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Journal of Applied Physics / Volume 104 / Issue 10 / LASERS, OPTICS, AND OPTOELECTRONICS
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J. Appl. Phys. 104, 103107 (2008); http://dx.doi.org/10.1063/1.3021310 (8 pages)

Simulation of the bulk and surface modes supported by a diamond lattice of metal wires

M. A. Shapiro1, K. R. Samokhvalova1, J. R. Sirigiri1, R. J. Temkin1, and G. Shvets2

1Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
2Department of Physics, University of Texas at Austin, Austin, Texas 78712, USA

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(Received 3 April 2008; accepted 4 October 2008; published online 18 November 2008)

We present a numerical study of the electromagnetic properties of the three-dimensional metallic wire lattices operating at microwave frequencies with applications to advanced accelerating structures and microwave sources. The metallic lattices can be considered as “artificial plasmas” because they demonstrate the properties of plasmas with a negative dielectric constant. Bulk modes in a diamond lattice of metal wires and surface modes on its interface are calculated. It is shown that the lattice can be modeled as an anisotropic medium with spatial dispersion. In contrast to a simple cubic lattice, the diamond lattice allows the existence of three different interfaces—one isotropic and two anisotropic. The surface modes supported by these interfaces are affected by spatial dispersion, in sharp contrast with the surface mode on an isotropic vacuum/plasma interface. For particle accelerator applications, we identify the electromagnetic mode confined by a plasmonic waveguide formed as a defect in a diamond lattice. All deleterious higher order modes excited as wakefields from the accelerating particle are found to be leaky. The diamond lattice is also useful as a research tool for studying particle radiation in media with spatial dispersion.

© 2008 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. BULK MODES
  3. SPATIAL DISPERSION
  4. SURFACE MODES
  5. SURFACE MODE ON THE INTERFACE OF A MEDIUM WITH SPATIAL DISPERSION
  6. PLASMONIC WAVEGUIDE
  7. DISCUSSION
  8. CONCLUSIONS

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KEYWORDS and PACS

Keywords

metals, microwave materials, optical waveguide theory, permittivity, photonic crystals, plasmonics, solid-state plasma

PACS

  • 42.70.Qs

    Photonic bandgap materials

  • 84.40.-x

    Radiowave and microwave (including millimeter wave) technology

  • 42.79.Gn

    Optical waveguides and couplers

  • 77.22.Ch

    Permittivity (dielectric function)

  • 73.20.Mf

    Collective excitations (including excitons, polarons, plasmons and other charge-density excitations)

  • 78.66.Bz

    Metals and metallic alloys

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.3021310

PUBLICATION DATA

ISSN

0021-8979 (print)  
1089-7550 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

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Figures (10) Tables (1)

Figures (click on thumbnails to view enlargements)

FIG.1
Cubic cell of diamond wire lattice [(a) and (b)]. (a) Anisotropic interface (100) is determined by the crystallographic direction [100]. The surface wave can propagate in the [01math] direction. (b) Isotropic interface (111) is determined by the [1math1] direction. The surface wave can propagate in the directions [111] and [11math]. (c) Anisotropic interface (011) is determined by the [01math] direction. The surface wave can propagate in the [100] direction.

FIG.1 Download High Resolution Image (.zip file) | Export Figure to PowerPoint

FIG.2
Simulation of bulk modes in the diamond wire lattice using the primitive cell. A longitudinal plasma mode at 6.25 GHz is shown for the lattice cubic cell length a = 2.3 cm and the wire radius r = 0.07 cm.

FIG.2 Download High Resolution Image (.zip file) | Export Figure to PowerPoint

FIG.3
Normalized plasma frequency of bulk modes as a function of the ratio of rod radius r to cubic cell length a (red solid line), analytical representation of Eq. ( 1 ) (dashed line), and normalized resonance frequency of the surface mode on the anisotropic (100) interface (blue line).

FIG.3 Download High Resolution Image (.zip file) | Export Figure to PowerPoint

FIG.4
Dispersion of longitudinal (plasmon) and transverse (photon) waves. One plasmon and two photons are calculated for each of the following directions: Γ-X (black), Γ-W (green), Γ-U (magenta), Γ-K (red), and Γ-L (blue). Dashed-dotted straight line is the light dispersion in vacuum.

FIG.4 Download High Resolution Image (.zip file) | Export Figure to PowerPoint

FIG.5
Comparison of wave dispersion in the lattice (solid lines) and the SD medium (dashed lines): Γ-X plasmon and photons (black), Γ-L plasmon (blue), and Γ-K plasmon (red).

FIG.5 Download High Resolution Image (.zip file) | Export Figure to PowerPoint

FIG.6
Stack of cells used for surface mode simulation on (a) the anisotropic (100) interface, (b) isotropic (111) interface, and (c) anisotropic (110) interface. The electric field distribution in the surface modes is shown.

FIG.6 Download High Resolution Image (.zip file) | Export Figure to PowerPoint

FIG.7
Dispersion of bulk waves and surface waves on the isotropic interface (111) and anisotropic interfaces (100) and (011) of the diamond metallic lattice. The cubic cell period is a = 2.3 cm and wire radius r = 0.07 cm. The dashed line depicts the light dispersion in vacuum. The frequency of the isotropic (111) interface mode tends to the plasma frequency, which disagrees with the “artificial plasma” model.

FIG.7 Download High Resolution Image (.zip file) | Export Figure to PowerPoint

FIG.8
Accelerator structure using a defect in 3D metallic diamond wire lattice. An electron beam traverses in the x-direction.

FIG.8 Download High Resolution Image (.zip file) | Export Figure to PowerPoint

FIG.9
Simulation of plasmonic waveguide. The defect mode is a longitudinal TM mode propagating in the x-direction. The electric field distribution is shown.

FIG.9 Download High Resolution Image (.zip file) | Export Figure to PowerPoint

FIG.10
Dispersion of plasmonic waveguide modes. The defect mode is an accelerating mode. Dashed line is the light dispersion in vacuum. The cubic cell length a = 2.3 cm and wire radius r = 0.07 cm.

FIG.10 Download High Resolution Image (.zip file) | Export Figure to PowerPoint

Tables

Table I. Phase advance range for Brillouin diagram simulation.

View Table


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