review of tm and ho materials;

National Aeronautics andSpace Administration

Laser Physics WorkshopTrondheim, Norway (June/July 2008)

Brian M. WalshNorman P. Barnes

NASA Langley Research CenterHampton, VA 23681 USA

Review of Tm and Ho Materials;Spectroscopy and Lasers

Laser Physics Workshop - Trondheim, Norway (June 30 - July 4, 2008)



“Lanthanum has only one oxidation state, the +3 state. Withfew exceptions, this tells the whole boring story about theother 14 lanthanides.”

G.C. Pimentel & R.D. Sprately,"Understanding Chemistry",Holden-Day, 1971, p. 862

So much for ‘Understanding Chemistry’…Let’s do some physics!

Prelude



Activity Input ResultsX-ray data andrefractive index

Energy levels, transitionprobabilities, ET parameters

QuantumMechanics

SpectroscopySmall spectroscopicSamples - inexpensive

Cross sections, lifetimes,energy levels, ET parameters

Laser research Laser quality samples(rods, discs, fibers

Laser demonstration,modeling

Materials meeting requirements

Best Materials Only

NASA - Laser Material Research



Remote Sensing Applications

2 Micrometerlaser

1 Micrometerlaser

Lower Troposphere & clouds

2X

DIAL: CO24XBackscatter Lidar: Aerosols/Clouds

2X OPO

Coherent Winds:

Altimetry:Surface Mapping

Oceanography

DIAL: OzoneBackscatter Lidar: Aerosols/Clouds

Noncoherent Winds:Mid/Upper Atmosphere

3X



E4

E3

relaxation

pump laser

relaxation

E2

E1

E3

E2

relaxation

pump laser

E1

(a) Three level laser (b) Four level laser

Quasi-4-Level Lasers

g0= ! e " Nu # " # 1( )CANs$% &' (small signal gain)

! = 1+flfu

γ = 2 for true 3-level-laser γ = 1 for true 4-level-laser

It looks like a three level laser, but behaves more nearly like a 4-level laser!

Criteria: γ < 1.5; Laser is quasi-4-level γ >1.5; Laser is quasi-3-level

Quasi-4-level Examples:

Nd: 4I3/2 → 4I9/2 (~ 0.94 µm)Yb: 2F5/2 → 2F7/2 (~ 1.0 µm)Er: 4I13/2 → 4I15/2 (~ 1.5 µm)Tm: 3F4 → 3H6 (~1.9 µm)Ho: 5I7 → 5I8 (~ 2.0 µm)

3-level example:Cr:Al2O3 - Ruby2E → 4A2 (0.69 µm)4-level example:Nd:Y3Al5O12 - YAG4F3/2 → 4I9/2 (1.064 µm)



z

y

x

z

y

x

Rrs

ra

rs • ra - 3 (ra• R )( rs• R )/ R2

Dipole-dipole Energy transferDexter averages over dipole orientation, integrates over distances

PSA = CDA/R6

Real situation: orientation and distance set by crystal lattice

N.P. Barnes, et al.,IEEE JQE, 32, 92 (1996)



Energy Transfer: Tm-Tm, Ho-Ho

Tm-Tm Energy transfer Ho-Ho Energy transferN.P. Barnes, B.M. Walsh, et al.,J. Opt. Soc. Am. B, 20, 1212 (2003)

B.M. Walsh, N.P. Barnes, et al., J. Non-Cryst. Sol., 352, 5344 (2006)



0

2000

4000

6000

8000

10000

12000

14000

16000

En

erg

y (

cm-1

)

Tm3+ Ho3+

3H6

3F4

3H5

3H4

5I8

5I5

5I6

5I7

P28 P

28

P41

P41

P38

P38

P27

P27

1

3

5

6

7

8

4

2

P71 P

71

P22

P22

P61

P61

P51

P51

!5

!3

!2

!4

!6

!7

3F33F2

5I4

5F5

Energy Transfer: Tm-Ho

Tm-Ho Energy transferB.M. Walsh, N.P. Barnes, et al., J. Appl Phys., 95, 3255 (2004)



0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.5 1.0 1.5 2.0

Ho:YAG decay

Tm:YAG decay

Norm

aliz

ed i

nte

nsi

ty

Time (ms)

0.0

0.2

0.4

0.6

0.8

1.0

0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0

Ho:YAG decay

Tm:YAG decay

Norm

aliz

ed i

nte

nsi

ty

Time (ms)

Short times: energy transfer Long times: thermalization

Decay of Tm 3F4 and Ho 5I7

Excitation of Tm 3F4 manifold



P28 P71 P28 P71

E7ZL

E7

E8

E2ZL

E2

E1

Ho Tm

Forward and Backward transferP28/P71 = [Z7T Z1T/Z2T Z8T] exp[(E2ZL - E7ZL)/kT]



Laser Modeling

• Useful tool- Predicting and diagnosing laser performance- Understanding the physics

• Rate equation approach- Coupled set of complex equations- Laser simulation on the computer

• Many parameters needed- Laser parameters- Spectroscopic parameters- Quantum Mechanical Model

• Modeling of pulsed Tm:Ho lasers- Agrees reasonably well with experiment



Ng

N1

N2

N3 fast decay

fast decay

laserpump

Ng+ N

2= N

t

dN2

dt= Wp Ng ! BqN2 !

