Electro-magnetic
waves in matter
Linear media:
vc 00
velocity:
oo
n
refractionofindex
n
cv
1
most materials:
10 rn
Reflection, transmission and refraction
Boundary conditions
011
)
0)
0)
0)
||2
2
||1
1
||2
||1
_|_2
_|_1
_|_22
_|_11
BB
EE
iv
iii
BBii
EEi
Normal incidence
011
)
0)
0)
0)
||2
2
||1
1
||2
||1
_|_2
_|_1
_|_22
_|_11
BB
EE
iv
iii
BBii
EEi
Reflection coefficient
Transmission coefficient
2
21
21
nn
nn
I
IR
I
R
221
21
)(
4
nn
nn
I
IT
I
T
1TR
Lens coating
http://www.canon.com/technology/s_labo/light/003/03.html
,...4
5,
4
3,
4
2,...
2
5,
2
3,
20cos
sincos
cossin
11
111
111
2
1
a
aakak
akiakn
akakin
n
n1n 2n
Oblique incidence
011
)
0)
0)
0)
||2
2
||1
1
||2
||1
_|_2
_|_1
_|_22
_|_11
BB
EE
iv
iii
BBii
EEi
Plane of incidence The incident, reflected and transmitted wave vectors lie in a plane, which also includes the normal to the surface.
angle of incidence Iangle of reflection
Rangle of refraction
T
Law of reflection RI
Law of refraction (Snell’s Law)
2
1
sin
sin
n
n
I
T
Willebrord Snell, 1621
12 nn
1n
Total internal reflection
Binoculars
Jewelry
Diamonds
ocr
n
25
4.2
Fiber optics
Near field optical scanning microscope
Application of evanescent waves:
Muscle fiber
Intensity and polarization
011
)
0)
0)
0)
||2
2
||1
1
||2
||1
_|_2
_|_1
_|_22
_|_11
BB
EE
iv
iii
BBii
EEi
Fresnel’s Laws
TE polarizationE of I, R, and T are perpendicular to the plane of incidence (B in)
IT
IR
EE
EE
00
00
~1
2~
,~
1
1~
TM polarizationE of I, R, and T are in the plane of incidence (B perpendicular)
IT
IR
EE
EE
00
00
~2~
,~~
12
21
22
11
cos
cos
n
n
v
v
I
T
Intensities 021
1cos
cos RT
I
R
2
21
21
2
21
21
coscos
cos2
coscos
coscos
TI
I
I
T
TI
TI
I
R
nn
nn
I
IT
nn
nn
I
IR
TM polarization
2
12
21
2
12
12
coscos
cos2
coscos
coscos
TI
I
I
T
TI
TI
I
R
nn
nn
I
IT
nn
nn
I
IR
1
2tann
nB Brewster’s
angle
BP
1938 Polaroid film
Polarization measurements Crossed polarizers
Egg nebula
Materials under stress rotate the polarization plane.