Ellipsometry: finding n, kor thicknesses, roughness…

Wikipedia

http://www.gaertnerscientific.com/ellipsometers/l116sf.htm

12

3

cossin

00p

s

rr

2

2

cos sin cossin cos sin

starts linear, angle

does something

linear polarizer, angle

Any light with information (e.g. pulsing) has to contain more than one frequency.

Superposition of Waves

Any light created in the universe has more than one frequency (it had a beginning).

Superposition of Waves

Addition of two waves, equal magnitude:

1 1 2 2cos( ) cos( )k x t k x t

cos( ) cos( ) 2cos cos2 2a b a ba b

Superposition of Waves

Phase velocity =

( ) ( )pcvn k

speed of phase oscillations

Group velocity gdv

k dk

speed of “envelope”, pulse, signal, image, energy, information

(this definition not valid when absorption is strong)

n

Dispersion due to n()

kRe ()=n() /c

Dispersion is when vphase

is not constant: k() or (k) are not linear:

Wave speed depends on

vphase =c/n()

Does group velocity exceed c?kRe ()=n() /c

Look at slope for vg :

1

g

dkd v

Where our definition is valid (low absorption),

even when g pv c v c

1

p

kv

k/ 1/c

If in some strange system, then the group velocity is

a)

b)

c)

d)

4

33o

kck

3

33po

kv ck

3

312po

kv ck

4

3po

kv ck

3

3go

kv ck

If in some strange system, the group velocity is

a)

b)

c)

d)

2

o

kc

3

3go

v c

2o

gv c

2

2go

v c

2go

v c

) ), j ji k r tj

j

E r t E e

) ), j ji k r tj j

j j

k EB r t e

) ) ) ,

1, Re Rej j m mi k r t i k r tj m m

j m m o

S r t E e k E e

Energy and superimposed plane waves

) ) )*

,2

j j m mi k r t i k r toj m

j m

n cI r t E e E e

Two restrictions for this result to be true: ____________

Energy and superimposed plane wavesPracticing simple addition of waves

You add two 1-D waves, of amplitude E1 and 2E1. In some places they add constructively, and some places destructively. E1 by itself corresponds to intensity I1 .

The brightest intensities seen in the interference pattern are:

a) 3I1

b) 4I1

c) 6I1

d) 9I1

e) 25I1

You add two coherent 1-D waves, of amplitude I1 and 9I1. In some places they add constructively, and some places destructively.

The dimmest intensities seen in the interference pattern are:

a) 2I1

b) 3I1

c) 4I1

d) 6I1

e) 8I1

Show that ) 11 ( )g pv v f

( )f and find in terms of

a) I did itb) I tried

( )n