Dispersion relations, surface plasmon polaritons

At the surface of metals, the surface plasmon-polaritons, also called "surface plasmons," are not the same as the "bulk" plasmons these surface plasmons are affected (i.e., shifted slightly in energy) by monolayer adsorbates thus Surface Plasmon Resonance (SPR) spectroscopy yields information about the nature of the binding of the adsorbates onto a metal surface. The surface plasmons are excited by a p-polarized electromagnetic wave (polarized in the plane of the film) that crosses a glass medium (1), such as a prism, and is partially reflected by a metallic film (2) and back into the glass medium the dispersion relation is... 

Equation (1.163) represents the dispersion relation of the surface plasmon polariton mode (SPP-mode), i.e. the relationship between the frequency co and the in-plane wavevector for SPPs propagating along the interface between a metal and a dielectric. 

From the surface plasmon-polariton wavevector (Eq. (1.163)) we can then obtain the wavelength of the surface plasmon-polariton A-spp which represents the period of the surface charge density oscillation and of the associated field distribution of the mode (see Fig. 1.6). In particular, the SPP wavelength can be found from the complex dispersion relation Eq. (1.163) by taking the real part. Writing the complex relative permittivity of the metal as m(ft>) = —1 I-pie" we can write the complex SPP wavevector as kx =... 

Problem 3.8. Neglecting relaxation, obtain the dispersion relation of surface plasmon polariton at an interface between two metals having the plasma frequencies cOpi and cOp2- In what frequency range can a surface plasmon polariton exist Find its frequency in the nonretarded limit (c —s- 00). 

C0p2)/ 2] and co > cOp2 provided that copi < C0p2- However, in the latter range both e and 62 are positive, thus contradicting Eq. (3.88) from which the dispersion relation follows. Therefore, a surface plasmon polariton can... 

Plasmon surface polaritons (PSPs) or surface plasmons are transverse magnetic waves that propagate along a metal-dielectric interface, their field amplitudes decaying exponentially perpendicular to the interface [29,30]. Their dispersion relation is given by... 

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