1. Larmor-resonant Sodium Excitation for Laser Guide Stars
Ron Holzlöhner
S. Rochester 1
D. Budker 2,1
D. Bonaccini Calia
ESO LGS Group
1 Rochester Scientific LLC, Dept. of Physics, UC Berkeley
AO4ELT3
Florence, 28 May 2013

2. Are E-ELT LGS lasers powerful enough?
E-ELT laser baseline: 20W cw with 12% repumping  5 Mph/s/m2 at Nasmyth (at zenith in median sodium; 12 Mph/s/m2 on ground)
There may be situations when flux is not sufficient for some instruments (low sodium, large zenith angle, non-photometric night, full moon, etc.)
No unique definition of LGS availability; details quite complicated
E-ELT Project has expressed interest in exploring paths to raise the return flux
Two avenues:
Raise cw power  Laser development (e.g., Raman fiber amplifiers)
Raise coupling efficiency sce  Explore new laser formats
Will focus on option 2

3. Sim. cw return flux on ground [106 ph/s/m2]
ζ = 60° B
3.6!
Sky Maps Paranal
Becoming more independent of field angle would be particularly beneficial in Paranal:
Flux varies strongly with angle to B-field
B-field inclination is only 21°  most of the time this angle is large

4. What factors limit the return flux?
Three major impediments of sodium excitation:
1) Larmor precession (m: angular momentum z-component)
2) Recoil (radiation pressure) 
3) Transition saturation
(at 62 W/m2 in fully pumped sodium) B m θ v
Laser
+ 50 kHz
spont.
emission
time
excited (P3/2)
ground (S1/2)

5. Visualization of Atomic Polarization
Draw 3D surface where distance from origin equals the probability to be found in a stretched state (m = F) along this direction.
Unpolarized
Sphere centered
at origin,
equal probability
in all directions. z x y
Oriented
“Pumpkin” pointing
in z-direction 
preferred direction. z x y
Aligned
“Peanut” with axis
along z 
preferred axis. z x y
Credit: D. Kimball, D. Budker et al., Physics 208a course at UC Berkeley

6. Precession in Magnetic Field
torque causes polarized atoms to precess:
  B
Credit: D. Kimball, D. Budker et al., Physics 208a course at UC Berkeley
Credit: E. Kibblewhite

7. Efficiency per Atom with Repumping
Peak efficiency
Model narrow-line cw laser, circular polarization
ψ : Return flux per atom, normalized by irradiance [unit ph/s/sr/atom/(W/m2)]
θ: angle of laser to B-field (design laser for θ = π/2)
Symbols: Monte Carlo simulation, lines: Bloch
Blue curve peaks near 50 W/m2, close to Na saturation at 60 W/m2: Race to beat Larmor
Irradiance (W/m2)
20W cw laser
in mesosphere
Transition
saturation
62 W/m2
Is there a way to harness the efficiency at peak of green curve?

8. Larmor Resonant Pulsing
Pulse the laser resonantly with Larmor rotation: like stroboscope, Larmor period: 3 – 6.2 μs (Field in Paranal: G at 92km)
Used for optical magnetometry: Yields bright resonance in D2a of about 20% at 0.3…1.0 W/m2, narrow resonance of ca. 1.5% FWHM *)
Recent proposal by Hillman et al. to pulse at 9% duty cycle, 20W average power, 47/0.09 = 522 W/m2 and a linewidth of 150 MHz  47/15 ≈ 3 W/m2/vel.class  near optimum avg. power
Paranal simulation: sce = 374 ph/s/W/(atoms/m2), vs.
ca. sce ≈ 250 for cw (all at 90° and Paranal conditions)
hence about 1.5 times more (!)
sce becomes almost independent of field angle
Increased irradiance also broadens the resonance
*) PNAS  /pnas (2011) (arXiv: )

9. Some Simulation Details
B = 0.23 G, θ = 90°, q = 9%, 150 MHz linewidth
Return is fairly linear vs. irradiance
Steady state reached after ca. 50 periods = 300μs (S- damping time)

10. Simulated Performance
Can achieve 14 Mph/s/m2 at 10W, 28 Mph/s/m2 at 20W (D2a+D2b)
Peak efficiency reached above 10W
Very strong atomic polarization towards (F=m=2) of 60–70%
F = m = 2
F = m = 1
582 W/m2
Ground States
Excited States

