Understanding the Refractive Index in QED by Feynman

[jobyts]

(I'm still reading the QED book by Feynman...)

What property of the material causes a specific refractive index for a particular medium? (in other words, from the FAQ section by ZapperZ, "So the lattice does not absorb this photon and it is re-emitted but with a very slight delay.". How is the delay different between different materials.)

 

[Manchot]

Classically, it comes down to how easily a material can form electric or magnetic dipoles. In a dielectric, for example, when an electric field is applied, the bound electrons will move further away from their host nuclei, forming dipoles which will in turn reinforce that field. For most materials the polarization of the material is proportional to the applied field, and the constant of proportionality is wrapped up into the electric permittivity. Likewise, applied magnetic fields will often induce a proportional response in the magnetic polarization: this is wrapped up into a constant known as the permeability. Together, the permittivity and permeability determine the speed of field propagation through the material, which in turn gives the index.

 

[Claude Bile]

Note too that the refractive index can be influenced by external factors as well such as applied E-field and temperature. The things Manchot mentions don't just affect the refractive index, but also how the refractive index changes as a function of these external factors.

Claude.

 

[Manchot]

Yeah, and you should also note that the refractive index may not even be well-defined for some situations. For example, in some materials like crystals or polymers, the polarization responds to an applied field anisotropically, meaning that certain directions are preferred over others. In these cases, the permittivity and index must be described by matrices. In other materials, the polarization responds to an applied field non-linearly, in which case the index is a function of field amplitude. As a matter of fact, all materials are essentially nonlinear for large fields: when a field larger than the breakdown field strength is applied, a dielectric becomes conductive, and all of this goes out the window.