Reading Assignment : Chapter 17 Homework Assignment #9 ∇ E /

Reading Assignment ∇: Chapter
17
× E = −∂B /∂t
ΑΒΓΔΕΖΗΘΙΚΛΜΝΞΟΠΡΣΤΥΦΧΨΩ
αβγδεζηθικλμνξοπρςστυφχψω
+<=>|~±×÷′″⁄⁒←↑→↓⇒⇔ ∂Δ∇∈∏∑
(ε1 e1 + ε2 e2 )
∇∙E=0
∇∙B=0
∇ × B = + μ0ε0 ∂E /∂t
Homework Assignment #9
e−iωt due Halloween
∓∔⁄∗∘∙√∞∫∮∴
≂≃≄≅≆≠≡≪≫≤≥
ε
−
Waves in Simple Matter ---Reflection
and Refraction at a planar interface
between dielectrics
Consider a planar interface between two
simple materials; regions Ri and RT .
Suppose a plane wave is incident on the
interface, at angle of incidence θi .
These boundary conditions are required:
1. Dnormal is continuous
2. Etangential is continuous
3. Bnormal is continuous
4. Htangential is continuous.
We’ll use these to determine the reflection
and transmission intensities.
(Fresnel’s equations)
S polarization (or, TE polarization)
The E field of the incident wave is
polarized in the direction parallel to
interface (i.e., the y direction).
P polarization (or, TM polarization)
The B field of the incident wave is
polarized in the direction parallel to
interface (i.e., the y direction).
Note: Recall for plane waves __
μ H0 = μ Z-1 E0 = SQRT[εμ] E0
= (n/c) E0
Two equations for two unknowns
S polarization. (D = εE and B = μH)
Boundary Conditions
Dnormal : 0 = 0
Etangential : E0 + E0R = E0T
Bnormal : −μ1 H0 sin θ1 −μ1 H0R sin θ1 = −μ2 H0T sin θ2
n1 (E0 + E0R) sin θ1 = n2 (E0T) sin θ2
E0 + E0R = E0T again
Htangential : H0 cos θ1 − H0R cos θ1 = H0T cos θ2
Z1-1 (E0 − E0R) cos θ1 = Z2-1 (E0T) cos θ2
Z2 (E0 − E0R) cos θ1
= Z1 (E0 + E0R) cos θ2
E0R =
E0
Z2 cos θ1 − Z1 cos θ2
Z2 cos θ1 + Z1 cos θ2
E0T =
E0
2 Z2 cos θ1
Z2 cos θ1 + Z1 cos θ2
rS
tS
E0R
=
E0
E0T
=
E0
Z2 cos θ1 − Z1 cos θ2
Z2 cos θ1 + Z1 cos θ2
2 Z2 cos θ1
Z2 cos θ1 + Z1 cos θ2
rS
tS
P polarization (or, TM polarization)
Similarly,
E0R =
E0
Z1 cos θ1 − Z2 cos θ2 r
Z1 cos θ1 + Z2 cos θ2 P
E0T
2 Z2 cos θ1
=
E0
Z1 cos θ1 + Z2 cos θ2
tP
Energy conservation in
reflection and transmission
Exercise.
Show that R + T = 1 , as it must be for
conservation of energy.
Brewster’s angle
For P polarization,
rP = 0 at θ1 = θB .
E0R
E0
Z1 cos θ1 − Z2 cos θ2
Z1 cos θ1 + Z2 cos θ2
Calculation of θB ___
We have
Z1 cos θ1 = Z2 cos θ2
and
n1 sin θ1 = n2 sin θ2
Polarization by reflection
Define relative polarization
Π (θI ) = | ( Rs− Rp) / (Rs + Rp) |
(times 100 percent)
At Brewster’s angle,
Rp = 0 so Π = 100% .
What happens at
★ Grazing incidence --★ Normal incidence --★ Brewster’s angle --?
Other optical phenomena associated
with Fresnel’s equations __
★
Total internal reflection
★
Phase changes at reflection
“Light waves change phase by 180 degrees when they
reflect from the surface of a medium with higher index
of refraction than that of the medium in which they are
travelling.The phase changes that take place upon
reflection play an important part in thin film
interference.”
★
“A totally reflected wave is elliptically
polarized. Fresnel exploited this fact
to convert linearly polarized light into
circularly polarized light.” Fresnel
Rhomb
★
Evanescent waves. At total internal
reflection, there is an interfacial wave,
exponentially decreasing in the region
R2. Read Sec 17.3.6.
Magnitude and phase of r:
air → glass
glass → air
Reading Assignment ∇: Chapter
17
× E = −∂B /∂t
ΑΒΓΔΕΖΗΘΙΚΛΜΝΞΟΠΡΣΤΥΦΧΨΩ
αβγδεζηθικλμνξοπρςστυφχψω
+<=>|~±×÷′″⁄⁒←↑→↓⇒⇔ ∂Δ∇∈∏∑
(ε1 e1 + ε2 e2 )
∇∙E=0
∇∙B=0
∇ × B = + μ0ε0 ∂E /∂t
Homework Assignment #9
e−iωt due Halloween
∓∔⁄∗∘∙√∞∫∮∴
≂≃≄≅≆≠≡≪≫≤≥
ε
−