N2

"

dq

dt= V

aBqN

2!q

"c

Nt = total density of laser atoms (1/cm3)Ni = population density of states (1/cm3)τ = spontaneous lifetime of level 2 (s)τc = lifetime of photons in the resonator (s)Va = laser-active volume (cm3)Wp = pump rate from g to 3 (1/s)B = Stimulated emission coefficient (1/s)q = number of photons in cavity (no units)

(See O. Svelto, “Principles of Lasers”)

Rate Equation Approach



Coupled Rate Eqns. - Tm:Ho Model

dn1dt

= !Rp 1! exp(!"a!n1)#$ %& +n2' 2

+(41' 4n4 + n2n8p28 ! n7n1p71 ! n4n1p41 + n2

2p22

+n2n7p27 ! n5n1p51 ! n6n1p61 + n3n8p38dn2dt

= !n2' 2

+(32' 3n3 +

(42' 4n4 ! n2n8p28 + n7n1p71 + 2n4n1p41 ! 2n2

2p22 ! n2n7p27 + n5n1p51

dn3dt

= !n3' 3

+(43' 4n4 + n6n1p61 ! n3n8p38

dn4dt

= Rp 1! exp(!"a!n1)#$ %& !n4' 4

! n4n1p41 + n22p22

dn5dt

= !n5' 5

+ n2n7p27 ! n5n1p51

dn6dt

= !n6' 6

+(56' 5n5 ! n6n1p61 + n3n8p38

dn7dt

= !n7' 7

+(67' 6n6 +

(57' 5n5 + n2n8p28 ! n7n1p71 ! n2n7p27 + n5n1p51 ! " se (f7n7 ! f8n8 ))

dn8dt

= !n7' 7

! n2n8p28 + n7n1p71 +" se (f7n7 ! f8n8 ))

d)dt

= !)' c

+ c!

Lopt

" se (f7n7 ! f8n8 )) + c!

Lopt

n7' 7B



Spectroscopic Parameterslevel I.R. E (exp.)

(cm-1)

E (theo.)

(cm-1)

!E

(cm-1)

level I.R. E (exp.)

(cm-1)

E (theo.)

(cm-1)

!E

(cm-1)

1 "3,4 0 0 0 14 "2 5157.1 5157.5 0.4

2 "2 7.5 6.1 0.4 15 "3,4 5161.5 5161.1 0.4

3 "2 27.6 26.9 0.7 16 "1 5167.0 5167.4 0.4

4 "1 47.2 48.2 1.0 17 "2 5168.6 5169.5 0.9

5 "1 57.8 55.1 2.7 18 "3,4 5190.6 5189.4 0.6

6 "3,4 76.2 77.8 1.6 19 "1 5211.7 5210.1 1.6

7 "1 222.0 222.1 0.1 20 "3,4 5229.6 5233.4 3.8

8 "1 - 279.7 - 21 "2 5235.3 5239.1 3.8

9 "3,4 - 284.9 - 22 "2 5295.0 5295.2 0.2

10 "2 - 288.9 - 23 "3,4 5299.1 5297.3 1.2

11 "1 - 305.1 - 24 "1 5301.6 5298.2 2.4

12 "3,4 315.0 315.6 0.6

13 "2 332.0 333.7 1.7

Energy Levels(Thermal population)

0.0

0.10

0.20

0.30

0.40

740 750 760 770 780 790 800 810 820 830 840

Tm:YLF

Tm:LuLF

Cro

ss S

ecti

on (

x10

-20 c

m2)

Wavelength (nm)

Pump absorption(absorption cross section)

0.0

0.20

0.40

0.60

0.80

1.00

1.2

1850 1900 1950 2000 2050 2100 2150

Ho:YLF

Ho:LuLF

Cro

ss S

ecti

on (

x10

-20 c

m2)

Wavelength (nm)

Laser emission(emission cross section)

0.0

0.20

0.40

0.60

0.80

1.0

0 10 20 30 40 50 60 70 80

Ho:YLF

Ho:YAG

Norm

aliz

ed I

nte

nsi

ty

Time (ms)

Ho: 5I7 ! 5I

8 decay

Decay Dynamics(ET parameters, lifetimes)

Judd-Ofelt Analysis(Radiative lifetime, branching ratios)



Laser ParametersLaser crystal

Pumped volume

Active volume of the laserLaser mode volume l

M1 M2

Va =1

E0

2E(x, y, z)

2dxdydz

!"

