4 nov 2012 1 paths to a brighter sodium laser guide star paul hillman, tom kane, and craig denman...

4 Nov 2012 1

Paths to a Brighter Sodium Laser Guide Star

Paul Hillman, Tom Kane, and Craig DenmanCfAO Fall Science Retreat - Laser Workshop

FASORtronics LLC

4 Nov 20122012 CfAO Fall Science Retreat - Laser Workshop 2

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


History of Laser Guide Star returns

Facility YearReturn

(ph/cm2/sec/W)Average Power

(W)Spot Size, 2/e2

(arcsec)

~ ψ (ph/atom/sr/sec

/(W/m2))

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


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.


Sodium D2 Transitions

• Using circular polarization, ∆mF = 1 for each absorption.

• ∆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, m⬌ F’=2

• transition dominates.

• All 8 ground state levels equally populated at thermal equilibrium as:

• ∆E < KT.

• Method 1: pump atoms out of lower ground state.

3p

3s

2P3/2

2 P1/2

D1D2

2S1/2

F ' = Δν =

F = Δν =

012

M F' = -3 -2 -1 0 1 2 3

1

“Bohr”Mod el

N a D FineStructure

Na D 2 H yp erfine

Structu re

λ =

589.15833 nm

3 42.4 MH z

-15.9 MH z-50.3 MH z-66.1 MH z

664.4 M Hz

-1107.3 M Hz

2

D2a

λ = 589.15905 nm

D2b

λ = 589.15709 nm


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


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.


Method 2: Increasing the Linewidth

• Intensity: 500 W/m2

• D2b fraction: 14%

• 40% improvement over 0 MHz

• As intensity increases optimum linewidth increases (until linewidth approaches Doppler width).

• Without Repump return actually decreases with increasing linewidth!

Intensity(W/m2)

Optimal Linewidth (MHz)

20 7

47 9

100 12

200 20

500 30

1000 50

2000 100


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.


Method 3: Chirp Demonstration

• Average Return: ψ = 592 ph/atom/sr/sec/(W/m2)*.

• No chirp Return: ψ = 330 ph/atom/sr/sec /(W/m2)*.

• Chirp rate dependent on Intensity.

• Less effective for broad linewidths.

• *B = 0 G, so ψ is higher in these examples.

Doppler Shift (MHz) or Velocity Group

Vel

ocity

Gro

up P

opul

atio

n (

a.u.

)

Intensity: 47 W/m2

Chirp Rate: 0.75 MHz/µs

Linewidth: 0 MHz

Repump ratio: 10%

total ground states

total excited states


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.


Decreased Return When Beam is not Parallel with B

• As previously theorized and shown in sky tests, return flux decreases as the angle between the beam and geomagnetic field approaches 90°.

CW beamLineWidth = 9 MHz

Repump = 15%

B field = 0.5 Gauss

Intensity for CW beam = 47 W/m2


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.


Decreased Return When Beam is not Parallel with B

• Return from pulsed beam 80% greater for angles > 60° for same average power.

• Pulse frequency does not depend on Intensity.

Pulsed at Larmor freq.LineWidth = 150 MHz

Repump = 9.2%DutyCycle = 9%

CW beamLineWidth = 9 MHz

Repump = 15%

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


What Observatories Could Benefit?

• Inclination for Hawaii (H) is ~35°

• For zenith propagation angle between beam and B is 55°

• Inclination for Antofagasta, Chile (A) is ~ 20°

• For zenith propagation angle between beam and B is 70°

Geomagnetic Main Field Inclination

NOAA/NGDC & CIRES - 2010

H

A

Green line is 0°Bold Contours are 20° intervals


Summary of Results - Pulsed at Larmor Frequency

Pulsed at Larmor FrequencyAverage 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


Summary of Results - CW

CWAverage 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



Comparison of Efficiencies

• 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.

Pulsed at fL

CW



Photon Flux at Telescope, 0.6 - 1 arcsec seeing

Pulsed at fL CW

Average Intensity(W/m2)

laser Power(W)

Flux(ph/cm2/

sec)

StellarMagnitude

Flux(ph/cm2/

sec)

StellarMagnitude

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).


Various values used

spin relation rate 250 µsSodium column

density4 x 1013

atoms/m2

velocity changing collision rate

50 µsMean sodium layer height

92 km

rate atoms enter and leave the beam

100 sec-1

Mesosphere Temperature 185 K

Geomagnetic Field 0.5 GAngle between

beam and B field, unless noted

90°


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.

• 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

Intensity = 3.7 W/m2 frequency = 30.4 kHz

For both plots:Peak Intensity = 500 W/m2

Pulse length = 0.26 µs Linewidth = 150 MHz,Repump = 9%(Parameters were not optimized)


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


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.

4 nov 2012 1 paths to a brighter sodium laser guide star paul hillman, tom kane, and craig denman...

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