Spoof surface plasmon

SPP oscillation in between a metal-dielectric interface

Surface plasmon polaritons (SPP) result from the coupling of delocalized electron oscillations ("surface plasmon") to electromagnetic waves ("polariton"). SPPs propagate along the interface between a positive- and a negative-permittivity material. These waves decay perpendicularly from the interface ("evanescent field"). For a plasmonic medium that is stratified along the z-direction in Cartesian coordinates, dispersion relation for SPPs can be obtained from solving Maxwell's equations:[3]

${\displaystyle k_{x}={\frac {\omega }{c}}\left({\frac {\varepsilon _{1}\varepsilon _{2}}{\varepsilon _{1}+\varepsilon _{2}}}\right)^{\frac {1}{2}}}$

where

• ${\displaystyle k_{x}}$ is the wave vector that is parallel to the interface. It is in the direction of propagation.
• ${\displaystyle \omega }$ is the angular frequency.
• ${\displaystyle c}$ is the speed of light.
• ${\displaystyle \varepsilon _{1}}$ and ${\displaystyle \varepsilon _{2}}$ are the relative permittivies for metal and the dielectric.

Per this relation, SPPs have shorter wavelengths than light in free space for a frequency band below surface plasmon frequency; this property, as well as subwavelength confinement, enables new applications in subwavelength optics and systems beyond the diffraction-limit.[3] Nevertheless, for lower frequency bands such as microwave and terahertz, surface plasmon polariton modes are not supported; metals function approximately as perfect electrical conductors with imaginary dielectric functions in this regime.[4] Per the effective medium approach, metal surfaces with subwavelength structural elements can mimic the plasma behaviour, resulting in artificial surface plasmon polariton excitations with similar dispersion behaviour.[4][5][6]

For the canonical case of a metamaterial medium that is formed by thin metallic wires on a periodic square lattice, the effective relative permittivity can be represented by the Drude model formula:[4]

${\displaystyle \varepsilon _{eff}=1-{\frac {\omega _{p}^{2}}{\omega \left(\omega +i{\frac {\varepsilon _{0}a^{2}\omega _{p}^{2}}{\pi r^{2}\sigma }}\right)}}}$

${\displaystyle \omega _{p}^{2}={\frac {2\pi c^{2}}{a^{2}ln(a/r)}}}$

where

• ${\displaystyle \omega _{p}}$ is the effective plasma frequency of the medium.
• ${\displaystyle \varepsilon _{0}}$ is the vacuum permittivity.
• ${\displaystyle a}$ is the lattice period.
• ${\displaystyle r}$ is the radius of the constitutive wires.
• ${\displaystyle \sigma }$ is the electrical conductivity of the metal.

The use of subwavelength structures to induce low-frequency plasmonic excitations was first theorized by John Pendry et al. in 1996; Pendry proposed that a periodic lattice of thin metallic wires with a radius of 1 μm could be used to support surface-bound modes, with a plasma cut-off frequency of 8.2 GHz.[4] In 2004, Pendry et al. extended the approach to metal surfaces that are perforated by holes, terming the artificial SPP excitations as "spoof surface plasmons."[5][6]

In 2006, terahertz pulse propagation in planar metallic structures with holes were shown via FDTD simulations.[8] Martin-Cano et al. has realized the spatial and temporal modulation of guided terahertz modes via metallic parallelepiped structures, which they termed as "domino plasmons."[9] Designer spoof plasmonic structures were also tailored to improve the performance of terahertz quantum cascade lasers in 2010.[10]

Spoof surface plasmons were proposed as a possible solution for decreasing the crosstalk in microwave integrated circuits, transmission lines and waveguides.[2] In 2013, Ma et al. demonstrated a matched conversion from coplanar waveguide with a characteristic impedance of 50Ω to a spoof-plasmonic structure.[11] In 2014, integration of commercial low-noise amplifier with spoof plasmonic structures was realized; the system reportedly worked from 6 to 20 GHz with a gain around 20 dB.[12] Kianinejad et al. also reported the design of a slow-wave spoof-plasmonic transmission line; conversion from quasi-TEM microstrip modes to TM spoof plasmon modes were also demonstrated.[13]

Khanikaev et al. reported nonreciprocal spoof surface plasmon modes in structured conductor embedded in an asymmetric magneto-optical medium, which results in one-way transmission.[14] Pan et al. observed the rejection of certain spoof plasmon modes with an introduction of electrically resonant metamaterial particles to the spoof plasmonic strip.[15] Localized spoof surface plasmons were also demonstrated for metallic disks in microwave frequencies.[16][17]

• Photonic crystal
• Plasmonic metamaterial
• Split-ring resonator
• Superlens
• Terahertz metamaterial

• Huidobro, Paloma Arroyo; Fernández-Domínguez, Antonio I.; Pendry, John B.; Martín-Moreno, Luis; Garcia-Vidal, Francisco J. (January 2018). Spoof Surface Plasmon Metamaterials. Cambridge University Press. doi:10.1017/9781108553445. ISBN 9781108553445. S2CID 139524223.