1

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 (Lecture notes) 9 Sep.23 (We) 394; 4:00-5:15 Passive Optical Resonators (Lecture notes). 10 Sep.28 (Mo) 394; 4:00-5:15 Passive Optical Resonators (Lecture notes). Physical significance of ’ and

’’ (Ch.2.8-2.9). Homework 3: read Ch.2 & notes. Work out problems. Due Oct. 5

11 Sep.30 (We) 394; 4:00-5:15 Optical Resonators Containing Amplifying Media (4.1-2). 12 Oct. 5 (Mo) 394; 4:00-5:15 Optical Resonators Containing Amplifying Media (Ch.4.3-4.7) Homework

4: Ch. 4 problems 4.7 and 4.9. Due Oct 12. 13 Oct. 7 (We) 394; 4:00-5:15 Laser Radiation (Ch. 5.1-5.4) 14 Oct. 12 (Mo) 394; 4:00-5:15 Control of Laser Oscillators (6.1-6.3) Homework 5: Ch. 5 problems 5.1 and

5.5. Due Oct 19. 15 Oct. 14 (We) 394; 4:00-5:15 Control of Laser Oscillators (6.4-6.5) and exam 2 review 16 Oct. 19 (Mo) 394; 4:00-5:15 Optically Pumped Solid State Lasers (7.1-7.11) 17 Oct. 21 (We) 394; 4:00-5:15 Optically Pumped Solid State Lasers (7.1-7.11) 18 Oct. 26 (Mo) 394; 4:00-5:15 Exam 2 Over Chapters 4-6 Grades for exam 2

Exam 2 correct solution; Homework 6 Due Nov. 4; Article on Cr:CdSe 19 Oct. 28 (We) 394; 4:00-5:15 Optically Pumped Solid State Lasers (7.16-7.17) 20 Nov. 2 (Mo) 394; 4:00-5:15 Optically Pumped Solid State Lasers (7.16-7.17) Homework 7 Due Nov.11 21 Nov. 4 (We) 394; 4:00-5:15 Optically Pumped Solid State Lasers (7.14-7.15) Supplemental material for

Homework 6–diode pumped LiF:F2- laser

22 Nov. 9 (Mo) 394; 4:00-5:15 Spectroscopy of Common Lasers and Gas Lasers (Ch. 8.1-8.10 and class material)

23 Nov. 11 (We) 394; 4:00-5:15 Gas lasers (Ch. 8.4 -8.10); Molecular Gas lasers I (Ch. 9.1-9.5) 24 Nov. 16 (Mo) 394; 4:00-5:15 Molecular Gas lasers I (Ch. 9.1-9.5) Homework 8 Due Nov. 30 25 Nov. 18 (We) 394; 4:00-5:15 Molecular Gas Lasers II (Ch. 10.1-10.8) and review for exam 3 (Ch. 10.1-

10.8) 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 7-10 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 1-10 (4:15-6:45pm) in CH 394 Final

Grades

Review for Final

2

3

LASER PHYSICS I PH 481/581-VT (MIROV) Exam 3 (11/30/15)

STUDENT NAME: ____key_________________ STUDENT id #: ___________________________ ------------------------------------------------ -------------------------------

Graduate -ALL QUESTIONS ARE WORTH 50 POINTS. Undergraduate- 75 ------------------------------------------------------------------------------------------------------------------------------------------NOTE: Clearly write out solutions and answers (circle the answers) by section for each part (a., b., c., etc.)

1. A Nd YAG rod 5 mm in diameter, 6 cm long, with 100% and 90% reflectivity mirrors depositedon its facets is pumped by a pulsed flashlamp with a pulse duration much shorter than thelifetime of Nd ions. The average wavelength of excitation is 810 nm and all the pump radiationis completely absorbed by a rod. Nd YAG cross section of emission of is 9x10-23 m2 and branching ratio is equal to 1. Assume the distributed loss in the cavity is 0.01 cm-1.

a) Calculate threshold population inversion. b) Calculate the absorbed pumped energy corresponding to threshold. c) Calculate the electrical pump energy of a lamp at threshold, assuming that the rod is

uniformly pumped with an overall pump efficiency=efg=1%.

