Plane wave properties Jan. 25, 2018

• Intensity of wave: Average Poynting vector [equation]
For plane wave [equation] and [equation] where [equation] is wave impedance.
[equation]

• General form of plane wave: [equation]
Derivation of plane wave solution
Example for a plane wave propagating on axis with [equation]
Example for a oblique incident plane wave, i.e. propagating off axis.

Group velocity: Signal travels in a packet on the top of a carrier. Signal speed is determined by group velocity [equation]. (pp. 731-732 2nd Ed, 769-770 3rd Ed.)

• Wave natural of light is responsible for interference, diffraction and polarization effects etc. which determine operations of passive optical devices.

• To understand the conversion between light and electricity, i.e. actions in lasers and photodetectors, we need to consider particle natural of light, photon.
Photon energy [equation] where [equation] is the Planck's constant.
Or [equation] where [equation] where [equation].
Linewidth [equation] (pp. 28-31 2nd Ed., 26-29 3rd Ed.).

• Reflection and refraction: Snell's law -- [equation] and [equation]
Results of matching the phase at the boundary.

• Amplitude relations: From Maxwell's equations, we can find the reflection coef [equation] and transmission coef [equation].
Procedure for setting the directions at a boundary
2 polarizations TE or S-polarized ( [equation] to plane of incidence) and TM or P-polarized ([equation] to plane of incidence).
For [equation] polarization, it is not reflected at Brewster angle [equation].
For [equation], totally internal reflection results when [equation].
Fresnel equations --
[equation], [equation]
[equation], [equation].

Deriving reflection coefficient for s-polarized wave
Deriving reflection coefficient for p-polarized wave
Examples for application of reflection and refraction: polarizing beam splitter, sunglass for fishing at a pond or working in a snow covering ground.


Last Modified: January 22, 2018
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