Paths to a Brighter Sodium Laser Guide Star
Paul Hillman, Tom Kane, and Craig Denman
CfAO Fall Science Retreat - Laser Workshop
FASORtronics LLC
4 Nov 2012
1
Outline
• Review Laser Guide Star Brightness
• History of LGSPulsed Computer Code
• Sodium atom energy levels/states
• Brightness increase method 1: Repumping
• Na Doppler velocity distribution in mesosphere
• Brightness increase method 2: Linewidth broadening
• Atomic Recoil
• Brightness increase method 3: Chirp
• Atomic precession in geomagnetic field
• Brightness increase method 4: Resonant pulsing at Larmor frequency
• Results, comparison to CW
• Frequency of short pulses to eliminate spot elongation
• Possible Laser Design
• Conclusion
2012 CfAO Fall Science Retreat - Laser Workshop
4 Nov 2012
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History of Laser Guide Star returns
Average Power
(W)
Spot Size, 2/e2
(arcsec)
~ψ
(ph/atom/sr/sec/(
W/m2))
Facility
Year
Return
(ph/cm2/sec/W)
UofA
1997
1200
1
3
274
Lick
1996
10
12
2
21
Keck
2001
10
12 - 15
1.8 x 2.3
21
Palomar
2005
60 - 80
6-8
3
169
SOR
2005
100
40 - 50
4 x 3.4
212
Gemini North 2007
27
6 @ meas
1.3
114
VLT
2006
54
10
1.25
114
SOR
2006
200
40a + 10b
4 x 3.4
423
2012 CfAO Fall Science Retreat - Laser Workshop
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LGSPulsed Computer Code History
• Atomic Density Matrix (Simon Rochester, Dmitry Budker, UC Berkeley)
• a package for Mathematica that facilitates analytic and numerical
density-matrix calculations in atomic and related systems
• LGSBloch (Simon Rochester, Rochester Scientific, Ron Holzlöhner, ESO)
• A Mathematica package which is an extension to the Atomic Density
Matrix package that contains routines for calculating the return flux from
optically excited alkali atoms, specifically designed for Na atoms in the
mesosphere. Mostly CW beams as it computes the steady state
solution to atomic states for each velocity class.
• LGSPulsed (Simon Rochester, Rochester Scientific)
• A subset of LGSBloch in C to deal mostly with dynamics of pulsed
beams.
2012 CfAO Fall Science Retreat - Laser Workshop
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Sodium D2 Transitions
• Using circular polarization, ∆mF
= 1 for each absorption.
M F' = - 3
2P
-2
-1
0
1
2
3
F'=
3
 =
4 2.4 MH z
3/2
2
1
0
3p
- 1 5.9 MH z
- 5 0.3 MH z
- 6 6.1 MH z
D2a
2P
1/2
 = 5 8 9 .1 5 90 5 n m
• ∆mF = 1, 0, -1 for each
spontaneous emission.
• Driven to mF = 2 in the ground
state, atoms become optically
trapped and the
• F=2, mF=2⬌F’=3, mF’=2
D1
D2
=
5 89 .1 5 8 3 3 n m
• transition dominates.
D 2b
 = 5 8 9 .1 5 7 09 n m
F=
2
3s
2S
 =
6 6 4.4 M Hz
1/2
1 - 11 0 7.3 M Hz
“Bohr”
M od el
N a D Fine
S truc ture
Na D 2 H yp erfin e
Stru ctu re
• All 8 ground state levels
equally populated at thermal
equilibrium as:
• ∆E < KT.
•
Method 1: pump atoms out of
lower ground state.
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Method 1: increasing the repump ratio
• Promotes atoms out of the lower
ground so they don’t accumulate
there.
• Assumed D2b intensity
obtained by phase modulation
at 1.72 GHz, there is a
second sideband of equal
power that does not interact
with sodium.
• Over a 3x improvement over
no repump.
• fraction power at D2b slightly
dependent intensity.
Intensity 47 W/m2
Linewidth: 9 MHz
B = 0.5 g and 90° to beam in this and all
following examples unless noted
2012 CfAO Fall Science Retreat - Laser Workshop
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Maxwell Boltzmann Velocity Distribution
• Natural linewidth of Na is 10
MHz.
• Doppler broadened linewidth
is about 1 GHz or 100
velocity groups.
• Method 2: As atoms become
saturated at higher
intensities, widening the
linewidth of the laser lowers
the spectral intensity and
excites other nearby velocity
classes.
