Tentative Schedule: Date, Place & Time Topics

1 Aug.24 (Mo) 394; 4:00- 5:15 Introduction, Spontaneous and Stimulated Transitions (Ch. 1) – Lecture Notes

2 Aug.26 (We) 394; 4:00-5:15 Spontaneous and Stimulated Transitions (Ch. 1) – Lecture Notes Homework 1: PH481 Ch.1 problems 1.4 &1.6 PH581 Ch.1 problems 1.4, 1.6 & 1.8 due Sep.2 before class

3 Aug.31 (Mo) 394; 4:00-5:15 Optical Frequency Amplifiers (Ch. 2.1-2.4) – Lecture Notes Problem solving for Ch.1

4 Sep.2 (We) 394; 4:00-5:15 Optical Frequency Amplifiers (Ch. 2.5-2.10) – Lecture Notes Homework 2: PH481 Ch.2 problems 2.2 (a,b), 2.4 & 2.5 (a,b) PH581 Ch.2 problems 2.2 (a,b), 2.4 & 2.5 (a,b,c,d) due Sep.16 before class

Sep.7 (Mo) No classes Labor Day Holiday5 Sep.9 (We) 394; 4:00-5:15 Problem solving for Ch.2

Introduction to two Practical Laser Systems (The Ruby Laser, The Helium Neon Laser) (Ch. 3) – Lecture Notes

6 Sep.14 (Mo) 394; 4:00-5:15 Review Chapters 1 & 2 – Lecture Notes 7 Sep.16 (We) 394; 4:00-5:15 Exam 1 Over Chapters 1-3; Grades for exam 1 8 Sep.21 (Mo) 394; 4:00-5:15 Exam 1 problem solving. Passive Optical Resonators (Ch. 4.1-4.5) 9 Sep.23 (We) 394; 4:00-5:15 Passive Optical Resonators (Ch. 4.6-4.7). 10 Sep.28 (Mo) 394; 4:00-5:15 Passive Optical Resonators updated(Ch. 4.6-4.7). Physical significance of ’

and ’’ (Ch.2.8-2.9). Homework 3: read Ch.2 & Ch.4. Problems from CH.4: 4.2 & 4.4. Due Oct. 5

11 Sep.30 (We) 394; 4:00-5:15 Optical Resonators Containing Amplifying Media (5.1-2). 12 Oct. 5 (Mo) 394; 4:00-5:15 Optical Resonators Containing Amplifying Media (Ch.5.3-5.7) Homework

4: Ch. 5 problems 5.7 and 5.9. Due Oct 12. 13 Oct. 7 (We) 394; 4:00-5:15 Laser Radiation (Ch. 6.1-6.4) 14 Oct. 12 (Mo) 394; 4:00-5:15 Control of Laser Oscillators (7.1-7.3) Homework 5: Ch. 6 problems 6.1 and

6.5. Due Oct 19. 15 Oct. 14 (We) 394; 4:00-5:15 Control of Laser Oscillators (7.4-7.5) and exam 2 review 16 Oct. 19 (Mo) 394; 4:00-5:15 Optically Pumped Solid State Lasers (8.1-8.11) 17 Oct. 21 (We) 394; 4:00-5:15 Optically Pumped Solid State Lasers (8.1-8.11) 18 Oct. 26 (Mo) 394; 4:00-5:15 Exam 2 Over Chapters 4-7 Grades for exam 2

Exam 2 correct solution; Homework 6 Due Nov. 2; Article on Cr:CdSe 19 Oct. 28 (We) 394; 4:00-5:15 Optically Pumped Solid State Lasers (8.15-8.16) 20 Nov. 2 (Mo) 394; 4:00-5:15 Optically Pumped Solid State Lasers (8.15-8.16) Supplemental material for

Homework 6–diode pumped LiF:F2- laser/ Homework 7 Due Nov.9

21 Nov. 4 (We) 394; 4:00-5:15 Optically Pumped Solid State Lasers (8.15-8.16) 22 Nov. 9 (Mo) 394; 4:00-5:15 Spectroscopy of Common Lasers and Gas Lasers (Ch. 9.1-9.10 and class

material) 23 Nov. 11 (We) 394; 4:00-5:15 Gas lasers (Ch. 9.4 -9.10); Molecular Gas lasers I (Ch. 10.1-10.5) 24 Nov. 16 (Mo) 394; 4:00-5:15 Molecular Gas lasers I (Ch. 10.1-10.5) Homework 8 Due Nov. 30 25 Nov. 18 (We) 394; 4:00-5:15 Molecular Gas Lasers II (Ch. 11.1-11.8) and review for exam 3 (Ch. 11.1-

11.8) Homework 9 Due Dec 2 Nov.23 (Mo) No classes Thanksgiving - no classes held Nov.25 (We) No classes Thanksgiving - no classes held 26 Nov. 30 (Mo) 394; 4:00-5:15 Exam 3 Over Chapters 8-11 Grades; Exam 3 Correct solution 27 Dec. 2 (We) 394; 4:00-5:15 Review for Final28 Dec. 9 (Wed) in CH 394 FINAL EXAM Over Chapters 1-11 (4:15-6:45pm) in CH 394 Final

Grades

2

Laser Physics I PH481/581-VT (Mirov)

Lecture 6. Review of chapters 1-2

Fall 2015C. Davis, “Lasers and Electro-optics”

Spectral radiancy

Thermal radiation: The radiation emitted by a body as a result of temperature.

Blackbody : A body that surface absorbs all the thermal radiation incident on

them.

