Slender-body theory for plasmonic resonance

We develop a slender-body theory for plasmonic resonance of slender metallic nanoparticles, focusing on a general class of axisymmetric geometries with locally paraboloidal tips. We adopt a modal approach where one first solves the plasmonic eigenvalue problem, a geometric spectral problem which governs the surface-plasmon modes of the particle; then, the latter modes are used, in conjunction with spectral-decomposition, to analyse localized-surface-plasmon resonance in the quasi-static limit. We show that the permittivity eigenvalues of the axisymmetric modes are strongly singular in the slenderness parameter, implying widely tunable, high-quality-factor, resonances in the near-infrared regime. For that family of modes, we use matched asymptotics to derive an effective eigenvalue problem, a singular non-local Sturm–Liouville problem, where the lumped one-dimensional eigenfunctions represent axial voltage profiles (or charge line densities). We solve the effective eigenvalue problem in closed form for a prolate spheroid and numerically, by expanding the eigenfunctions in Legendre polynomials, for arbitrarily shaped particles. We apply the theory to plane-wave illumination in order to elucidate the excitation of multiple resonances in the case of non-spheroidal particles

Plasmonic resonances of slender nanometallic rings

We develop an approximate quasistatic theory describing the low-frequency plasmonic resonances of slender nanometallic rings and configurations thereof. First, we use asymptotic arguments to reduce the plasmonic eigenvalue problem governing the geometric (material- and frequency-independent) modes of a given ring structure to a one-dimensional periodic integrodifferential problem in which the eigenfunctions are represented by azimuthal voltage and polarization-charge profiles associated with each ring. Second, we obtain closed-form solutions to the reduced eigenvalue problem for azimuthally invariant rings (including torus-shaped rings but also allowing for noncircular cross-sectional shapes), as well as coaxial dimers and chains of such rings. For more general geometries, involving azimuthally nonuniform rings and noncoaxial structures, we solve the reduced eigenvalue problem using a semianalytical scheme based on Fourier expansions of the reduced eigenfunctions. Third, we used the asymptotically approximated modes, in conjunction with the quasistatic spectral theory of plasmonic resonance, to study and interpret the frequency response of a wide range of nanometallic slender-ring structures under plane-wave illumination

Constraint preserving boundary conditions for the Z4c formulation of general relativity

We discuss high order absorbing constraint preserving boundary conditions for the Z4c formulation of general relativity coupled to the moving puncture family of gauges. We are primarily concerned with the constraint preservation and absorption properties of these conditions. In the frozen coefficient approximation, with an appropriate first order pseudo-differential reduction, we show that the constraint subsystem is boundary stable on a four dimensional compact manifold. We analyze the remainder of the initial boundary value problem for a spherical reduction of the Z4c formulation with a particular choice of the puncture gauge. Numerical evidence for the efficacy of the conditions is presented in spherical symmetry.Comment: 18 pages, 8 figure

Scenario analysis for derivatives portfolios via dynamic factor models

A classic approach to financial risk management is the use of scenario analysis to stress test portfolios. In the case of an S&P 500 options portfolio, for example, a scenario analysis might report a P&L of −1m in the event the S&P 500 falls 5% and its implied volatility surface increases by 3 percentage points. But how accurate is this reported value of −1m? Such a number is typically computed under the (implicit) assumption that all other risk factors are set to zero. But this assumption is generally not justified as it ignores the often substantial statistical dependence among the risk factors. In particular, the expected values of the non-stressed factors conditional on the values of the stressed factors are generally non-zero. Moreover, even if the non-stressed factors were set to their conditional expected values rather than zero, the reported P&L might still be inaccurate due to convexity effects, particularly in the case of derivatives portfolios. A further weakness of this standard approach to scenario analysis is that the reported P&L numbers are generally not back-tested so their accuracy is not subjected to any statistical tests. There are many reasons for this but perhaps the main one is that scenario analysis for derivatives portfolios is typically conducted without having a probabilistic model for the underlying dynamics of the risk factors under the physical measure P. In this paper we address these weaknesses by embedding the scenario analysis within a dynamic factor model for the underlying risk factors. Such an approach typically requires multivariate state-space models that can model the real-world behavior of financial markets where risk factors are often latent, and that are sufficiently tractable so that we can compute (or simulate from) the conditional distribution of unstressed risk factors. We demonstrate how this can be done for observable as well as latent risk factors in examples drawn from options and fixed income markets. We show how the two forms of scenario analysis can lead to dramatically different results particularly in the case of portfolios that have been designed to be neutral to a subset of the risk factors

High-performance 16-way Ku-band radial power combiner based on the TE01-circular waveguide mode

This work presents a 16-way Ku-band radial power combiner for high power and high frequency applications, using the very low loss TE01 circular waveguide mode. The accomplished design shows an excellent performance: the experimental prototype has a return loss better than 30 dB, with a balance for the amplitudes of ( 0.15 dB) and ( 2.5 ) for the phases, in a 16.7% fractional bandwidth (2 GHz centered at 12 GHz). For obtaining these outstanding specifications, required, for instance, in highfrequency amplification or on plasma systems, a rigorous step-by-step procedure is presented. First, a high-purity mode transducer has been designed, from the TE10 mode in the rectangular waveguide to the TE01 mode in the circularwaveguide, with very high attenuation (>50 dB) for the other propagating and evanescent modes in the circularwaveguide. This transducer has been manufactured and measured in a back-to-back configuration, validating the design process. Second, an E-plane 16-way radial power divider has been designed, where the power is coupled from the 16 non-reduced-height radial standardwaveguides into the TE01 circularwaveguide mode, improving the insertion loss response and removing the usual tapered transformers of previous designs limiting the power handling. Finally, both the transducer and the divider have been assembled to make the final radial combiner. The prototype has been carefully manufactured, showing very good agreement between the measurements and the full-wave simulationsThe authors would like to thank INMEPRE S.A., the diligence in the manufacturing process. This work was supported by the Spanish government under Grant (ADDMATE) No. TEC2016-76070-C3-1/2-R (AEI/FEDER/UE) and the program of Comunidad de Madrid S2013/ICE-3000 (SPADERADARCM