Silicon Photonics: Fundamentals and Devices

4.2 Optical Constants

In this section, the relationship between different optical constants in a conductor or dielectric and their interrelationship will be presented. The starting equations are the following four Maxwell's equations related to the behavior of electromagnetic waves.

(4.1a)

(4.1b)

(4.1c)

(4.1d)

where F and H are the electric and magnetic fields, , and J and ρ are the current and charge densities, respectively. The electric and magnetic fields are expressed in terms of vector potential A and scalar potential as follows:

(4.2)

(4.3)

Taking curl of the second Maxwell equation and using the third one, we may write

(4.4)

We note that . It is usual to assume the Coulomb gage ...