1

Tentative Schedule:

Date, Place & Time Topics1 Aug. 28 (Mo) 394; 5:00- 6:15 Introduction, Spontaneous and Stimulated Transitions (Ch. 1) – Lecture

Notes2 Aug. 30 (We) 394; 5:00-6:15 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.6 before class

Sep.4 (Mo) No classes Labor Day Holiday3 Sep. 6 (We) 394; 5:00-6:15 Optical Frequency Amplifiers (Ch. 2.1-2.4) – Lecture Notes

Problem solving for Ch.14 Sep. 11 (Mo) 394; 5:00-6:15 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.20 before class

5 Sep. 13 (We) 394; 5:00-6:15 Problem solving for Ch.2 Introduction to two Practical Laser Systems (The Ruby Laser, The Helium Neon Laser) (Ch. 3) – Lecture Notes

6 Sep. 18 (Mo) 394; 5:00-6:15 Review Chapters 1 & 2 – Lecture Notes7 Sep. 20 (We) 394; 5:00-6:15 Exam 1 Over Chapters 1-3; Grades for exam 18 Sep. 25 (Mo) 394; 5:00-6:15 Exam 1 problem solving. Passive Optical Resonators (Lecture notes)9 Sep. 27 (We) 394; 5:00-6:15 Passive Optical Resonators (Lecture notes). 10 Oct. 2 (Mo) 394; 5:00-6:15 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. 9

11 Oct. 4 (We) 394; 5:00-6:15 Optical Resonators Containing Amplifying Media (4.1-2).12 Oct. 9 (Mo) 394; 5:00-6:15 Optical Resonators Containing Amplifying Media (Ch.4.3-4.7) Homework

4: Ch. 4 problems 4.7 and 4.9. Due Oct 16.13 Oct. 11 (We) 394; 5:00-6:15 Laser Radiation (Ch. 5.1-5.4)14 Oct. 16 (Mo) 394; 5:00-6:15 Control of Laser Oscillators (6.1-6.3) Homework 5: Ch. 5 problems 5.1 and

5.5. Due Oct 23.15 Oct. 18 (We) 394; 5:00-6:15 Control of Laser Oscillators (6.4-6.5) and exam 2 review16 Oct. 23 (Mo) 394; 5:00-6:15 Optically Pumped Solid State Lasers (7.1-7.11)17 Oct. 25 (We) 394; 5:00-6:15 Optically Pumped Solid State Lasers (7.1-7.11)18 Oct. 30 (Mo) 394; 5:00-6:15 Exam 2 Over Chapters 4-6 Grades for exam 2

Exam 2 correct solution; Homework 6 Due Nov.6; Article on Cr:CdSe19 Nov. 1 (We) 394; 5:00-6:15 Optically Pumped Solid State Lasers (7.16-7.17)20 Nov. 6 (Mo) 394; 5:00-6:15 Optically Pumped Solid State Lasers (7.16-7.17) Homework 7 Due Nov. 1321 Nov. 8 (We) 394; 5:00-6:15 Optically Pumped Solid State Lasers (7.14-7.15) Supplemental material for

Homework 6–diode pumped LiF:F2- laser

22 Nov. 13 (Mo) 394; 5:00-6:15 Spectroscopy of Common Lasers and Gas Lasers (Ch. 8.1-8.10 and class material) Voluntary supplemental homework 6A design of RT CW Fe:ZnSe laser Due Nov.27

23 Nov. 15 (We) 394; 5:00-6:15 Gas lasers (Ch. 8.4 -8.10); Molecular Gas lasers I (Ch. 9.1-9.5) Nov.20 (Mo) No classes Thanksgiving - no classes held Nov.22 (We) No classes Thanksgiving - no classes held 24 Nov. 27 (Mo) 394; 5:00-6:15 Molecular Gas lasers I (Ch. 9.1-9.5) Homework 8 Due Dec. 425 Nov. 29 (We) 394; 5:00-6:15 Molecular Gas Lasers II (Ch. 10.1-10.8) and review for exam 3 (Ch. 10.1-

10.8) Homework 9 Due Dec 6 26 Dec. 4 (Mo) 394; 5:00-6:15 Exam 3 Over Chapters 7-10 Grades; Exam 3 Correct solution27 Dec. 6 (We) 394; 5:00-6:15 Review for Final 28 Dec. 11 (Mon) in CH 394 FINAL EXAM Over Chapters 1-10 (4:15-6:45pm) in CH 394 Final

Grades

2

Laser Physics II (PH582 Spring 2018) Tentative Schedule: # Date Text Topics1 Jan 8 (Mo) LEO Ch11.1-11.4, Class Lecture Tunable Lasers, Organic Dye Lasers 2 Jan 10 (We)

LEO Ch11.1-11.4, Class Lecture Tunable Solid State Lasers, Alexandrite & Ti-Sapph.

