Presented at the Laser Physics Workshop - Trondheim, Norway (June 30 - July 4, 2008) Publication Reference: B.M. Walsh, “A Review of Tm and Ho Materials; Spectroscopy and Lasers,” Laser Physics, 19, 855-866 (2009).

1. Review of Tm and Ho Materials;
Spectroscopy and Lasers
Brian M. Walsh
Norman P. Barnes
NASA Langley Research Center
Hampton, VA 23681 USA
Laser Physics Workshop - Trondheim, Norway (June 30 - July 4, 2008)
National Aeronautics and Laser Physics Workshop
Space Administration Trondheim, Norway (June/July 2008)

2. Prelude
“Lanthanum has only one oxidation state, the +3 state. With
few exceptions, this tells the whole boring story about the
other 14 lanthanides.”
G.C. Pimentel & R.D. Sprately,
quot;Understanding Chemistryquot;,
Holden-Day, 1971, p. 862
So much for ‘Understanding Chemistry’…
Let’s do some physics!
National Aeronautics and Laser Physics Workshop
Space Administration Trondheim, Norway (June/July 2008)

3. NASA - Laser Material Research
Activity Input Results
Quantum X-ray data and Energy levels, transition
Mechanics refractive index probabilities, ET parameters
Materials meeting requirements
Small spectroscopic Cross sections, lifetimes,
Spectroscopy Samples - inexpensive energy levels, ET parameters
Best Materials Only
Laser quality samples Laser demonstration,
Laser research
(rods, discs, fibers modeling
National Aeronautics and Laser Physics Workshop
Space Administration Trondheim, Norway (June/July 2008)

4. Remote Sensing Applications
4X DIAL: CO2
Backscatter Lidar: Aerosols/Clouds
2 Micrometer
laser Coherent Winds:
Lower Troposphere & clouds
3X
Noncoherent Winds:
Mid/Upper Atmosphere
1 Micrometer
2X Altimetry:
laser Surface Mapping
Oceanography
2X OPO
DIAL: Ozone
Backscatter Lidar: Aerosols/Clouds
National Aeronautics and Laser Physics Workshop
Space Administration Trondheim, Norway (June/July 2008)

5. Quasi-4-Level Lasers
It looks like a three level laser, but behaves more nearly like a 4-level laser!
E3 E4
relaxation relaxation
E2 E3
3-level example:
Cr:Al2O3 - Ruby
2E → 4A (0.69 µm)
2 pump laser pump laser
4-level example:
Nd:Y3Al5O12 - YAG
3/2 → I9/2 (1.064 µm)
4F 4 E2
relaxation
E1 E1
Quasi-4-level Examples: (a) Three level laser (b) Four level laser
g0 = ! e $quot; Nu # ( quot; # 1) C A Ns &
% ' (small signal gain)
Nd: 4I3/2 → 4I9/2 (~ 0.94 µm)
Yb: 2F5/2 → 2F7/2 (~ 1.0 µm) fl γ = 2 for true 3-level-laser
! = 1+
Er: 4I13/2 → 4I15/2 (~ 1.5 µm) fu γ = 1 for true 4-level-laser
Tm: 3F4 → 3H6 (~1.9 µm)
Criteria: γ < 1.5; Laser is quasi-4-level
Ho: 5I7 → 5I8 (~ 2.0 µm)
γ >1.5; Laser is quasi-3-level
National Aeronautics and Laser Physics Workshop
Space Administration Trondheim, Norway (June/July 2008)

6. Dipole-dipole Energy transfer
Dexter averages over dipole orientation, integrates over distances
PSA = CDA/R6
Real situation: orientation and distance set by crystal lattice
z N.P. Barnes, et al.,
IEEE JQE, 32, 92 (1996)
z
ra
y
R
rs
y x
x rs • ra - 3 (ra• R )( rs• R )/ R2
National Aeronautics and Laser Physics Workshop
Space Administration Trondheim, Norway (June/July 2008)

