Incremental dynamic mode decomposition: A reduced-model learner operating at the low-data limit

The present work aims at proposing a new methodology for learning reduced models from a small amount of data. It is based on the fact that discrete models, or their transfer function counterparts, have a low rank and then they can be expressed very efficiently using few terms of a tensor decomposition. An efficient procedure is proposed as well as a way for extending it to nonlinear settings while keeping limited the impact of data noise. The proposed methodology is then validated by considering a nonlinear elastic problem and constructing the model relating tractions and displacements at the observation points.     

Scattering coefficients for a sphere in a visco-acoustic medium for arbitrary partial wave order

Analytical solutions are reported for the scattering coefficients of a solid elastic sphere suspended in a viscous fluid for arbitrary partial wave order. Expressions are derived for incident compressional and shear wave modes, taking into account the viscosity of the surrounding fluid and resultant wave mode conversion. The long compressional wavelength limit is employed to simplify the derivation, whereas no restriction is placed on the shear wavelength in the fluid compared to the particle dimension. The analytical approximations are compared with numerical results obtained from matrix inversion of the boundary equations and agree within the validity domain of the solutions.     

Curvature investigation in tapered fibers and its application to sensing and mode conversion

Non-adiabatic tapered fibers are basic photonic components used in a wide range of applications. Here we investigate a way to increase their utility through the controllable bending of one of their tapered sections. The experiments carried out explain, for the first time, the mechanics of this approach showing how these tapers can be used to build more sensitive sensors. Their use as highly efficient mode converters is also discussed.     

Disentangling stochastic signals superposed on short localized oscillations

We introduce a procedure for separating periodic oscillations superposed on a stochastic signal. The procedure combines empirical mode decomposition (EMD) of a signal with tools of data analysis based on stochastic differential equations, namely nonlinear Langevin equations. Taking the set of modes retrieved from the EMD of the signal, our procedure is able to separate them into two groups, one composing the periodic signal and another composing the stochastic signal. The framework is robust for a broad family of localized oscillations, in the range of large frequencies. In particular, we show that, in this context, the EMD method outperforms a low-pass filter and is robust for a wide interval of different frequency ranges and amplitudes of the periodic oscillation, as well as for a broad family of different non-linear Langevin processes.     

Diffraction mode selection in planar Bragg resonators of optical and microwave wavelength ranges

Using the coupled waves approach complemented by the time-domain quasi-optical approximation, we solve a 2D diffraction problem which allows to evaluate the eigenfrequencies, quality factors and spatial structures of eigenmodes in planar Bragg resonators with a finite length and width of the corrugated area. We find the values of the Fresnel parameter determined by the geometrical dimensions of the system which allows for efficient transverse mode discrimination due to the larger diffraction losses of the modes with higher transverse numbers.     

Broadband mode converter and multiplexer based on dielectric-loaded plasmonic waveguides

We theoretically demonstrate a broadband mode converter and multiplexer based on plasmonic waveguides loaded with structured dielectrics. The proposed device can realize conversions between a fundamental TM₀ mode and a first order TM₁ mode, as well as (de)multiplex them with another TM₀ mode. Our design exhibits as wide as 400 nm bandwidth and as short as 6~7 μm coupling length. This work has potential application in high density photonic integrated devices for both computing and communication applications.     

Stereospecific Oxycyanation of Alkenes with Sulfonyl Cyanide

Oxycyanation of alkenes would allow the direct construction of useful β-hydroxy nitrile scaffolds. However, only limited examples of such reactions have been reported, and some problems including limited substrate scope and the lack of diastereocontrol in the case of the oxycyanation of internal alkenes have arisen. We herein report on the intermolecular oxycyanation of alkenes using p-toluenesulfonyl cyanide (TsCN) in the presence of tris(pentafluorophenyl)borane (B(C₆F₅)₃) as a catalyst, affording products that contain a sulfinyloxy group and a cyano group at the vicinal position. The reaction features a stereospecific syn-addition. The reaction also shows a broad substrate scope with good functional group tolerance. Mechanistic investigations by experimental studies and density functional theory (DFT) calculations revealed that the reaction proceeds via an unprecedented stereospecific mechanism through the electrophilic cyanation of alkenes, in which B(C₆F₅)₃ efficiently activates TsCN through the coordination of the cyano group to the boron center.