2024-03-25 EM Waves in Matter

Review

• We went over EM waves in vacuum
• Electric and magnetic waves are $\perp$
• Linear materials designate materials where the electric field is independent from external electric field

Electromagnetic Waves in matter

• Maxwell’s Laws remain about the same, with ampere’s law changing to

$$\vec{\nabla }\times \vec{B}=\mu ϵ\vec{\dot{B}}$$

Speed of waves in material is equal to

$$\frac{C}{n}=v=\frac{1}{\sqrt{\mu ϵ}}$$

Reflections and Refraction

Using Snell’s Law we can calculate the refraction angle between two substances

$$n_1\sin \tan {\theta }_1=n_2\sin ({\theta }_2)$$

Boundary Conditions:

• Face of Waves must be continuous at interface
• Reflected Wave must have the same wave-vector as the incident wave

$$k\sin {\theta }_i=k^{\prime }\sin {\theta }_t=k\sin {\theta }_r$$

Total internal Reflection

Polarization!

Polarization has two different meanings in EM theory Meaning 1: Macroscopic Electric polarization $\mathbf{P}$ of a dielectric material

Meaning 2: Polarization of the electromagnetic wave $\mathbf{E}(\mathbf{r},t)$. (linear circular or elliptic)

Brewster Angle

• angle of incidence wherein there is no reflected EM wave.
• Makes lasers !!!1!!

9.18 9.38