11. Larmor Detuning
A small rep rate detuning shows up first at low peak irradiance
Reduces pumping efficiency, induces polarization oscillations
Variation in Paranal: –0.22%/year, –0.39%/10km altitude
On resonance
1% detuned
2% detuned
Ip = 221 W/m2
Ip = 27 W/m2

12. Best Laser Format?
Lasers with pulses of ~0.5 μs and peak power 200W hard to build (150/2=75 MHz linewidth not large enough to sufficiently mitigate SBS)
Multiplex cw laser to avoid wasting beam power?
Spatiotemporally: use one laser to sequentially produce multiple stars
In frequency: Chirp laser continuously, e.g. from – MHz (11 vel.c.)
In frequency: Periodically address several discrete velocity classes
Or modulate the polarization state? (probably less beneficial)
Can in principle profit from “snowplowing” by up-chirping, although chirp rate of ~110 MHz/6.2μs = 17.7 MHz/μs is very high
Numerical optimization of modulation scheme; runs are time- consuming (order 48–72 CPU h per irradiance step)
Issue: Avoid F=1 downpumping, in particular at 60 MHz offset

13. Prefer (F = 2, m = ±2)  (F = 3, m = ±3) cycling transition
Downpumping
3S1/2  3P3/2 transition
F = I + J : Total angular momentum
I = 3/2 : Nuclear spin
J = L + S : Total electronic angular momentum (sum of orbital and spin parts)
40 MHz grid
D2b
Excitation from D2a
narrow-band laser
Graphic by Unger
D2a
Prefer (F = 2, m = ±2)  (F = 3, m = ±3) cycling transition

14. Frequency Scanning Schemes
Scan across >= 9 discrete velocity classes
Blue-shift to achieve “snowplowing” via atomic recoil
Avoid downpumping  leave 40 MHz or >> 60 MHz gaps, but…
…without exceeding the sodium Doppler curve (1.05 GHz FWHM)
9 × 40 MHz
4 × 110 MHz

15. Hyperfine State Populations
Excitation 
F = 1
ground
states
Plot hyperfine state evolution for a selection of velocity classes
Visualize Larmor precession, downpumping, excitation
F = 2
ground
states
Time 
excited
states
Larmor
period
first
pulse

16. Hyperfine State Analysis: 9 × 40 MHz

17. Conclusions CW laser format is good, but leaves room for improvement
Larmor precession reduces the return flux efficiency by factor 2; forces high irradiance to combat population mixing
Can mitigate population mixing by stroboscopic illumination resonant with Larmor frequency (~160 kHz in Chile, ~330 kHz in continental North America and Europe)
Realize with pulsed laser of ~20W average power and < 10% duty cycle, 150 MHz linewidth: Raise efficiency by factor 1.5 !
…which is hard to build (> 200 W peak power, M2 < 1.1)
Alternative: Frequency modulation (chirping/frequency multiplexing schemes)
Caveats: Observe 60 MHz downpumping trap and target ~3–5 W/m2/v.c. on time average, frequency sensitive, modulator not easy to build
Format optimization is work in progress
CW laser format is good, but leaves room for improvement

18. F I N E Grazie!
Slide 18

19. Frequency Shifters
Would like to frequency modulate over 100 MHz (or even 300 MHz) at >80% efficiency
Either sawtooth or step function with 160 kHz rep rate (Paranal)
Need to maintain excellent beam quality and beam pointing
Option1: Free-space AOM. Pro: Proven technique, reasonable efficiency. Con: 100+ MHz is very broadband, variation of beam pointing or position when changing frequency?
Option 2: Free-space EOM using carrier-suppressed SSB. Requires an interferometric setup, may be difficult to realize at high power+efficiency
Option 3: Modulate seed laser. Pro: Possibly reduce SBS (fiber transmission time is in μs range). Con: Cavity locking difficult (piezo bandwidth would need to be in MHz range), combine with PDH sidebands?

