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,
2 Dept. of Physics, UC Berkeley
AO4ELT3
Florence, 28 May 2013
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:
1. Raise cw power  Laser development (e.g., Raman fiber amplifiers)
2. Raise coupling efficiency sce  Explore new laser formats
Will focus on option 2
Slide 2
Sky Maps Paranal
Sim. cw return flux on ground [106 ph/s/m2]
ζ = 60°
 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
3.6!
B
What factors limit the return flux?
 Three major impediments of sodium excitation:
1) Larmor precession (m: angular momentum z-component)
B
m
Laser
θ
2) Recoil (radiation pressure) 
v
+ 50 kHz
spont.
emission
time
excited (P3/2)
3) Transition saturation
(at 62 W/m2 in fully pumped sodium)
ground (S1/2)
Slide 4
Draw 3D surface where distance from origin equals the probability
to be found in a stretched state (m = F) along this direction.
z
z
y
z
y
x
y
x
x
Unpolarized
Oriented
Aligned
Sphere centered
at origin,
equal probability
in all directions.
“Pumpkin” pointing
in z-direction 
preferred direction.
“Peanut” with axis
along z 
preferred axis.
Credit: D. Kimball, D. Budker et al., Physics 208a course at UC Berkeley
Visualization of Atomic Polarization

B
torque causes polarized atoms to precess:
Credit: E. Kibblewhite
Credit: D. Kimball, D. Budker et al., Physics 208a course at UC Berkeley
Precession in Magnetic Field
Efficiency per Atom with Repumping
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
500
=0
400
q = 0.12
300
200
100
0
-2
10
(ph/s/sr/atom)/(W/m 2)
Model narrow-line cw
laser, circular polarization
 (ph/s/sr/atom)/(W/m 2)
Peak efficiency
250
 = /2
circular
-1
10
0
1
2
10
10
Irradiance (W/m2)
10
3
10
200
150
100
20W cw laser
in mesosphere
q = 0.12
Transition
saturation
62 W/m2
Is there a way to harness the efficiency
at peak of green curve?
50
linear
q=0
Slide 7
Larmor Resonant Pulsing
Pulse the laser resonantly with Larmor rotation: like stroboscope,
Larmor period: 3 – 6.2 μs (Field in Paranal: 0.2251G 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
 (ph/s/sr/atom)/(W/m 2)
Paranal simulation: sce = 374 ph/s/W/(atoms/m2), vs.
500
ca. sce ≈ 250 for cw (all at 90° and Paranal conditions)
400
hence about 1.5 times more (!)
=0
sce becomes almost independent of field angle 300
200
Increased irradiance also broadens the resonance
100
*) PNAS 10.1073/pnas.1013641108 (2011) (arXiv:0912.4310)
2)
0
-2
10
 = /2
circular
-1
10
0
10
1
10
10
250
Slide 8
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 (Sdamping time)
Slide 9
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%
Ground States
582 W/m2
Excited States
F=m=1
Slide
10
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
Ip = 221 W/m2
Ip = 27 W/m2
1% detuned
2% detuned
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 –55... +55 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 timeconsuming (order 48–72 CPU h per irradiance step)
Issue: Avoid F=1 downpumping, in particular at 60 MHz offset
Slide
12
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
Graphic by Unger
D2b
Excitation from D2a
narrow-band laser
D2a
Prefer (F = 2, m = ±2)  (F = 3, m = ±3) cycling transition
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
Slide
14
Hyperfine State Populations
Excitation 
Time 
F=1
ground
states
Larmor
period
F=2
ground
states
Plot hyperfine state evolution for a
selection of velocity classes
Visualize Larmor precession,
downpumping, excitation
excited
states
first
pulse
Slide
15
Hyperfine State Analysis: 9 × 40 MHz
60 MHz
Slide
16
Conclusions
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
Slide
17
FINE
GRAZIE!
Slide 18
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?
Slide
19
Hyperfine State Analysis: 4 ×110 MHz
Slide
20
Some Commercial Frequency Shifters 1
Brimrose Corp.
http://www.brimrose.com/pdfandwordfiles/aofshift.pdf
Slide
21
No More Plots…How Do We Build it?
Slide
22
Some Commercial Frequency Shifters 2
Brimrose Corp.
http://www.brimrose.com/pdfandwordfiles/aofshift.pdf
Slide
23
Some Commercial Frequency Shifters 3
A.A
http://opto.braggcell.com/index.php?MAIN_ID=102
REFERENCE
Materi Wavelength
Aperture(mm²) Frequency(MHz)
al
(nm)
Polar
Deflection angle
Efficiency
(mrd)
MQ200-B30A0.7-244266-Br
SiO2
244-266
0.7 x 3
200 +/- 15
Lin
1.3 @266nm
> 60
MQ110-B30A1-UV
SiO2
325-425
1x2
110 +/- 15
Lin
1.8 @355nm
> 60
Quartz
458-650
2x2
110 +/- 15
Lin
2.8 @ 532nm
> 70
MT350-B120-A0.12-VIS TeO2-L
450-700
0.12 x 2
350 +/- 50
Lin
15.2 @532nm
> 60
MT250-B100-A0.5-VIS
TeO2-L
450-700
0.5 x 2
250 +/- 50
Lin
12.6 @532nm
> 60
MT250-B100-A0.2-VIS
TeO2-L
450-700
0.2 x 1
250 +/- 50
Lin
12.6 @532nm
> 60
MT200-B100A0.5-VIS
TeO2-L
450-700
0.5 x 2
200 +/- 50
Lin
12.6 @532nm
> 60
MT200-B100A0.2-VIS
TeO2-L
450-700
0.2 x 1
200 +/- 50
Lin
12.6 @532nm
> 60
MT110-B50A1-VIS
TeO2-L
450-700
1x2
110 +/- 25
Lin
6.3 @532nm
> 60
MT110-B50A1.5-VIS
TeO2-L
450-700
1.5 x 2
110 +/- 25
Lin
6.3 @532nm
> 60
MT80-B30A1-VIS
TeO2-L
450-700
1x2
80 +/- 15
Lin
3.8 @532nm
> 65
MT80-B30A1.5-VIS
TeO2-L
450-700
1.5 x 2
80 +/- 15
Lin
3.8 @532nm
> 65
MCQ110-B30A2-VIS
Slide
24
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)
Egg-laying wool milk swine:
Broadband, highly efficient,
high power, no aberrations,
constant pointing.
And cheap!
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?
Slide
25
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, http://budker.berkeley.edu/ADM/

Written in Mathematica v.6+, publicly available
[“Optimization of cw sodium laser guide star efficiency”, Astronomy & Astrophysics 520, A20]
Slide
26
EOMs for Repumping
Vendors: New Focus,
Qubig
Taken from www.qubig.de
Used free-space EOM in
“Wendelstein”
transportable LGS system
Affordable way to retrofit pulsed lasers
Issues with peak power
(photodarkening, coatings,
cooling)
Slide
27
What is crucial for good return flux?
Most Important:
Laser power, sodium abundance (seasonal)
Circular polarization state ☼
D2b repumping (power fraction q≈12%, 1.710 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 (☼)
Slide
28
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
http://budker.berkeley.edu/Physics208/D_Kimball/
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
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
Optical pumping
Optical pumping process polarizes atoms.
Optical pumping is most efficient when
laser frequency (l) is tuned to
atomic resonance frequency (0).
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

dF

, F
dt
 
= B =


 
gF  B F  B
L = gF B B