Spectral radiancy : The spectral distribution of blackbody radiation.)(TR:)( dRT

represents the emitted energy from a unit area per unit time between and at absolute temperature T. d

radiancy

dRR TT )(0

Stefan’s law (1879):

4284 /1067.5, KmWTR oT

Energy Density and Spectral Radiancy

energy density between ν and ν+dν: 1

8)( /3

2

kThT e

hc

118)()()(

)()(

/52

kThcTTT

TT

ehcc

dddd

Ex: Show )()/4()( TT Rc

dA

dV

r22 4

cos4

ˆr

dAr

rAd

solid angle expanded by dA is

spectral radiancy:

)(4

sin4cos)(

)/()4

cos()()(

2220

2/

0

2

0

2

T

tc

T

TT

c

drrtr

dd

tdAr

dAdVR

Stefan’s law

Ex: Use the relation between spectral radiancy

and energy density, together with Planck’s radiation law, to derive

Stefan’s law

dcdR TT )()/4()(

32454 15/2, hckTRT

44

3

4

2

0

3

3

4

2

0 /

3

200

15)(2

1)(2

12)(

4)(

Th

kTc

dxe

xh

kTc

de

hc

dcdRR

x

kThTTT

15/)1/(

/4

0

3

dxex

kThxx

32

45

152

hck

5 23 48

8 2 34 3 2 4

2 (1.38 10 ) 5.67 1015(3 10 ) (6.63 10 )

Wm K

6

Problem. Compute the radiation flux or power in watts coming from a surface of temperature 300K (near room temperature) and area 0.02 m2 over a wavelength interval 0.1 m at a wavelength of 1.0 m.

118)()()(

)()(

/52

kThcTTT

TT

ehcc

dddd

2

5 /

2( , ) ( )4 1

The total radiancy emitted from the blackbody surface within a specific wavelengthinterval would then be expressed as

( , , ) ( , )Specific values of spectr

T hc kT

T T T

c hcR Te

R R T R T

25

25 0.0144/

al radiancy ( , , ) in units of power per unit area (intensity)can be obtained from the following empirical expression for

3.75 10( , ) , 1

where in meters, in nanometer

T

T T

R T

WR Tm nme

25

155 0.0144/(1000 300)

s, and T in K. Remember that these expressions are for the radiation into 2 steradian solid angle.

3.75 10( , ) 100 0.02 1.06 101000 1

We can see that at RT the power

TP R T A We

radiated from a blackbody within this wavelength region is almost too small to be measurable.

7

5 23 48

8 2 34 3 2 4

4 72

2 (1.38 10 ) 5.67 1015(3 10 ) (6.63 10 )

for sun temperature 5778

6.32 10T

Wm K

T KWR Tm

82RT/c

9

7 8 2 26

263

2 11 2 2

Total power radiated by the sun is 6.32 10 4 (6.96 10 ) 3.85 10

Power density at the surface of the earth3.85 10 1.36 10

4 4 (1.5 10 )ignoring losses due to absorption and

T sun

e

P R A W

P WID m

6 2

62

scattering in atmospherePressure on aluminum sheet of area 10 situated on the surface of the earth

2 9 10

The total force produced by the photon pressure of the Sun on aluminum sheet

e

she

mI Npc m

F p A

9et N

10

11

Problem 1.8. What would the spectral energy density distribution be if ”black-body” radiation could occupy only two photon states? Namely, theonly allowed energies for the various modes of a cavity would beEn=(2n+1) h

12

13

14

15

16

17

18

19

Problem. Find the relation between spontaneous emission lifetime and cross section for a simple atomic transition.

22212 2

Cross-section of emission at frequency ( , )( ) ( , ) (1)

8 8

where / is the wavelength (in vacuum) of an e.m. wave whose frequencycorresponds to the center of the line.

E

o oo

o sp

o o

gc A gn

c

quation (1) can be used either to obtain the value of , when is known,

or the value of when is known.

If ( ) is known, to calculate from (1) we multiply both sides by

d and integrate.

sp

sp

sp

2

2

Since ( ) 1 we get:

18 ( )

osp

g d

n d

20

Problem. Radiative lifetime and quantum yield of the ruby laser transition.The R1 laser transition of ruby has to a good approximation a Lorentzian shape of width (FWHM) 330 GHz at room temperature. The measured peak transition cross-section is =2.5x10-20 cm2. Calculate the radiative lifetime (the refractive index is n=1.76). Since the observed room temperature lifetime is 3 ms, what is the fluorescence quantum yield.

222 1

2 2

2

2

( , )F r o m ( ) ( , ) ( 1 ) w e h a v e8 8

( , ) ( 2 )8

F o r a L o r e n tz i a n l i n e s h a p e a t w e h a v e 2( 0 )

F o r 6 9 4 , w e o b t a in f r o m e q . ( 2 ) t h es p o n ta n e o u s e m is s io n l i f e t

o oo

o s p

o os p

o

o

o

gc A gn

gn

g

n m

2

2

im e ( i .e . t h e r a d ia t i v e l i f e t im e )2 4 .7 8

8F lu o r e s c e n c e q u a n tu m y ie ld i s d e f in e d a s t h e r a t i o o f t h e n u m b e r o f o f e m i t t e d p h o to n s t o t h e n u m b e r o f a to m s in i t i a l ly r a i s e d t o t h e le v e l 2

os p

o

m sn

0 .6 2 5

w h e r e o b s e r v e d l i f e t im e g iv e n b y1 1 1

r

r n r

24

5.

26

6.