3D laser nano-printing on fibre paves the way for super-focusing of multimode laser radiation

Multimode high-power laser diodes suffer from inefficient beam focusing, leading to a focal spot 10–100 times greater than the diffraction limit. This inevitably restricts their wider use in ‘direct-diode’ applications in materials processing and biomedical photonics. We report here a ‘super-focusing’ characteristic for laser diodes, where the exploitation of self-interference of modes enables a significant reduction of the focal spot size. This is achieved by employing a conical microlens fabricated on the tip of a multimode optical fibre using 3D laser nano-printing (also known as multi-photon lithography). When refracted by the conical surface, the modes of the fibre-coupled laser beam self-interfere and form an elongated narrow focus, usually referred to as a ‘needle’ beam. The multiphoton lithography technique allows the realisation of almost any optical element on a fibre tip, thus providing the most suitable interface for free-space applications of multimode fibre-delivered laser beams. In addition, we demonstrate the optical trapping of microscopic objects with a super-focused multimode laser diode beam thus rising new opportunities within the applications sector where lab-on-chip configurations can be exploited. Most importantly, the demonstrated super-focusing approach opens up new avenues for the ‘direct-diode’ applications in material processing and 3D printing, where both high power and tight focusing is required

Microarray analysis and scale-free gene networks identify candidate regulators in drought-stressed roots of loblolly pine (P. taeda L.)

<p>Abstract</p> <p>Background</p> <p>Global transcriptional analysis of loblolly pine (<it>Pinus taeda </it>L.) is challenging due to limited molecular tools. PtGen2, a 26,496 feature cDNA microarray, was fabricated and used to assess drought-induced gene expression in loblolly pine propagule roots. Statistical analysis of differential expression and weighted gene correlation network analysis were used to identify drought-responsive genes and further characterize the molecular basis of drought tolerance in loblolly pine.</p> <p>Results</p> <p>Microarrays were used to interrogate root cDNA populations obtained from 12 genotype × treatment combinations (four genotypes, three watering regimes). Comparison of drought-stressed roots with roots from the control treatment identified 2445 genes displaying at least a 1.5-fold expression difference (false discovery rate = 0.01). Genes commonly associated with drought response in pine and other plant species, as well as a number of abiotic and biotic stress-related genes, were up-regulated in drought-stressed roots. Only 76 genes were identified as differentially expressed in drought-recovered roots, indicating that the transcript population can return to the pre-drought state within 48 hours. Gene correlation analysis predicts a scale-free network topology and identifies eleven co-expression modules that ranged in size from 34 to 938 members. Network topological parameters identified a number of central nodes (hubs) including those with significant homology (E-values ≤ 2 × 10^-30) to 9-cis-epoxycarotenoid dioxygenase, zeatin O-glucosyltransferase, and ABA-responsive protein. Identified hubs also include genes that have been associated previously with osmotic stress, phytohormones, enzymes that detoxify reactive oxygen species, and several genes of unknown function.</p> <p>Conclusion</p> <p>PtGen2 was used to evaluate transcriptome responses in loblolly pine and was leveraged to identify 2445 differentially expressed genes responding to severe drought stress in roots. Many of the genes identified are known to be up-regulated in response to osmotic stress in pine and other plant species and encode proteins involved in both signal transduction and stress tolerance. Gene expression levels returned to control values within a 48-hour recovery period in all but 76 transcripts. Correlation network analysis indicates a scale-free network topology for the pine root transcriptome and identifies central nodes that may serve as drivers of drought-responsive transcriptome dynamics in the roots of loblolly pine.</p

Decomposed Implicit Models of Piecewise - Linear Networks

The general matrix form of the implicit description of a piecewise-linear (PWL) network and the symbolic block diagram of the corresponding circuit model are proposed. Their decomposed forms enable us to determine quite separately the existence of the individual breakpoints of the resultant PWL characteristic and their coordinates using independent network parameters. For the two-diode and three-diode cases all the attainable types of the PWL characteristic are introduced

Generalized Canonical State Models of Third-Order Piecewise-Linear Dynamical Systems And Their Applications

The elementary canonical state models of the third-order autonomous dynamical systems, topologically conjugate to Chua's circuit family, are generalized for any continuous and odd symmetrical piecewise-linear (PWL) feedback function. Their state equations are in accordance with the basic form of the Lur'e systems and the corresponding circuit model contains the multiple PWL feedback. The general results are applied for the simplest three-region case defined by three sets of the equivalent eigenvalue parameters. The application of these results is demonstrated on the double-scroll chaotic attractor with global attracting properties. As an example its utilization in synchronized chaos is shown

Simple Model of Synchronized System for the Chaotic-Masked Communication

In this paper the simplest form of the compound dynamical system is considered, i.e. the second-order subsystem homogeneously synchronized by the third-order autonomous subsystem where the synchronized block is identical to a part of the synchronizing block. Simplified design formulas are defined for the case of a stable synchronized subsystem and arbitrarily chosen dynamical behaviour of the whole system including any type of chaos. The resultant state equations and the corresponding integrator-based circuit models are shown. Their utilization in chaotic-masked signal communications is suggested

Simple Model of Synchronized System for the Chaotic-Masked Communication

In this paper the simplest form of the compound dynamical system is considered, i.e. the second-order subsystem homogeneously synchronized by the third-order autonomous subsystem where the synchronized block is identical to a part of the synchronizing block. Simplified design formulas are defined for the case of a stable synchronized subsystem and arbitrarily chosen dynamical behaviour of the whole system including any type of chaos. The resultant state equations and the corresponding integrator-based circuit models are shown. Their utilization in chaotic-masked signal communications is suggested

New Reference State Model of the Third-Order PWL Dynamical Systems

Starting from the first elementary canonical state model, the newsimple state model of the third-order dynamical systems that belong toClass C is derived. A typical property of this new model is a verysimple form of its partial transformation matrix in the conditions oflinear topological conjugacy, which represents the unity matrix.Complete state equations and the corresponding integrator-based blockdiagram of this model are shown and relation to the first canonicalform is graphically illustrated

New Canonical State Models of Chua's Circuit Family

Two new modified types of canonical state models simulating chaotic phenomena in piecewise-linear dynamical systems are derived. Both are topologically conjugate to Class C similarly as Chua's circuit family. Their state matrix equations and corresponding integrator-based circuit models are proposed including their relations with the first elementary canonical state model. As an example the phase portraits of typical chaotic attractor are shown

Optimized Second-Order Dynamical Systems and Their RLC Circuit Models with PWL Controlled Sources

Complementary active RLC circuit models with a voltage-controlledvoltage source (VCVS) and a current-controlled current source (CCCS)for the second-order autonomous dynamical system realization areproposed. The main advantage of these equivalent circuits is the simplerelation between the state model parameters and their correspondingcircuit parameters, which leads also to simple design formulas