Lasers, TM:II-VI Lasers(Class Lecture) Homework 1, Due January 24, 2016

3 Jan 15 (Mo) MLK Holiday No classes 4 Jan 17 (We)

LEO Ch11.1-11.4, Class Lecture Tunable Solid State Lasers, Alexandrite & Ti-Sapph.

Lasers, TM:II-VI Lasers(Class Lecture) Jan 22 (Mo) Class Lecture Color Center Lasers5 Jan 24 (We) Exam 1 - Grades Exam 1 over chapter 11 – Correct Solution 6 Jan 29 (Mo) Ch 12.1-12.7 and class lecture Semiconductor Lasers, Semiconductor Physics

Background 7 Jan 31 (We) Ch 12.1-12.7 and class lecture Semiconductor Lasers, Semiconductor Physics

Background, Homework 2, Due February 7, 20168 Feb 5 (Mo) (Ch.12.8-12.15) Semiconductor Lasers9 Feb 7 (We) (Ch.12.8-12.15)

(Class Lecture, Ch.13) Semiconductor Lasers Ray Tracing in an Optical System Homework 3, Due March 5, 2016

10 Feb 12 (Mo) (Class Lecture, Ch.13) Semiconductor problem Solving Ray Tracing in an Optical System

11 Feb 14 (We) (Class Lecture or Ch.16.1-16.7) Gaussian Beams12 Feb 19 (Mo) (Class Lecture or Ch.16.1-16.7) Gaussian Beams13 Feb 21 (We) (Class Lecture or Ch.15 and

Ch.16.8-16.14)Optical Cavities

14 Feb 26 (Mo) (Class Lecture or Ch.15 and Ch.16.8-16.14)

Optical Cavities; Three and four Mirror Focused Cavities

15 Feb 28 (We) (Ch.16.8-16.14) Optical Cavities; Cavities for Producing Spectral Narrowing of Laser Output Sample Problems for Test 2

16 Mar 5 (Mo) Exam 2 Grades Exam 2 over chapters 13-16 Correct Solutions17 Mar 7 (We) (LEO Ch. 17) Optics of Anisotropic Media Homework #4 problems

17.2; 17.3; 17.4; 17.5 ch.17 LEO Due March 16. Mar 12 (Mo) Spring Break No classes Mar 14 (We) Spring Break No classes 18 Mar 19 (Mo) (LEO Ch. 17) Optics of Anisotropic Media19 Mar 21 (We) (LEO Ch. 19, 20) Wave Propagation in Nonlinear Media Homework # 5 du

March 28 20 Mar 26(Mo) (LEO Ch. 19,20) 2nd Harm. Generation. Up and Down-Conversion, Optic

Parametr. Amplification;21 Mar 28 (We) (LEO Ch. 19,20) 2nd Harm. Generation. Up and Down-Conversion, Optic

Parametr. Amplification22 Apr 2 (Mo) (LEO Ch. 18) The Electro-Optics and Acousto-Optic Effects and

Modulaton of Light Beams Homework #6 due April 9 Homework #5 review

23 April 4 (We) (LEO Ch.21.1-21.6) Detection of Optical Radiation24 April 9 (Mo) (LEO Ch.21.6-21.8) Noise in Photodetectors Homework #7 due April 1625 April 11 (We) (LEO Ch.21.6-21.8) Photodiode Arrays and CCDs; Sample problems for test 26 April 16 (Mo) Exam 3 Grades Exam 3 over chapters 18-22 Correct Solutions27 April 18 (We) Review for Final Review for Final 28 April 23 (Mo) FINAL GRADES FINAL EXAM Over Chapters 11-22 and class notes

