Larmor-resonant Sodium Excitation for Laser Guide Stars
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Transcript of Larmor-resonant Sodium Excitation for Laser Guide Stars
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Larmor-resonant Sodium Excitation for Laser Guide Stars
Ron HolzlöhnerS. Rochester 1
D. Budker 2,1
D. Bonaccini CaliaESO LGS Group
1 Rochester Scientific LLC, 2 Dept. of Physics, UC Berkeley
AO4ELT3Florence, 28 May 2013
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Slide 2
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
Are E-ELT LGS lasers powerful enough?
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Sky Maps ParanalSim. cw return flux on ground [106 ph/s/m2]
ζ = 60°B
3.6!
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
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Slide 4
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)
What factors limit the return flux?
mB
Laser
time
v
spont.emission
excited (P3/2)
ground (S1/2)
+ 50 kHzθ
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Aligned“Peanut” with axis
along z preferred axis.
z
x
y
Oriented“Pumpkin” pointing
in z-direction preferred direction.
z
x
y
UnpolarizedSphere centered
at origin,equal probabilityin all directions.
z
x
y
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.
Cre
dit:
D. K
imba
ll, D
. Bud
ker e
t al.,
Phy
sics
208
a co
urse
at U
C B
erke
ley
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torque causes polarized atoms to precess: B
Precession in Magnetic Field
Credit: E. Kibblewhite Cre
dit:
D. K
imba
ll, D
. Bud
ker e
t al.,
Phy
sics
208
a co
urse
at U
C B
erke
ley
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Slide 7
Efficiency per Atom with Repumping
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
10-2
10-1
100
101
102
103
0
100
200
300
400
500
(
ph/s
/sr/a
tom
)/(W
/m2 )
circular
= 0
= /2
q = 0.12
10-2
10-1
100
101
102
103
0
50
100
150
200
250
(
ph/s
/sr/a
tom
)/(W
/m2 )
linear
q = 0.12
q = 0
10-2
10-1
100
101
102
103
0
100
200
300
400
500
I (W/m2)
(
ph/s
/sr/a
tom
)/(W
/m2 )
circular, q=0
= 0
= /2
no recoil
Irradiance (W/m2)
Is there a way to harness the efficiency at peak of green curve?
20W cw laserin mesosphere
Peak efficiency
Transitionsaturation62 W/m2
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Slide 8
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
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
Larmor Resonant Pulsing
10-2
10-1
100
101
102
103
0
100
200
300
400
500
(
ph/s
/sr/a
tom
)/(W
/m2 )
circular
= 0
= /2
q = 0.12
10-2
10-1
100
101
102
103
0
50
100
150
200
250
(
ph/s
/sr/a
tom
)/(W
/m2 )
linear
q = 0.12
q = 0
10-2
10-1
100
101
102
103
0
100
200
300
400
500
I (W/m2)
(
ph/s
/sr/a
tom
)/(W
/m2 )
circular, q=0
= 0
= /2
no recoil
*) PNAS 10.1073/pnas.1013641108 (2011) (arXiv:0912.4310)
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Slide 9
B = 0.23 G, θ = 90°, q = 9%, 150 MHz linewidthReturn is fairly linear vs. irradianceSteady state reached after ca. 50 periods = 300μs (S-damping time)
Some Simulation Details
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Slide 10
Can achieve 14 Mph/s/m2 at 10W, 28 Mph/s/m2 at 20W (D2a+D2b)
Peak efficiency reached above 10WVery strong atomic polarization towards (F=m=2) of 60–70%
Simulated Performance
F = m = 2
F = m = 1
582 W/m2Ground States Excited States
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A small rep rate detuning shows up first at low peak irradianceReduces pumping efficiency, induces polarization oscillationsVariation in Paranal: –0.22%/year, –0.39%/10km altitude
Larmor Detuning
On resonance 1% detuned 2% detuned
Ip = 27 W/m2
Ip = 221 W/m2
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Slide 12
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 highNumerical 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
Best Laser Format?
