Plasma Electrodynamics

1
Reflection and Refraction of Plane Waves

• Laws of Reflection and Refraction
• E Perpendicular to the Plane of Incidence
• E Parallel to the Plane of Incidence
• Total Reflection
• Energy Relation
• Reflection at the Surface of a Conductor
• Continuously Varying Index of Refraction

2
Laws of Reflection and Refraction
Boundary conditions without free charges and free
surface currents
kr
1
2
kt
Laws of Reflection and Refraction give
?r
Snells law of refraction
?t
for
?i
Critical angle
ki
for
Total reflection
3
E Perpendicular to the Plane of
Incidence (S-component of polarization, TE wave)
Boundary conditions
kr
Hr
1
2
kt
with
Et
Er
Ht
ki
normal incidence
for
Ei
Hi
Fresnels eqn
4
E Parallel to the Plane of Incidence (P-component
of polarization, TM wave)
Boundary conditions
kr
Er
1
2
kt
Ht
Hr
Et
normal incidence
ki
Hi
for
Ei
Fresnels eqn
5
Fresnels Equation for n1ltn2
normal incidence
normal incidence
Brewster angle polarizing angle
6
Total Reflection (n1gtn2, ?igt?c)
x
Speed of the wave
1
2
Since
travel more slowly
z
?i
ki
total reflection
Change from linear to elliptical polarization !
7
Energy Relations

• Reflection coefficient

where
normal incidence with ?1?2

• Transmission coefficient

normal incidence with ?1?2
Energy conservation
8
Reflection at the Surface of a Conductor
Only for normal incidence,
Boundary conditions give
9
Continuously Varying Index of Refraction
Index of refraction for plasma
Propagation of a wave in the ionosphere