4:15-6:45pm CH 394

Review for Final

3

4

5

What we want to find is as follows: 1) Saturation intensity at pump and lasing wavelength 2) Effective length of the crystal  3) Optimal output coupler  4) Survival (photon) factor S for the passive cavity 5) Threshold power for a mode diameter of 200 m  6) Pump power necessary for providing 30W of 4400nm output power 

Solution: 1) Saturation intensity at 4400 nm

834

95 2

18 2 92

3 10 /6.62 104400 10

1.08 10 /1.1 10 380 10

es

e

m sJsmhvI W cm

cm s

 

2

834

95 2

18 2 9

1 ; 1 (branching factor)( )

3 10 /6.62 102800 10

2.07 10 /0.9 10 380 10

psp p

p a p

sp

hvI

v

m sJsm

I W cmcm s

 

6

2) Effective length of the crystal

0 18 19 1

1

Assume absorption utilization efficiency 0.90.9 10 1 10 9

Assume pump intensity is 3 times above pump saturation intensity0.9 3 3

9

a

p a o

paeff o

p sp

N cm

Id mm

I cm

 

1) Optimal output coupler  

20

2 218 2 19 3 1

1 12

2 2

2

2

Assuming high gain medium approximation1ln

1 11.1 10 1 10 111ln 11 0.3 0.03 0.3 3.291

1 1Assume 0.50; Actual 1.69Assume 0.70; Act

eff loss eff

o e

T d dT T

N cm cm cmT cm cm cm cm

T TTT

2

2

ual 3.53Assume 0.65; Actual 2.91Assume 0.68; Actual 3.265Optimal transmission of the output coupler is 68%.

TT

 

7

4) Survival (photon) factor S for the passive cavity   

2 2 0.5 0.32(1 ) 0.32 0.237loss effdS e T e  

5) Threshold power for a mode diameter of 100 m  

( )

5 25 2

( )

25 2

( ) ( )

1ln

28001; 0.9; 0.636; 0.0074400

(1.08 10 / ) 1ln 2.72 10 /1 0.9 0.636 0.237

(0.01)2.72 10 / 214

sp thr

p a q

pp a q qe

e

p thr

p thr p thr

IIs

W cmI W cm

P I A W cm W

 

 

R1  R2 

8

6) Pump power necessary for providing 30W of 4400nm output power

( )

2

( ) ( )

( )

30

0.02 0.531 1 0.9625

1 0.9 0.636 0.53 0.30

30 1000.30

100 21 121 - realistic from the first glance

q

out

out p a c p p thr

c

out p p thr p p thr

p p thr

p

P W

P P P

TS

P P P P P

P P W

P W

 

7) Experimental verification of spinning disk Fe:ZnSe laser of radius 11 mm rotating with 10000 rev/min and pumped by 40 W at 2800 nm radiation from spinning ring Cr:ZnSe laser demonstrated no lasing at all. The reason of the failure is that the experimental arrangement was not able to sustain room temperature of the active zone of the crystal. Our estimation of the steady state temperature of the active zone in spite of the using compressed air for cooling of the spinning Fe:ZnSe element the temperature of the pumped zone exceeded 100C which stimulated temperature quenching of Fe:ZnSe up to 20 ns.  

9

6 2

5 224

At this temperature the lifetime of Fe:ZnSe decreased to 20 ns due to temperature quenching .

increased by factor 19 and reached 3.9 10 / . At pump intensity

40 5.1 10 / , whic100 10

4

sp

p

I W cm

WI W cm

h is ~8 times smaller than we don't saturate

the gain medium, and hence, don't have lasing.

spI

10

8) What is the reason of temperature increase in the active zone of a spinning Fe:ZnSe gain element. 

4

4

Let us calculate time necessary for active zone of the spinning element with radius R=1.1 cm spinjing at 10000rev/min to pass through the pump causitcs of diameter 100 m.

100 10

100 10

t

rt cm

cmt

6

263 11 3

6

8.7 101min 210000 1.1min 60sec 1

During this time the pumped volume of Fe:ZnSe of diameter 100um and length 3 mm

100 10(3 10 ) 2.36 10

4

will absorb energy 40 8.7 10

srev cmrad

mV m m

Q P t W s

4

3 11 33

0.35

Since

3.5 10 8.30.339 10 5270 2.36 10

mJ

Q c V T

Q JT Cc V J kg m

kg C m

11

This temperature increase of the pump volume happens in 8.7 us of pumping.