Opened textbook

Graduate fellows WORK ONLY 3 questions Undergraduate – 2 questions

1 11 2

22 3

3 3

1 11) ln 0.01 ln 1 0.9 0.019 1.96

2) 2.1 10

3) 5.2 10 /( )

4)

th

thth

th pth

Threshold gain R R cm ml

Population inversion N m

N hvThe absorbed pump energy density U J m

vThe absorbed pump energy

6.15) 6.1 / 0.01 0.61

thU V mJThe electrical pump energy mJ J

4

2. Consider the rigid rotation of biatomic molecule, made of two atoms with masses M1 and M2 at intermolecular distance Ro. The moment of inertia I about an axis passing through the center of mass and

perpendicular to the internuclear axis can be obtained as 2 21 2

1 2o r o

M MI R M RM M

. Recalling the

quantization rule of angular momentum, 2 2 ( 1)L J J and the facts that rotational kinetic energy of a rigid body rotating around a given axis can be written as E=L2/2I and rotational energies of the biatomic molecule can be expressed as EJ

rot=J(J+1)Bhc, express the rotational constant B of the molecule as a function of the reduced mass and intermolecular distance.

2

2

2 2

11

2

2 8 4 4 r o

J JE J J Bhc

IhB

I hc Ic Ic cM R

5

4. Consider a Nd:YLF laser (n=1.448) to be Q-switched as shown in Figure depicted below. The Nd:YLF rod has a cross-sectional area of 0.2 cm2, is 8 cm in length, and is placed in a cavity 20cm long. The Q-switch is 1 cm long and its index of refraction is 1.45. The transmission of thecavity output coupler is 30% and the internal loss per pass is 5%. Assuming a stimulatedemission cross section 1.9x10-19 cm2 of Nd:YLF at the laser wavelength and that the energy ofthe pump pulse is twice the threshold. (a) Find the maximum peak output power of this laser. (b) Find the output energy in the Q-switched pulse. (c) Estimate the pulse width.

Laser medium

Shutter Pump

l

d

2 2 21 2

21

1 ) C o m p u te th e th resh o ld g a in co effic ien t. R o u n d trip g a in m u st b e g rea te r th an 1 fo r an o sc illa to r an d eq u a l to 1 fo r th resh o ld :

1;

1 1 1 1ln ln2 2

s s thl la b c d

sth s

a b c d

R R T T T T e e

ll l lR T T T T

22

1

11 7 3

2 1 1 9 2

1 1 1 1ln 0 ln2 8 2 8 0 .71 0 .9 5

0 .0 0 6 4 0 0 .0 2 2 3 0 .0 2 8 70 .0 2 8 72 ) T h e th resh o ld in vers io n ( ) 1 .5 1 1 0

1 .9 1 03 ) T h e to ta l # o f in verted a to m s in th e cav ity a t th resh o ld is

thth

th

R

cmcmN N cm

cm

n

1 7 3 2 1 72 1

1 7

1 .5 1 1 0 0 .2 8 2 .4 2 1 0

4 ) B ecau se o f th e sp ec ifica tio n o f b e in g p u m p ed to tw o tim es th resh o ld w e a lso k n o w th e in itia l in vers io n 2 4 .8 4 1 0

th

o th

N N A l cm cm cm a to m s

n n a to m s

R T 10 10

1 2

Problem 4 continuation.5) Photon lifetim e of the passive cavity. First let us calculate the cavity round trip tim e

2 2 20 8 1 1.45 1 1.448 8 48.068 1.603 10 3 10

1

air s s g

RTo

a b c

l n l n lns

c

R R T T T

2 2 022

17 17 16m ax

cpl

1 .6 4.341 1 0.7 0.95

6) M axim um photon # in the cavity

Φ ln 1.21 10 1.21 10 ln 2 3.71 102 2

7) C alculate coupling efficiencycoupling loss per

ss sll

d

o th th o

th

nseT e

n n n n photonsn

2 02

8 1634m ax

m ax 6 9

round trip 1 0.7 0.3 0.815total loss per round trip 1 1 0.7 0.95 0.368

8) T he output pow er at the m axim um of the pulse3 10 3.71 100.815 6.6 10 1.3

1.053 10 4.34 10

sl

cplo

e

P h

0817 34

6

1

9) Assum e that the fraction of the initial inversion converted to photons

0.65

3 104.84 10 6.6 10 1.053 1010) T he output energy 0.815 0.652 2

24

11) T he pulse w

o fx

oout cpl x

M W

n nn

n hvW

m J

6m ax

0.024idth 181.31 10

outWt nsP

8

1.946 um

Laser Physics I PH 481/581-3A (Mirov)Exam II (10/24/11)

=12 m

Two important methodological problems related to diode pumped solid state lasers

Assume ring cavity & clockwise traveling wave

R=1

R=1R=1

Exper. 1: R1<1; Exper. 2: R2<1;

1. Internal lossestimation