on precision ablation of a thin metal layer deposited on the surface of the sample to create a mask. After that an ion-exchange process in the melt of Ag-containing salts allows quick and low-cost fabrication of shallow waveguides and other components of integrated optics. This approach covers the gap in direct fs inscription of shallow waveguide. Perspectives and future developments of direct femtosecond micro-fabrication are also discussed.

Inscription of in-fibre photonic devices by an infrared femtosecond laser

In this work, a point by point method for the inscription of fibre Bragg gratings using a tightly focused infrared femtosecond laser is implemented for the first time. Fibre Bragg gratings are wavelength-selective, retro-reflectors which have become a key component in optical communications as well as offering great potential as a sensing tool. Standard methods of fabrication are based on UV inscription in fibre with a photosensitive core. Despite the high quality of the gratings, a number of disadvantages are associated with UV inscription, in particular, the requirements of a photosensitive fibre, the low thermal stability and the need to remove the protective coating prior to inscription. By combining the great flexibility offered by the point by point method with the advantages inherent to inscription by an infrared femtosecond laser, the previous disadvantages are overcome. The method here introduced, allows a fast inscription process at a rate of ~1mm/s, gratings of lengths between 1cm and 2cm exhibiting reflections in excess of 99%. Physical dimensions of these gratings differ significantly from those inscribed by other methods, in this case the grating is confined to a fraction of the cross section of the core, leading to strong and controllable birefringence and polarisation dependent loss. Finally, an investigation of the potential for their exploitation towards novel applications is carried out, devices such as directional bend sensors inscribed in single-mode fibre, superimposed but non-overlapping gratings, and single-mode, single-polarisation fibre lasers, were designed, fabricated and characterised based on point by point femtosecond inscription.

Line-by-line fiber Bragg grating made by femtosecond laser

In this letter, we report on the inscription of a fourth-order fiber Bragg grating made line-by-line in the optical fiber using a femtosecond laser. Strong Bragg resonance (~17 dB) and low insertion loss (~0.5 dB) were obtained with only 2000 periods. Measured refractive index change of these inscribed lines reaches up to 7 × 10-3. The grating was fully characterized and the low insertion loss together with low polarization-dependent loss were realized compared to gratings made by the point-by-point method. The high temperature annealing experiment shows the grating can survive up to at least 800°C.

Microstructured waveguides in z-cut LiNbO3 by high-repetition rate direct femtosecond laser inscription

We report on the operational parameters that are required to fabricate buried, microstructured waveguides in a z-cut lithium niobate crystal by the method of direct femtosecond laser inscription using a highrepetition-rate, chirped-pulse oscillator system. Refractive index contrasts as high as −0.0127 have been achieved for individual modification tracks. The results pave the way for developing microstructured WGs with low-loss operation across a wide spectral range, extending into the mid-infrared region up to the end of the transparency range of the host material.

Control of the properties of micro-structured waveguides in LiNbO3 fabricated by direct femtosecond laser inscription

This paper reports on buried waveguides fabricated in lithium niobate (LN) by the method of direct femtosecond (fs) laser inscription. 5% MgO doped LiNbO3 was chosen as the host material because of its high quality and damage threshold, as well as relatively low cost. Direct fs inscription by astigmatically shaped beam in crystals usually produces multiple 'smooth' tracks (with reduced refractive index), which encircle the light guiding 'core', thus creating a depressed cladding WG. A high-repetition rate fs laser system was used for inscription at a depth of approximately 500 μm. Using numerical modelling, it was demonstrated that the properties of fs-written WGs can be controlled by the WG geometry. Buried, depressed-cladding WGs in LN host with circular cross-section were also demonstrated. Combining control over the WG dispersion with quasi-phase matching will allow various ultralow-pump-power, highly-efficient, nonlinear light-guiding devices - all in an integrated optics format.

Evolution of lace knitting stitch patterns by genetic programming

In this paper we study the generation of lace knitting stitch patterns by using genetic programming. We devise a genetic representation of knitting charts that accurately reflects their usage for hand knitting the pattern. We apply a basic evolutionary algorithm for generating the patterns, where the key of success is evaluation. We propose automatic evaluation of the patterns, without interaction with the user. We present some patterns generated by the method and then discuss further possibilities for bringing automatic evaluation closer to human evaluation. Copyright 2007 ACM.

Pulse width modulation (PWM) method for power components estimation in power meters

The scope of this paper is to present the Pulse Width Modulation (PWM) based method for Active Power (AP) and Reactive Power (RP) measurements as can be applied in Power Meters. Necessarily, the main aim of the material presented is a twofold, first to present a realization methodology of the proposed algorithm, and second to verify the algorithm’s robustness and validity. The method takes advantage of the fact that frequencies present in a power line are of a specific fundamental frequency range (a range centred on the 50 Hz or 60 Hz) and that in case of the presence of harmonics the frequencies of those dominating in the power line spectrum can be specified on the basis of the fundamental. In contrast to a number of existing methods a time delay or shifting of the input signal is not required by the method presented and the time delay by n/2 of the Current signal with respect to the Voltage signal required by many of the existing measurement techniques, does not apply in the case of the PWM method as well.