1The period of one complete revolution is 61min10000min 60sec

During this time the heat cannot dissipate completely fro

msrev

m the pumped zone and

after one revolution the pumped zone will be further heated to 16.6 and so on until

the pumped zone will reach 100C steady state temperature.

Possible soution - use spining cavi

C

ty approach with effective cooling of the Fe:ZnSe element

through a headspreader.

12

LASER PHYSICS I PH 581-VT (MIROV) Exam 3 (12/04/17)

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

ALL QUESTIONS ARE WORTH 50 POINTS ------------------------------------------------------------------------------------------------------------------------------------------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 andbranching 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

WORK ONLY 3 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

13

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

14

3. Consider a laser system made of a cascade of three lasers: a laser, emitting at 500 nm that pumps Ti:Al2O3

laser, that pumps a Nd:YAG laser. Suppose that the green laser has a threshold power Pth1=0.75 W and aslope efficiency s1=13%, the Ti:Al2O3 laser has a threshold power Pth2=1.7 W and a slope efficiencys2=15% and the Nd:YAG laser has a threshold power Pth3=1 W and a slope efficiency s3=12%. Calculatethe pump power that must be provided to the green laser to get an output power Pout3=0.75 W from theNd:YAG laser.

3 3 2 3

The expression for the output power from the Nd:YAG laser is

(1)

Eq 1 can be rewritten by expressing the output power from t

out s p thP P P

2

3 3 2 1 2 3

1

3 3 2 1 1

he Ti-sapphire laser

(2)

Eq 2 can be rewritten by expressing the output power from the green laser

p

out s s p th th

p

out s s s p th t

P

P P P P

P

P P P P

2 3

3 3 3 3 2 2 3 2

(3)

where is the pump power provided to the green laser.

One can readily solve eq 3 to obtain a a function of other variables

h th

p

p

out s th s s th s sp

P

P

P

P P PP

1 1

1 2 3

2

(4)

0.75 0.12 1 0.12 0.15 1.7 0.12 0.15 0.13 0.75 385.6 3.9 100.13 0.15 0.12

s th

s s s

p

P

P W W

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

5.

Exam 1 (09/20/17)

-487.571

1.85x10-10 J

LASER PHYSICS I PH 581-VTA (MIROV) Exam II (10/30/17)

STUDENT NAME: _____Key________________ STUDENT id #: ___________________________ --------------------------------------------------------------------------------------------------------------------------------------------

ALL QUESTIONS ARE WORTH

37.5 POINTS (WORK OUT ANY 4 PROBLEMS) ------------------------------------------------------------------------------------------------------------------------------------------

NOTE: Clearly write out solutions and answers (circle the answers) by section for each part (a., b., c., etc.) 1. A Fabry-Perot interferometer consisting of two identical mirrors, air-spaced by a distance

L, is illuminated by a monochromatic em wave of tunable frequency. From ameasurement of the transmitted intensity versus the frequency of the input wave we findthat the free spectral range of the interferometer is 3x109 Hz and its resolution is 30 MHz.Calculate the spacing L of the interferometer, its finesse, and the mirror reflectivity.

Opened textbook, opened notes

11 1

9 1

1) For a Fabry-Perot interferometer made of air-spaced mirrors, the free spectral range is:

. Hence, the mirror spacing in our case is given by:2

3 10 502 2 3 10

2) The fine

FSR

FSR

cvL

c mm sL mmv s

9

6

sse of the interferometer, i.e. the ratio of free spectral range to width of the3 10transmission peak, is : 100

30 103) The finesse is a function of mirror reflectivity, in the case of

FSRv HzFv Hz

22

equal mirrors

we have , which gives the equation1

2 1 0,

the solution of which is 0.968

RFR

R RF

R

26

3. A laser (=10.6 m, =3x10-25 m2, =4 s) measured to have an intensity of 0.3 W/cm2

emerging from one end of the laser, which has two identical mirrors each with a transmission of 10%. The gain of the laser is also measured to be 0.5. What is the optimum output mirror transmission?

