810: Oblique Incidence at a Plane Dielectric Boundary

1

• 8-10 Oblique Incidence at a Plane Dielectric
  Boundary
• A plane wave propagating in
• where

x
z
2

• When a plane wave impinges on a plane dielectric
  boundary, the normal of the boundary and the
  incident ray form a plane called the plane of
  incidence.
• If the E-field of the incident wave

polarization
to
The plane wave of incidence, then
polarization
to
3
Configuration of polarization
4

• 8-10.2 Perpendicular (Horizontal) Polarization

(8.196)
(8.197)
5

• The reflected wave
• The transmitted wave

(8.198)
(8.199)
(8.200)
(8.201)
6

• Boundary conditions at z0 lead to
• Since (8.202) and (8.203) are held for arbitrary
  x
• Phase (continuity) matching condition

(8.202)
(8.203)
7

• Referring to the angle of incidence qi,
  reflection qr, and
• transmission qt, we see
• The phase matching condition is now
• which provides
• where refractive index n (not impedance ) is
  defined as

Snells law of reflection
(8-183)
Snells law of refraction
(8-184)
8

• We can obtain the magnitude of the three wave
  vectors by
• and
• We find
• In the combination with the phase matching, we
  obtain

9

• Using (8.202) we have
• Using (8.203),

(8.208)
(8.206)
(8.207)