7. Energy Transfer: Tm-Tm, Ho-Ho
Tm-Tm Energy transfer Ho-Ho Energy transfer
B.M. Walsh, N.P. Barnes, et al., N.P. Barnes, B.M. Walsh, et al.,
J. Non-Cryst. Sol., 352, 5344 (2006) J. Opt. Soc. Am. B, 20, 1212 (2003)
National Aeronautics and Laser Physics Workshop
Space Administration Trondheim, Norway (June/July 2008)

8. Energy Transfer: Tm-Ho
16000 3F 5F
3 5
3F
14000 2
5I
4 3H 4
4
12000 5I
5 5
P 41 P 22 !4
!5
Energy (cm-1 )
10000 P 27 P 51
3H 5I 6
3 5 6
8000
P 38 P 61 !3 P 38 P 61 !6
6000 2 3F
4 5I 7
7
4000
P 28 P 71 P 41 P 22 P 27 P 51 !2 P 28 P 71 !7
2000
1 3H 5I 8
0 6 8
Tm3+ Ho3+
Tm-Ho Energy transfer
B.M. Walsh, N.P. Barnes, et al., J. Appl Phys., 95, 3255 (2004)
National Aeronautics and Laser Physics Workshop
Space Administration Trondheim, Norway (June/July 2008)

9. Decay of Tm 3F4 and Ho 5I7
Excitation of Tm 3F4 manifold
Short times: energy transfer Long times: thermalization
1.0 1.0
Ho:YAG decay
Tm:YAG decay
0.8 0.8
Normalized intensity
Normalized intensity
0.6 0.6
0.4 0.4
0.2 Ho:YAG decay 0.2
Tm:YAG decay
0.0 0.0
0.0 0.5 1.0 1.5 2.0 0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0
Time (ms) Time (ms)
National Aeronautics and Laser Physics Workshop
Space Administration Trondheim, Norway (June/July 2008)

10. Forward and Backward transfer
P28/P71 = [Z7T Z1T/Z2T Z8T] exp[(E2ZL - E7ZL)/kT]
E2
E7
E7ZL E2ZL
P28 P71 P28 P71
E1
E8
Ho Tm
National Aeronautics and Laser Physics Workshop
Space Administration Trondheim, Norway (June/July 2008)

11. 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
National Aeronautics and Laser Physics Workshop
Space Administration Trondheim, Norway (June/July 2008)

12. Rate Equation Approach
N g + N2 = N t
(See O. Svelto, “Principles of Lasers”)
dN 2 N
= Wp N g ! BqN 2 ! 2
dt quot;
N3 fast decay dq q
= Va BqN 2 !
N2 dt quot;c
Nt = total density of laser atoms (1/cm3)
pump laser Ni = population density of states (1/cm3)
τ = spontaneous lifetime of level 2 (s)
N1 τc = lifetime of photons in the resonator (s)
Va = laser-active volume (cm3)
fast decay
Ng Wp = pump rate from g to 3 (1/s)
B = Stimulated emission coefficient (1/s)
q = number of photons in cavity (no units)
National Aeronautics and Laser Physics Workshop
Space Administration Trondheim, Norway (June/July 2008)

