Chapter 2

Laser and Atom Interaction

1

2

00

1 c

tie 0EE 001 Ec

B

)1(21 2

0

20 BE

W

20 EW

)(1

0

BEI

20 EcS

2

2

22 1

tc

EE

2.1 Planck Radiation and Einstein A and B

Maxwell Equations

Energy Density and Flux of EM Wave

2

Lnk x

,2,1,0n

2

2

3 )(ShellinModesofNumber

dkkkdL

cck

22

3

28cdd

0i

TkBieq

2

k

Metal Cavity with Length L

qeP

Tk

i

Bi

Partition Function

Probability Distribution

3

hnii )21(

)1()()(

)(

00

2

2TkhnTkh

n

nTkh

nTkh

n

TkhnTkh

TkhnTkh

iBiB

i

iB

iB

i

BiB

BiB

eee

e

ee

eeP

0 0 1))(1()(

i nTkhi

TkhnTkhii

iB

BiB

ehhneeP

dec

hd TkhPlE B 1

18)( 33

Average energy per mode

We obtain Planck Energy Distribution

4

5

21122

1

21

)( BBNN

Ath

kTEEegg

NN )(

2

1

2

1 21

1)(21

12

2

1

21

21

0

BB

egg

BA

kT

th

121

12

2

1 BB

gg

303

21

21 8 ch

BA

32

30

21

21

cBA

10

21

21 kTth e

BA

21221212121 ANBNBN

dtdN

dtdN

Einstein A and B Coefficients

6If you know A21 or B12, you can obtain A21, B12, B21.

2.2 Photo-Excitation

7

8

Spherical HarmonicsRadial Wave Functions

No Perturbation

With Perturbation

19

Dipole Approximation

10

tV cosωreE 12012

11

12

Oscillator strength

Sum Rule

13

Spectral Cross Section (m2s-1)

Assume Lorentz Line Profile

Absorption

Emission

14

15

16

Atomic Processes

2

27

25

12

3

4

cos2mce

n

Differential Cross-section from a bound S-state

Total Cross-section from a bound S-state

27

25

12

3

6

32

mce

n

21 4

1 Z

Differential Cross-section from a bound P-state(l=1, m=-1,0,+1) No angular dependence

29

27

12

5

24 192

mce

nn

4Total Cross-section from a bound P-state

where

2.3 Photo-ionization

17

Photo-absorption Cross Section from K and L Shells of Fe

27

25

12

3

6

32

mce

n

18

npnss nnn

12

53

1 13

Important relation

Scatterings

0212log

83

Zsc

225200 cm1065.6

38 r

cm10818.2 132

2

0 cmc

er

Compton Scatt.

Thomson Scatt.

19

20

2.4 Electron Impact Excitation

21

22

2.5 Electron Impact Ionization

23

24

25

26

27

2.6 Detail Balance

2

1

12 21

Electron: Boltzmann Distribution

Photon: Planck Distribution

Assume LTE (Local Thermodynamic Equilibrium)

28

1. Multi-photon Ionization2. Tunneling Ionization3. Over-threshold Ionization4. Photo-ionization5. Collisional Ionization6. Pressure Ionization

2.7 Nonlinear Optics

29

30

31

32

33

34

2.8 Other Ways to Produce Plasmas