20. Hyperfine State Analysis: 4 ×110 MHz

21. Some Commercial Frequency Shifters 1
Brimrose Corp.

22. No More Plots…How Do We Build it?

23. Some Commercial Frequency Shifters 2
Brimrose Corp.

24. Some Commercial Frequency Shifters 3
A.A
REFERENCE
Material
Wavelength (nm)
Aperture(mm²)
Frequency(MHz)
Polar
Deflection angle (mrd)
Efficiency
MQ200-B30A Br
SiO2
0.7 x 3
200 +/- 15
Lin
> 60
MQ110-B30A1-UV
1 x 2
110 +/- 15
MCQ110-B30A2-VIS
Quartz
2 x 2
532nm
> 70
MT350-B120-A0.12-VIS
 TeO2-L
0.12 x 2
350 +/- 50
MT250-B100-A0.5-VIS
TeO2-L
0.5 x 2
250 +/- 50
MT250-B100-A0.2-VIS
0.2 x 1
MT200-B100A0.5-VIS
200 +/- 50
MT200-B100A0.2-VIS
MT110-B50A1-VIS
110 +/- 25
MT110-B50A1.5-VIS
1.5 x 2
MT80-B30A1-VIS
80 +/- 15
> 65
MT80-B30A1.5-VIS

25. To Frequency Shift, or not?
Seems that AOM/EOM specs are very challenging (no “eierlegende Wollmilchsau” in AOMs, quote by Mr. Jovanovic, Pegasus Optik GmbH)
Really no way to modulate in the IR and double?
Frequency shift is doubled, hence +/– 25 MHz may be enough
Could be done after seed laser with fiber-coupled AOM and thus also shift the PDH sidebands
Would need fast adjustment of optical path length in cavity (RF active crystal? LBO not suitable, but has been done e.g. with MgO:LiNbO3)
…or else consider a pulsed laser?
Egg-laying wool milk swine:
Broadband, highly efficient,
high power, no aberrations,
constant pointing.
And cheap!

26. Bloch Equation Simulation
Schrödinger equation of density matrix, first quantization
dρ/dt = Aρ + b = 0
Models ensemble of sodium atoms, 100–300 velocity groups
Takes into account all 24 Na states, Doppler broadening, spontaneous and stimulated emission, saturation, collisional relaxation, Larmor precession, recoil, finite linewidth lasers
Collisions change velocity and spin (“v-damping,S-damping”)
More rigorous and faster than Monte Carlo rate equations
Based on AtomicDensityMatrix package,
Written in Mathematica v.6+, publicly available
[“Optimization of cw sodium laser guide star efficiency”, Astronomy & Astrophysics 520, A20]

27. EOMs for Repumping Affordable way to retrofit pulsed lasers
Vendors: New Focus, Qubig
Used free-space EOM in “Wendelstein” transportable LGS system
Issues with peak power (photodarkening, coatings, cooling)
Taken from
Affordable way to retrofit pulsed lasers

28. What is crucial for good return flux?
Most Important:
Laser power, sodium abundance (seasonal)
Circular polarization state ☼
D2b repumping (power fraction q≈12%, GHz spacing) ☼
(Peak) power per velocity class ☼
Overlap with sodium Doppler curve (but: implicit repumping) ☼
For return flux on ground: zenith angle, atmospheric transmission2
Somewhat Important:
Angle to B-field (θ), strength of B-field |B| (hence geographic location)
Atomic collision rates (factor 10 variation across mesosphere)
Less Important:
Seeing, launched wavefront error, launch aperture (beware: spot size)
Sodium profile, spectral shape (for given number of velocity classes)
Could improve on the crucial parameters (☼)

29. Light linearly polarized along z can create alignment along z-axis.
Optical pumping
Light linearly polarized along z can create alignment along z-axis. z
F’ = 0
F = 1
MF = -1
MF = 0
MF = 1
Credit: D. Kimball, D. Budker et al., Physics 208a course at UC Berkeley

30. Optical pumping
Light linearly polarized along z can create alignment along z-axis. z
F’ = 0
F = 1
MF = -1
MF = 0
MF = 1
Medium is now transparent to light
with linear polarization along z !
Credit: D. Kimball, D. Budker et al., Physics 208a course at UC Berkeley

31. Optical pumping
Light linearly polarized along z can create alignment along z-axis. z
F’ = 0 .
F = 1
MF = -1
MF = 0
MF = 1
Medium strongly absorbs light
polarized in orthogonal direction!
Credit: D. Kimball, D. Budker et al., Physics 208a course at UC Berkeley

32. Optical pumping Optical pumping process polarizes atoms.
Optical pumping is most efficient when
laser frequency (l) is tuned to
atomic resonance frequency (0).

33. Precession in Magnetic Field
Interaction of the magnetic dipole moment
with a magnetic field causes the angular momentum
to precess – just like a gyroscope! 
 =   B  B 
 = dF dt  
, F
gF B F  B  dF dt
  B =  
L = gF B B