13. Coupled Rate Eqns. - Tm:Ho Model
dn1 n (
= !R p #1 ! exp(!quot; a !n1 ) % + 2 + 41 n 4 + n 2 n 8 p 28 ! n 7 n1p 71 ! n 4 n1p 41 + n 2 p 22
$ & '2 '4 2
dt
+n 2 n 7 p 27 ! n 5 n1p 51 ! n 6 n1p 61 + n 3n 8 p 38
dn 2 n ( (
= ! 2 + 32 n 3 + 42 n 4 ! n 2 n 8 p 28 + n 7 n1p 71 + 2n 4 n1p 41 ! 2n 2 p 22 ! n 2 n 7 p 27 + n 5 n1p 51
dt '2 '3 '4 2
dn 3 n 3 ( 43
=! + n + n 6 n1p 61 ! n 3n 8 p 38
dt '3 '4 4
dn 4 n
= R p #1 ! exp(!quot; a !n1 ) % ! 4 ! n 4 n1p 41 + n 2 p 22
$ & '4 2
dt
dn 5 n
= ! 5 + n 2 n 7 p 27 ! n 5 n1p 51
dt '5
dn 6 n (
= ! 6 + 56 n 5 ! n 6 n1p 61 + n 3n 8 p 38
dt '6 '5
dn 7 n ( (
= ! 7 + 67 n 6 + 57 n 5 + n 2 n 8 p 28 ! n 7 n1p 71 ! n 2 n 7 p 27 + n 5 n1p 51 ! quot; se (f7 n 7 ! f8 n 8 ))
dt '7 '6 '5
dn 8 n
= ! 7 ! n 2 n 8 p 28 + n 7 n1p 71 + quot; se (f7 n 7 ! f8 n 8 ))
dt '7
d) ) n
= ! + c ! quot; se (f7 n 7 ! f8 n 8 )) + c ! 7 B
dt 'c Lopt Lopt ' 7
National Aeronautics and Laser Physics Workshop
Space Administration Trondheim, Norway (June/July 2008)

14. Spectroscopic Parameters
0.40 1.2
Tm:YLF Ho:YLF level I.R. E (exp.) E (theo.) !E level I.R. E (exp.) E (theo.) !E
Tm:LuLF Ho:LuLF (cm-1) (cm-1) (cm-1) (cm-1) (cm-1) (cm-1)
1.00 quot;3,4 0 quot;2
Cross Section (x10-20 cm2)
Cross Section (x10-20 cm2)
1 0 0 14 5157.1 5157.5 0.4
0.30 2 quot;2 7.5 6.1 0.4 15 quot;3,4 5161.5 5161.1 0.4
3 quot;2 27.6 26.9 0.7 16 quot;1 5167.0 5167.4 0.4
0.80
4 quot;1 47.2 48.2 1.0 17 quot;2 5168.6 5169.5 0.9
5 quot;1 57.8 55.1 2.7 18 quot;3,4 5190.6 5189.4 0.6
0.20 0.60 quot;3,4 76.2 quot;1
6 77.8 1.6 19 5211.7 5210.1 1.6
7 quot;1 222.0 222.1 0.1 20 quot;3,4 5229.6 5233.4 3.8
8 quot;1 - 279.7 - 21 quot;2 5235.3 5239.1 3.8
0.40
9 quot;3,4 - 284.9 - 22 quot;2 5295.0 5295.2 0.2
0.10
10 quot;2 - 288.9 - 23 quot;3,4 5299.1 5297.3 1.2
0.20 11 quot;1 - 305.1 - 24 quot;1 5301.6 5298.2 2.4
12 quot;3,4 315.0 315.6 0.6
0.0 13 quot;2 332.0 333.7 1.7
0.0
740 750 760 770 780 790 800 810 820 830 840 1850 1900 1950 2000 2050 2100 2150
Wavelength (nm) Wavelength (nm)
Pump absorption Laser emission Energy Levels
(absorption cross section) (emission cross section) (Thermal population)
1.0
Ho:YLF
Ho: 5I7 ! 5I8 decay Ho:YAG
0.80
Normalized Intensity
0.60
0.40
0.20
0.0
0 10 20 30 40 50 60 70 80
Time (ms)
Judd-Ofelt Analysis Decay Dynamics
(Radiative lifetime, branching ratios) (ET parameters, lifetimes)
National Aeronautics and Laser Physics Workshop
Space Administration Trondheim, Norway (June/July 2008)

15. Laser Parameters
Laser crystal
Pumped volume
M1 M2
l
Laser mode volume Active volume of the laser
1 L quot; quot;
Va = 2 # # #
2 The volume of the laser mode that spatially overlaps
E(x, y, z) dxdydz with the pumped volume in the laser medium
E0 0 !quot; !quot;
1 c The cavity photon lifetime that accounts for the removal of
= ln(R m R L )
! c 2L opt photons due to mirror losses and internal losses.
National Aeronautics and Laser Physics Workshop
Space Administration Trondheim, Norway (June/July 2008)