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Method 2: Increasing the Linewidth
• As intensity increases
optimum linewidth
increases (until linewidth
approaches Doppler
width).
• Without Repump return
actually decreases with
increasing linewidth!
• Intensity: 500
W/m2
• D2b fraction: 14%
• 40% improvement over 0 MHz
Intensity
(W/m2)
Optimal Linewidth
(MHz)
20
7
47
9
100
12
200
20
500
30
1000
50
2000
100
2012 CfAO Fall Science Retreat - Laser Workshop
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Atomic Recoil
• Each absorption and
emission cycle causes a
50 kHz velocity shift.
• After many cycles atoms
move to a higher velocity
class and are not as
strongly resonant with
laser wavelength.
• Method 3: Chirp the
laser so its wavelength
follows the velocity group
with the highest
population.
2012 CfAO Fall Science Retreat - Laser Workshop
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Method 3: Chirp Demonstration
Velocity Group Population (a.u.)
• Average Return: ψ = 592
ph/atom/sr/sec/(W/m2)*.
• No chirp Return: ψ = 330
ph/atom/sr/sec /(W/m2)*.
total ground states
total excited states
• Chirp rate dependent on
Intensity.
• Less effective for broad
linewidths.
Doppler Shift (MHz) or Velocity Group
Intensity: 47 W/m2
Chirp Rate: 0.75 MHz/µs
Linewidth: 0 MHz
Repump ratio: 10%
• *B = 0 G, so ψ is higher in
these examples.
2012 CfAO Fall Science Retreat - Laser Workshop
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Atomic Precession
• The optically pumped Na atom
has a dipole cross section that is
shaped like a peanut, maximized
along the beam axis.
• The atoms precess around
magnetic field.
• Precession causes the long axis
of the ‘peanut’ to misalign from
the beam.
• The Larmor Precession
frequency, fL, is proportional to
the B field; at B= 0.5 G, fL = 350
kHz, or τ = 2.8 µs.
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Decreased Return When Beam is not Parallel with B
CW beam
LineWidth = 9 MHz
Repump = 15%
• As previously theorized and
shown in sky tests, return
flux decreases as the angle
between the beam and
geomagnetic field
approaches 90°.
B field = 0.5 Gauss
Intensity for CW beam = 47 W/m2
2012 CfAO Fall Science Retreat - Laser Workshop
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Method 4: SOLUTION, Pulse Resonantly at Larmor
• Use a pulsed beam with a
frequency equal to the Larmor
frequency, fL.
• Atom is only pumped when its
highest cross section is aligned with
the beam.
• To our knowledge this has not been
proposed before.
• Note: Just amplitude modulating a
CW beam is not beneficial, as
~90% of your light would be lost.
An appropriate pulsed laser is
necessary.
2012 CfAO Fall Science Retreat - Laser Workshop
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Decreased Return When Beam is not Parallel with B
Pulsed at Larmor freq.
LineWidth = 150 MHz
Repump = 9.2%
DutyCycle = 9%
CW beam
LineWidth = 9 MHz
Repump = 15%
• Return from pulsed beam
80% greater for angles > 60°
for same average power.
• Pulse frequency does not
depend on Intensity.
B field = 0.5 Gauss
Intensity for CW beam = 47 W/m2
Avg. Intensity = 47 W/m2,
Peak Intensity for pulsed beam = 522 W/m2
Pulse Frequency = 350 kHz
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What Observatories Could Benefit?
Geomagnetic Main Field Inclination
• Inclination for Hawaii (H) is
~35°
• For zenith propagation
angle between beam
and B is 55°
H
• Inclination for Antofagasta,
Chile (A) is ~ 20°
A
• For zenith propagation
angle between beam
and B is 70°
NOAA/NGDC & CIRES - 2010
Green line is 0°
Bold Contours are 20° intervals
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Summary of Results - Pulsed at Larmor Frequency
Pulsed at Larmor Frequency
Average Intensity
(W/m2)
Flux
(ph/atom/sr/sec)
ψ = Flux/Intensity
ph/atom/sr/sec
(W/m2)
Repump
Duty cycle
Linewidth (MHz)
20
7,311
365.6
0.098
0.088
82
47
17,220
366.4
0.092
0.09
150
100
34,160
341.6
0.088
0.1
220
200
60,540
302.7
0.096
0.12
275
500
117,750
235.5
0.11
0.15
370
1,000
184,908
184.9
0.10
0.17
490
2,000
281,180
140.6
0.11
0.22
550
Angle between beam and B field is 90°
B = 0.5 G
2012 CfAO Fall Science Retreat - Laser Workshop
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Summary of Results - CW
CW
Average Intensity
(W/m2)
Flux
(ph/atom/sr/sec)
ψ = Flux/Intensity
ph/atom/sr/sec
(W/m2)
Repump
Duty cycle
Linewidth (MHz)
20
3487
174
0.15
1
7
47
7847
167
0.15
1
9
100
16,334
163
0.14
1
12
200
32,600
163
0.14
1
20
500
78,946
158
0.12
1
30
1,000
160,217
160
0.14
1
50
2,000
314,034
157
0.12
1
100
Angle between beam and B field is 90°
B = 0.5 G
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Comparison of Efficiencies
Pulsed at fL
CW
• Plotted is the mesospheric
flux (ph/atom/sr/sec)
divided by Intensity.