34 102

4 25

0

3

6.6 10 3 101. 1.56 /10.6 10 3 10 4(1 ) 1.56 (1-A-0.9)2. ( ln ) 0.3= (0.5 ln 0.9)

2 2 1 2 1-0.92.5 10

3. 1; 0.0328 3%

s

out s

opt oopt o

hvI W cm

I I A R L RR

AT L T A L AA A

4. A helium-neon laser transition (0.6328 m) is Doppler broadened with a FWHM of1.5 GHz. Assume the pumping and the saturated signal gain coefficient are four timesthe threshold value, and the cavity is 100 cm long.

(a) Find the number of longitudinal modes that can oscillate simultaneously. (Hint: 2)(22ln

)()(

D

o

vvv

oth evv ). (b) Suppose all the modes are locked together: (1) What is the pulse spacing? (2) Estimate the pulse width.

6.7 ns

5. (a) What would be the minimum pulse duration of a mode-locked chromium doped ZnS laser (gain bandwidth is 600 nm, central wavelength o is 2350 nm)? (b) What would be the coherence time and coherence length of the output beam? (c) If the separation between mirrors is 1.8 m, the ZnS gain element is 1 cm long, and theindex of refraction of ZnS crystal is approximately 2.3. What would be the separationbetween mode-locked pulses?

8 913

2 9 2

a) the mode-locked pulse width (bandwidth limited)1 , where is the width of the gain profile

3 10 (600 10 ) 3.26 10(2350 10 )

~ 301b) ~ 30 ; 9

c) Pulse spacing

c c c

c Hz

fs

fs L c m

t

8

2 1 (1.8 0.01) (2.3 0.01)12.1

3 10ns

6. Consider the active medium Cr:ZnSe (refractive index n=2.49, gain bandwidth (FWHM) =860 nm, central wavelength o=2400 nm. (a) Consider first a resonator with length L=20 cm, employing a rod of length l=1 cm.

Find the number of longitudinal modes falling within the FWHM gain bandwidth. (b) Consider then a resonator made upon coating the end mirrors directly onto the active

material surfaces (microchip laser). What is the maximum thickness l that allows oscillation of only one longitudinal mode?

8 913

2 9 2

3 10 (860 10 ) 4.48 10(2400 10 )

c Hz

4.48x10^13 6.4

2.49x4.48x10^132.7 m

Three 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

Laser slope efficiency

Pout, W

Ppump, WPthr

tan

Laser slope efficiency= tan outs p a qe c

pump thr

PP P

Pout

Ppump

32

33

3. A continuous wave Ho:YAG (2090 nm) laser is longitudinally pumped at 1908 nm. The laser mode has a

spot size of 1 mm and the length of the cavity is 10 cm; the stimulated emission cross-section is e= 12.9x10-

21 cm2 and the upper level lifetime is =8.5 ms. Assume that an output coupler with a transmission T=30% isused, passive cavity losses are 2% per pass, branching ratio p=1, and a pump utilization efficiency a=80%.Calculate the threshold pump power, slope efficiency, as well as the pump power required to obtain anoutput power Pout=30W from this laser.

11 2

18 3

v 3

1 0.02 11) ln ln 1 0.70 0.019810 10

2) 1.54 10

3) P 25.9 /( )

4)

th

thth

th pth

qe a

Threshold gain R R cml

Population inversion N cm

N hvThe absorbed threshold pump power per unit volume W cm

v

The

2

2 0.02

834

25.9 0.1 / 4 10 2.0

(1 0.7) 305) 1 0.8 0.913 2.0 ; 2.0 47 ; =66.9%; Alternatively:[1 ( 0.7)] 0.669

3 106.6 10 2090 16)

vth th

out p a qe c p th p p slope

s

absorbed pump power P P V W

P P P P P We

hvI

92 2

21 3

2 0.02

2 0.02

0 864 / ; 864 0.1 / 4 6.812.9 10 8.5 10

1 6.87) ln (1 ) [1 ( 0.7)] 3.019081 0.82090

(1 0.7)8) 1 0.8 0.913 3.0 ;[1 ( 0.7)]

s s

s sth

p qe a p qe a

out p a qe c p th p

W cm P I A W

P PP S e WS

P P P Pe

30 3.0 46

0.669pP W