Surface Plasmon¶

The free electron gas is a part of the quantum system, subject to the periodic potential of the metal ions that make up the lattice. A plasmon is a quasi-particle—a particle that can be described by a collection of interacting particles—in this case, the electrons. Plasmons occur on the surface of metal, are quantized, and consist of collective oscillations(Plasma oscillation) of the free electron gas.

The important thing to note now is that plasmons are longitudinal waves i.e., the displacement of the electrons (relative to a uniform positive background formed by a positive ion) are parallel to the direction of propagation of the wave, so they cannot be excited by a transverse wave like an electromagnetic wave. Usually the most effective way to excite a plasmon is to use electrons. For example, an electron beam passing through a thin metal foil will lose energy when it excites a plasmon. This loss in energy is exhibited by a peak in the electron energy loss spectrum (commonly known as EELS).

Polaritons¶

Polaritons are quasiparticles that exist when an EM mode is strongly coupled to some other type of mode, i.e., if we have light strongly coupled to some other physical excitation then the particle picture is inaccurate if we treat the 2 degrees of freedom separately (because particle number is not conserved). So instead of saying we have some photons, and we have some particles representing the excitation, instead we have a hybrid particle that is simply called a polariton.

This paper¹ pointed out that the transverse optical (TO) phonon will couple to pa photon when their wave vectors and frequencies are the same. This coupling modifies the dispersion of both the optical phonon and photon. The resultant coupled TO phonon-photon mode was labeled by Huang as the polariton. The longitudinal optical (LO) phonon cannot couple to the photon since it is a longitudinal wave. This is the reason why plasmons in 3D cannot form polaritons.

In case of an interface, the situation is different because a photon can be incident on the interface at an angle. For a photon polarized in the plane of incidence (p-polarized) the polarization can be decomposed into two components with one perpendicular to the interface and the other parallel to the interface. The parallel component can then excite a surface plasmon because this component is now a longitudinal wave.

Surface plasmon polaritons¶

Surface plasmon polaritons (SPPs) are the quasiparticles of the coupled modes of an EM field and a surface plasma oscillation. Although surface plasmons are not the same as surface plasmon polaritons, from the context the two are rarely confused. In addition, the charge oscillations will create an EM field, and so we can't create a surface plasmon(SP) without it automatically being part of an SPP. And since “surface plasmon polaritons” is a mouthful, people often use the term SP even when they are referring to the entire excitation itself, and therefore they technically mean SPP.

To form an SPP, the photon, and surface plasmon resonance(SPR) must have the same frequency and wave vector. This means that the component of the photon wave vector parallel to the interface has to be equal to that of the SPR.