• CW is slightly lower than
Holzlöhner (2009) as that
work only considered
power going into a single
side band, not two as
here.
Angle between beam and B field is 90°
B = 0.5 G
2012 CfAO Fall Science Retreat - Laser Workshop
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Photon Flux at Telescope, 0.6 - 1 arcsec seeing
Pulsed at fL
CW
Average Intensity
(W/m2)
laser Power
(W)
Flux
(ph/cm2/sec)
Stellar
Magnitude
Flux
(ph/cm2/sec)
Stellar
Magnitude
20
8.7
1,037
7.1
495
7.9
47
20.4
2,443
6.2
1,113
7.0
100
43.5
4,847
5.4
2,317
6.2
200
87.0
8,590
4.8
4,625
5.5
500
217.4
16,706
4.1
11,201
4.5
1000
434.8
26,235
3.6
22,732
3.8
2000
869.6
39,894
3.1
44,556
3.0
LGS size similar to Holzlöhner (2009), equivalent Gaussian FWHM = 40.4 cm.
Magnitude V = 4.7 for a flux of 10,000; Drummond (2004).
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Various values used
250 µs
Sodium column
density
4 x 1013
atoms/m2
velocity changing collision rate
50 µs
Mean sodium layer
height
92 km
rate atoms enter and leave the
beam
100 sec-1
Mesosphere Temperature
185 K
Angle between beam
and B field, unless
noted
90°
spin relation rate
Geomagnetic Field
0.5 G
2012 CfAO Fall Science Retreat - Laser Workshop
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Extension to Single Pulse at a time in Mesosphere
• Outside sub-apertures of large
telescopes see an elongated spot
with CW lasers. Ideally only a
single short pulse in the
mesosphere at a time optimum.
Intensity = 3.7 W/m2 frequency = 30.4 kHz
• Technique is effective at fL / N
sub-harmonics. Rep. rate needs
to be < spin relaxation rate.
• Wrong pulse rep. rate could result
in a 40% decrease in photon
return.
Intensity = 3.9 W/m2 frequency = 29.2 kHz
For both plots:
Peak Intensity = 500 W/m2
Pulse length = 0.26 µs
Linewidth = 150 MHz,
Repump = 9%
(Parameters were not optimized)
2012 CfAO Fall Science Retreat - Laser Workshop
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Laser Design to Obtain Beam Pulse Format
• System still based on sum
frequency mixing in LBO
• LBO in 1.319µ laser cavity to
obtain high intensity
• 1.064µ is generated by a low
power laser, modulated, then
amplified. It is only single pass
through LBO.
• High power, single spatial
mode fiber amplifiers are
COTS.
• Since 1.064µ is not resonant in
a cavity, it can have a large
linewidth
• Modulation is done at low
power
• Only one resonant cavity
2012 CfAO Fall Science Retreat - Laser Workshop
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Conclusions
• For the 20 W average power lasers being considered for today’s sodium guide
stars, a 2.2 x higher return can be obtained by pulsing mesospheric sodium
resonantly at the Larmor frequency (~ 175 - 350 kHz)
• Improvement is noted even at fL/10, 35 kHz or τ = 28 µs, as this is still much
less than the spin relaxation rate of ~250µs. This is an ideal pulse format for
large telescopes that want a pulse format to eliminate LGS elongation.
• The higher return flux needed for AO in the visible is possible from sodium
laser guide stars, the return flux is not limited by sodium abundance or sodium
physics but by appropriate beam pulse format and laser power.
• Chirping a narrow linewidth laser can increase return by over a factor of 2, but
becomes less beneficial for broader linewidths.
2012 CfAO Fall Science Retreat - Laser Workshop
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