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Downpumping
D2b
D2a
Gra
phic
by
Ung
er
Prefer (F = 2, m = ±2) (F = 3, m = ±3) cycling transition
3S1/2 3P3/2 transition
F = I + J : Total angular momentumI = 3/2 : Nuclear spinJ = L + S : Total electronic angular momentum (sum of orbital and spin parts)
40 MHz grid
Excitation from D2anarrow-band laser
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Slide 14
Scan across >= 9 discrete velocity classesBlue-shift to achieve “snowplowing” via atomic recoilAvoid downpumping leave 40 MHz or >> 60 MHz gaps, but……without exceeding the sodium Doppler curve (1.05 GHz FWHM)
Frequency Scanning Schemes
9 × 40 MHz 4 × 110 MHz
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Slide 15
Hyperfine State PopulationsTi
me
Excitation
excitedstates
F = 1groundstates
F = 2groundstates
Larmorperiod
firstpulse
Plot hyperfine state evolution for a selection of velocity classesVisualize Larmor precession, downpumping, excitation
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Slide 16
Hyperfine State Analysis: 9 × 40 MHz
60 MHz
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Slide 17
Larmor precession reduces the return flux efficiency by factor 2; forces high irradiance to combat population mixingCan 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 buildFormat optimization is work in progress
Conclusions
CW laser format is good, but leaves room for improvement
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F I N EGRAZIE!
Slide 18
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Slide 19
Would like to frequency modulate over 100 MHz (or even 300 MHz) at >80% efficiencyEither sawtooth or step function with 160 kHz rep rate (Paranal)Need to maintain excellent beam quality and beam pointingOption1: 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+efficiencyOption 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?
Frequency Shifters
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Slide 20
Hyperfine State Analysis: 4 ×110 MHz
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Slide 21
Some Commercial Frequency Shifters 1
Brimrose Corp.http://www.brimrose.com/pdfandwordfiles/aofshift.pdf
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Slide 22
No More Plots…How Do We Build it?
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Slide 23
Some Commercial Frequency Shifters 2
Brimrose Corp.http://www.brimrose.com/pdfandwordfiles/aofshift.pdf
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Slide 24
Some Commercial Frequency Shifters 3A.Ahttp://opto.braggcell.com/index.php?MAIN_ID=102
REFERENCE Material
Wavelength (nm) Aperture(mm²) Frequency(MHz) Polar Deflection angle
(mrd) Efficiency
MQ200-B30A0.7-244-266-Br SiO2 244-266 0.7 x 3 200 +/- 15 Lin 1.3 @266nm > 60
MQ110-B30A1-UV SiO2 325-425 1 x 2 110 +/- 15 Lin 1.8 @355nm > 60
MCQ110-B30A2-VIS Quartz 458-650 2 x 2 110 +/- 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 1 x 2 110 +/- 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 1 x 2 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
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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? Slide 25
To Frequency Shift, or not?
Egg-laying wool milk swine:Broadband, highly efficient,high power, no aberrations,constant pointing.And cheap!
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Slide 26
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]
Bloch Equation Simulation
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Slide 27
EOMs for RepumpingVendors: New Focus, Qubig
Used free-space EOM in “Wendelstein” transportable LGS system
Issues with peak power (photodarkening, coatings, cooling)
Take
n fro
m w
ww
.qub
ig.d
e
Affordable way to retrofit pulsed lasers
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Slide 28
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)
What is crucial for good return flux?
Could improve on the crucial parameters (☼)
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MF = -1 MF = 0 MF = 1
z
F = 1
F’ = 0
Light linearly polarized along z can create alignment along z-axis.
Optical pumping
Credit: D. Kimball, D. Budker et al., Physics 208a course at UC Berkeleyhttp://budker.berkeley.edu/Physics208/D_Kimball/
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MF = -1 MF = 0 MF = 1
z
F = 1
F’ = 0
Light linearly polarized along z can create alignment along z-axis.
Medium is now transparent to lightwith linear polarization along z !
Optical pumping
Credit: D. Kimball, D. Budker et al., Physics 208a course at UC Berkeley
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MF = -1 MF = 0 MF = 1
z
F = 1
F’ = 0
Light linearly polarized along z can create alignment along z-axis.
Medium strongly absorbs lightpolarized in orthogonal direction!
Optical pumping
.
Credit: D. Kimball, D. Budker et al., Physics 208a course at UC Berkeley
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Optical pumping process polarizes atoms.
Optical pumping is most efficient whenlaser frequency (l) is tuned to
atomic resonance frequency (0).
Optical pumping
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Precession in Magnetic Field
Interaction of the magnetic dipole momentwith a magnetic field causes the angular momentum
to precess – just like a gyroscope!
= dF
dt
= B = B
gF B F B
dFdt B
= = L = gF B B
B
, F