16. Tm:Ho:YLF/LuLF Modeling
1.0 0.8
LuLF experiment LuLF model
YLF experiment 0.7 YLF model
0.8
0.6
Laser energy (J)
Laser energy (J)
0.5
0.6
0.4
0.4 0.3
0.2
0.2
0.1
0.0 0.0
2.5 3.5 4.5 5.5 6.5 7.5 2.5 3.5 4.5 5.5 6.5 7.5
Pump energy (J) Pump energy (J)
Diode laser side-pumped experiment vs. model
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%
Walsh, Barnes, Petros, Yu, Singh, J. Appl. Phys. 95, 3255 (2004)
National Aeronautics and Laser Physics Workshop
Space Administration Trondheim, Norway (June/July 2008)

17. Recent Developments: Tm-pump Ho
• 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
National Aeronautics and Laser Physics Workshop
Space Administration Trondheim, Norway (June/July 2008)

18. Tm-YLF Pump Ho:YAG Scheme
Pump lines Tm:YLF pumped Ho:YAG laser
Laser lines
Output mirror
0.5m RC
Diode Laser pumped Tm:YLF laser
Diode
Laser Dichroic
HR@1.9µm Output Ho:YAG HR
Tm:YLF RG-1000 Lens
HT@0.79µm mirror laser rod 2.1µm
disc filter f=100mm
Lens
f=125mm Aperture Dichroic
HR@2.1µm
HT@1.9µm
HR@1.9µm
0.5m RC
National Aeronautics and Laser Physics Workshop
Space Administration Trondheim, Norway (June/July 2008)

19. Tm-YLF Pump Ho:YAG (Pulsed)
0.50 0.50
0.40 0.40
Slope efficiency
Slope efficiency
0.30 0.30
0.20 0.20
0.10 0.10
0.0 0.0
0 4 8 12 16 20 24 28 32 36 0.00 0.05 0.10 0.15 0.20 0.25 0.30
Ho rod length (mm) -ln (R m)
0.50 5.0
Slope efficiency = 41%
0.40 4.0
Threshold = 3.28 mJ
Ho laser energy (mJ)
Slope efficiency
0.30 3.0
0.20 2.0
0.10 1.0
0.0 0.0
1.905 1.906 1.907 1.908 1.909 1.910 1.911 0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0
Pump wavelength (µm) Tm pump energy (mJ)
National Aeronautics and Laser Physics Workshop
Space Administration Trondheim, Norway (June/July 2008)

20. Tm-fiber Pump Ho:YAG Scheme
4
0.9
0.8
0.7 3
0.6
0.5 2
0.4
0.3 6.02 m
1
0.2 2.76 m
0.1 Grating
0.0 0
1.8 1.9 2.0 2.1
Wavelength in micrometers
600 g/mm
grating
Dichroic Tm:glass
Laser
diode
!/2
Laser HR
diode
Ho:YAG
National Aeronautics and Laser Physics Workshop
Space Administration Trondheim, Norway (June/July 2008)

21. Tm-fiber Pump Ho:YAG (cw)
Ho:YAG, 0.010 Ho, 8.0 mm
0.8
0.5
0.7 Ho:YAG
(!s = 0.37, E th = 1.45 W)
0.6 0.4
0.5
0.3
0.4
0.3 0.2
0.2
0.1
0.1
0.0 0.0
0.0 0.5 1.0 1.5 2.0 2.5 3.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0
Pump power in W Pump power in W
Absorption in Ho:YAG Ho:YAG Laser Performance
(absorption efficiency ≈ 0.35)
National Aeronautics and Laser Physics Workshop
Space Administration Trondheim, Norway (June/July 2008)

22. Summary
• 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
National Aeronautics and Laser Physics Workshop
Space Administration Trondheim, Norway (June/July 2008)

23. NASA Langley Brian M. Walsh
Research Center Laser Remote Sensing Branch
National Aeronautics and Laser Physics Workshop
Email: brian.m.walsh@nasa.gov
Space Administration Trondheim, Norway (June/July 2008)
Phone: 757 864-7112