Propagation Length and Skin Depth
| Condensed matter physics |
|---|
| Phases · Phase transition |
| States of matter Solid · Liquid · Gas · Bose-Einstein condensate · Fermionic condensate · Fermi gas · Fermi liquid · Supersolid · Superfluid · Luttinger liquid |
| Phase phenomena Order parameter · Phase transition |
| Electronic phases Electronic band structure · Insulator · Mott insulator · Semiconductor · Semimetal · Conductor · Superconductor · Thermoelectric · Piezoelectric · Ferroelectric |
| Electronic phenomena Quantum Hall effect · Spin Hall effect · Kondo effect |
|
Magnetic phases
Diamagnet · Superdiamagnet Paramagnet · Superparamagnet Ferromagnet · Antiferromagnet Metamagnet · Spin glass |
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Quasiparticles
Phonon · Exciton · Plasmon Polariton · Polaron · Magnon |
| Soft matter Amorphous solid · Granular matter · Liquid crystal · Polymer |
| Scientists Maxwell · Van der Waals · Debye · Bloch · Onsager · Mott · Peierls · Landau · Luttinger · Anderson · Bardeen · Cooper · Schrieffer · Josephson · Kohn · Kadanoff · Fisher |
As an SPP propagates along the surface, it loses energy to the metal due to absorption. The intensity of the surface plasmon decays with the square of the electric field, so at a distance x, the intensity has decreased by a factor of exp. The propagation length is defined as the distance for the SPP intensity to decay by a factor of 1/e. This condition is satisfied at a length
Likewise, the electric field falls off evanescently perpendicular to the metal surface. At low frequencies, the SPP penetration depth into the metal is commonly approximated using the skin depth formula. In the dielectric, the field will fall off far more slowly. The decay lengths in the metal and dielectric medium can be expressed as
where i indicates the medium of propagation. Surface plasmons are very sensitive to slight perturbations within the skin depth and because of this, surface plasmons are often used to probe inhomogeneities of a surface.
Read more about this topic: Surface Plasmon
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