Surface Plasmon Polaritons at Metal / Insulator Interfaces

[zakee.fancy]

Homework Statement

we are considering the surface plasmon mode at the interface between a dielectric and a plasma. Solve explicitly for the TM mode and identify the relationship
between dielectric and plasma permittivities that must be satisfied for the mode to exist.

Homework Equations

The Attempt at a Solution

I am trying to solve for TM modes , but i can't relate the permittivities and it is becoming difficult to identify relation between those permittivities

 

[mark726]

.

Hello,

The existence of the surface plasmon mode at the interface between a dielectric and a plasma is dependent on the relationship between the permittivities of the two materials.

To solve for the TM mode, you can use the boundary conditions at the interface between the two materials. These conditions require that the tangential components of the electric and magnetic fields are continuous across the interface.

In the case of a TM mode, the electric field is perpendicular to the plane of incidence, while the magnetic field is parallel to the plane of incidence. This means that the tangential component of the electric field must be continuous at the interface, while the tangential component of the magnetic field must be discontinuous.

Using the permittivity and permeability of the two materials, you can solve for the relationship between them that must be satisfied for the TM mode to exist. This relationship is known as the dispersion relation and can be derived from Maxwell's equations.

I hope this helps in your understanding of the surface plasmon mode. Let me know if you have any further questions.