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.