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

AO4ELT3Florence, 28 May 2013

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?

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

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

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.

Kim

ball,

D.

Bud

ker

et a

l., P

hys

ics

208

a co

urse

at

UC

Ber

kele

y

torque causes polarized atoms to precess: B

Precession in Magnetic Field

Credit: E. Kibblewhite Cre

dit:

D.

Kim

ball,

D.

Bud

ker

et a

l., P

hys

ics

208

a co

urse

at

UC

Ber

kele

y

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

/ato

m)/

(W/m

2 )

circular

= 0

= /2

q = 0.12

10-2

10-1

100

101

102

103

0

50

100

150

200

250

(ph/

s/sr

/ato

m)/

(W/m

2 )

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

/ato

m)/

(W/m

2 )

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

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

/ato

m)/

(W/m

2 )circular

= 0

= /2

q = 0.12

10-2

10-1

100

101

102

103

0

50

100

150

200

250

(ph/

s/sr

/ato

m)/

(W/m

2 )

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

/ato

m)/

(W/m

2 )

circular, q=0

= 0

= /2

no recoil

*) PNAS 10.1073/pnas.1013641108 (2011) (arXiv:0912.4310)

Slide 9

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)

Some Simulation Details

Slide 10

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%

Simulated Performance

F = m = 2

F = m = 1

582 W/m2Ground States Excited States

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

Larmor Detuning

On resonance 1% detuned 2% detuned

Ip = 27 W/m2

Ip = 221 W/m2

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 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

Best Laser Format?

Downpumping

D2b

D2a

Gra

ph

ic b

y U

ng

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

Slide 14

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)

Frequency Scanning Schemes

9 × 40 MHz 4 × 110 MHz

Slide 15

Hyperfine State PopulationsT

ime

Excitation

excitedstates

F = 1groundstates

F = 2groundstates

Larmorperiod

firstpulse

Plot hyperfine state evolution for a selection of velocity classes

Visualize Larmor precession, downpumping, excitation

Slide 16

Hyperfine State Analysis: 9 × 40 MHz

60 MHz

Slide 17

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

Conclusions

CW laser format is good, but leaves room for improvement

F I N E

GRAZIE!

Slide 18

Slide 19

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?

Frequency Shifters

Slide 20

Hyperfine State Analysis: 4 ×110 MHz

Slide 21

Some Commercial Frequency Shifters 1

Brimrose Corp.http://www.brimrose.com/pdfandwordfiles/aofshift.pdf

Slide 22

No More Plots…How Do We Build it?

Slide 23

Some Commercial Frequency Shifters 2

Brimrose Corp.http://www.brimrose.com/pdfandwordfiles/aofshift.pdf

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

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!

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

Slide 27

EOMs for Repumping

Vendors: New Focus, Qubig

Used free-space EOM in “Wendelstein” transportable LGS system

Issues with peak power (photodarkening, coatings, cooling)

Take

n fr

om w

ww

.qub

ig.d

e

Affordable way to retrofit pulsed lasers

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 (☼)

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/

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

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

Optical pumping process polarizes atoms.

Optical pumping is most efficient whenlaser frequency (l) is tuned to

atomic resonance frequency (0).

Optical pumping

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

dF

dt B

= =

L = gF B B

B

, F