Complex-k modes of plasmonic chain waveguides

Nanoparticle chain waveguide based on negative-epsilon material is investigated through a generic 3D finite-element Bloch-mode solver which derives complex propagation constant ($k$). Our study starts from waveguides made of non-dispersive material, which not only singles out "waveguide dispersion" but also motivates search of new materials to achieve guidance at unconventional wavelengths. Performances of gold or silver chain waveguides are then evaluated; a concise comparison of these two types of chain waveguides has been previously missing. Beyond these singly-plasmonic chain waveguides, we examine a hetero-plasmonic chain system with interlacing gold and silver particles, inspired by a recent proposal; the claimed enhanced energy transfer between gold particles appears to be a one-sided view of its hybridized waveguiding behavior --- energy transfer between silver particles worsens. Enabled by the versatile numerical method, we also discuss effects of inter-particle spacing, background medium, and presence of a substrate. Our extensive analyses show that the general route for reducing propagation loss of e.g. a gold chain waveguide is to lower chain-mode frequency with a proper geometry (e.g. smaller particle spacing) and background material setting (e.g. high-permittivity background or even foreign nanoparticles). In addition, the possibility of building mid-infrared chain waveguides using doped silicon is commented based on numerical simulation.Comment: 26 pages, many figures, now including "Supplementary Data". Accepted, Journal of Physics Communicatio

Combined large-N_c and heavy-quark operator analysis for the chiral Lagrangian with charmed baryons

The chiral $SU(3)$ Lagrangian with charmed baryons of spin $J^P=1/2^+$ and $J^P=3/2^+$ is analyzed. We consider all counter terms that are relevant at next-to-next-to-next-to-leading order (N$^3$LO) in a chiral extrapolation of the charmed baryon masses. At N$^2$LO we find 16 low-energy parameters. There are 3 mass parameters for the anti-triplet and the two sextet baryons, 6 parameters describing the meson-baryon vertices and 7 symmetry breaking parameters. The heavy-quark spin symmetry predicts four sum rules for the meson-baryon vertices and degenerate masses for the two baryon sextet fields. Here a large-$N_c$ operator analysis at NLO suggests the relevance of one further spin-symmetry breaking parameter. Going from N$^2$LO to N$^3$LO adds 17 chiral symmetry breaking parameters and 24 symmetry preserving parameters. For the leading symmetry conserving two-body counter terms involving two baryon fields and two Goldstone boson fields we find 36 terms. While the heavy-quark spin symmetry leads to $36-16=20$ sum rules, an expansion in $1/N_c$ at next-to-leading order (NLO) generates $36-7= 29$ parameter relations. A combined expansion leaves 3 unknown parameters only. For the symmetry breaking counter terms we find 17 terms, for which there are $17-9=8$ sum rules from the heavy-quark spin symmetry and $17-5=12$ sum rules from a $1/N_c$ expansion at NLO.Comment: 34 pages - one table - corrections applie

Counting permutations by alternating descents

We find the exponential generating function for permutations with all valleys even and all peaks odd, and use it to determine the asymptotics for its coefficients, answering a question posed by Liviu Nicolaescu. The generating function can be expressed as the reciprocal of a sum involving Euler numbers. We give two proofs of the formula. The first uses a system of differential equations. The second proof derives the generating function directly from general permutation enumeration techniques, using noncommutative symmetric functions. The generating function is an "alternating" analogue of David and Barton's generating function for permutations with no increasing runs of length 3 or more. Our general results give further alternating analogues of permutation enumeration formulas, including results of Chebikin and Remmel