"

#!"

"

#0L

# The volume of the laser mode that spatially overlapswith the pumped volume in the laser medium

1

!c

=c

2Lopt

ln(R mRL )The cavity photon lifetime that accounts for the removal ofphotons due to mirror losses and internal losses.



0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

2.5 3.5 4.5 5.5 6.5 7.5

LuLF model

YLF model

Las

er e

ner

gy (

J)

Pump energy (J)

0.0

0.2

0.4

0.6

0.8

1.0

2.5 3.5 4.5 5.5 6.5 7.5

LuLF experiment

YLF experiment

Las

er e

ner

gy (

J)

Pump energy (J)

Parameter YLF experiment LuLF experiment % difference YLF model LuLF model % difference

Threshold 3.22 J 2.74 J 14.9% 4.00 J 3.46 J 13.5 %

Slope efficiency 0.2003 0.2216 9.6% 0.2002 0.2168 7.6%

Tm:Ho:YLF/LuLF Modeling

Diode laser side-pumped experiment vs. model

Walsh, Barnes, Petros, Yu, Singh, J. Appl. Phys. 95, 3255 (2004)



• Laser physics predicts high efficiency- No Tm:Ho up-conversion or energy sharing- Ho:Ho up-conversion minimal

• Diode pumped Tm:YLF/Tm:fiber & direct diode pump- Overlaps with Ho:YAG/LuAG absorption

• Ho:YAG and Ho:LuAG- Ho:YAG has higher absorption- Ho:LuAG has lower thermal population

• Low quantum defect- implies low heat deposition- minimal thermal focusing

Recent Developments: Tm-pump Ho



Tm-YLF Pump Ho:YAG Scheme

Dichroic

[email protected]µm



0.5m RC

Diode

Laser

Lens

f=125mm

Dichroic


[email protected]µmTm:YLF

disc

Output

mirrorRG-1000

filter

Aperture

Lens

f=100mm

Ho:YAG

laser rod

HR

2.1µm

Output mirror

0.5m RC

Diode Laser pumped Tm:YLF laser

Tm:YLF pumped Ho:YAG laser

Laser lines

Pump lines



0.0

1.0

2.0

3.0

4.0

5.0

0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0

Ho

la

ser

ener

gy

(m

J)

Tm pump energy (mJ)

0.0

0.10

0.20

0.30

0.40

0.50

1.905 1.906 1.907 1.908 1.909 1.910 1.911

Slo

pe

effi

cien

cy

Pump wavelength (µm)

0.0

0.10

0.20

0.30

0.40

0.50

0.00 0.05 0.10 0.15 0.20 0.25 0.30

Slo

pe

effi

cien

cy

-ln (Rm

)

0.0

0.10

0.20

0.30

0.40

0.50

0 4 8 12 16 20 24 28 32 36

Slo

pe

effi

cien

cy

Ho rod length (mm)

Slope efficiency = 41%Threshold = 3.28 mJ

Tm-YLF Pump Ho:YAG (Pulsed)



Tm-fiber Pump Ho:YAG Scheme0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0.01.8 1.9 2.0 2.1

0

1

2

3

4

6.02 m2.76 mGrating

Wavelength in micrometers

!/2

Laserdiode

Laserdiode

Dichroic Tm:glass

600 g/mmgrating

HR

Ho:YAG



Tm-fiber Pump Ho:YAG (cw)

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0.00.0 0.5 1.0 1.5 2.0 2.5 3.0

Pump power in W

Absorption in Ho:YAG Ho:YAG Laser Performance(absorption efficiency ≈ 0.35)

0.5

0.4

0.3

0.2

0.1

0.00.0 0.5 1.0 1.5 2.0 2.5 3.0

Pump power in W

Ho:YAG

(!s = 0.37, Eth = 1.45 W)

Ho:YAG, 0.010 Ho, 8.0 mm



• Quasi-4-level lasers- Look like 3-level, behave more like 4-level.- Based on physics

• Energy transfer- Prolific in Tm and Ho materials- Distinction: classical vs. crystal

• Modeling- Based on rate equations- Agrees reasonably well with experiment

• Laser schemes- Tm:YLF pump Ho:YAG- Tm:fiber pump Ho:YAG

Summary



Brian M. WalshLaser Remote Sensing BranchEmail: [email protected]: 757 864-7112

NASA LangleyResearch Center

review of tm and ho materials;

Technology

levellaser tm

laser researchrods

laser performance

level laser g0

level ho

norway junejuly

level national aeronautics

tmho energy transfer