why understanding the physics of the sodium atom is important · why understanding the physics of...

Oct 29th 2007 Ringberg Workshop 2007 #1

Why understanding the physics of the sodium atomis important

Edward KibblewhiteUniversity of Chicago


Classical way of estimating sodium return

Method appears to give reasonable answers

• Take peak value of unsaturated Dopplerbroadened D2 line

• Convolve profile with laser linewidth• Multiply by column density to get

optical depth• Multiply by photon flux at layer• Multiply by factors to account for

optical pumping “factor of 1.5”• Take account of saturation using value

of 62.5 w/m2/natural linewidth.• Estimate return from laser flux

10x10-13 m2


Return analysis based on wrong Physics

• Absorption Cross-section is afunction of pumping– With full pumping of circular

polarized light cross-sectionincreases return by factor of60/28

– Additional factor of 1.5 dueto backscatteringenhancement

• MIT/LL Exp (1992) with 250mJ pulses (I ≈ 0.1 Isat)

Peak enhancement of 2.8

Reduction inFWHM of 70%


Wide Range of returns/watt

CW (10 MHz)5510VLT

CW (800 MHz)3510Gemini

“Long” pulse (1.8 GHz)30-1005Palomar

“Short”Pulse (3 GHz)5-2012Keck

“Long” Pulse (2 GHz ?)60-1101Sac Peak

CW single frequency1201MMT

CW single frequency40-25040SOR

CommentsReturn(ph/cm2/s/Watt)

Power onsky(watts)

LaserObservation

•Some variation between types of laser appears real

•Factor of 4 in seasonal return: Factor of two dusk to dawn


Sodium atom is not a two level atom

Classical theoryassumes “two level”transition

OscillatorStrength

Cross-section of

(2,2) ->(3,3 )

=3λ2/2π

after Ungar


Interaction with laser photons

• For a single CW line, only a small fraction of the atoms (1.5%)interact with the laser photons

• BUT atoms near center of line interact very strongly ( 105-107

ph/sec/atom)

Doppler broadenedline line ≈ 1.1 GHz

Natural linewidth≈ 10 MHzFWHM (15.5 MHz over line)


Interaction with photons

• Absorption and reemission of photons– Standard model

• Optical pumping– Increase in return/atom due to increase in cross-section ( 60/28) and

dipole backscattering (1.5) (Total factor 3.2)– Can also decrease in population in upper level

• Larmor precession in magnetic fields redistributes M levels– At low laser intensities this reduces increase in return

• Radiation pressure– Atom red shifted 50 kHz/photon absorbed– Pushed ≈ line width in 100 cycles


Interaction with molecules

• Typical collision lifetime ≈100 µs– 30 µs at bottom of layer– 500 µs at top of layer

• Rethermalisation of ground states is difficult toestimate– No interaction with N2 molecules– Spin exchange with O2and O (?)

• If we assume 20% of collisions with O2– and 1/2 interactions have same spin

Rethermalisation rate of 0.1/collision lifetime


Optical Pumping

• Even a single frequency lasertuned to the zero Dopplershift F=2 -> F=3 can excitetransitions F=2 -> F=2 and F=2->F=1 transitions.

• These transitions can opticallypump atoms to F=1 groundstate

F=0

F=1

F=2

F=3

F=2

F=1

245

2

15(2,2)->(3,3) transition has largestcross-section and cannot pump tplower ground level “Two level atom”

M=+3

M=+2M=+0

M=+1

M=+1

M=+1

432

60

10 1525 15

2515


Monte Carlo code developed at Chicago (atomicphysics 102)

• Full atomic modelincorporating oscillatorstrengths of all transitions

• Can include effects ofradiation pressure and laserfrequency chirping

• Three laser spectral formats– Single frequency (SOR)– Comb (Chicago/CTI)– Broad band

(Fiber/”modeless”)

Photon Return

Intensity in units of I sat(62.6 w/m2

Intensity in units of I sat(62.6 w/m2

Fraction lost in collision time


Comparison with SOR Data

• Monte carlo code calculates returnand loss from upper level assuming– Single CW line– 100 µs collision lifetime– 10% rethermalisation/collision

lifetime– No Larmor (magnetic) effects

• Data taken from Dec 2005,– 75cm FWHM spot diameter

• Column density adjusted to fitcurve– 3.9x 1013 atoms/m2

Ph/cm2/sec

Laser Power

Code

SOR data


Circular polarized light pumps to (2,2) -> (3,3) state

(2,2)->(3,3)

F=1 Ground states

Other F=2 Ground states

Atom pumped to (2,2) ->(3,3) state in ≈15 cycles

Return increases from 8 to 15 ph/at/µs @ I =0.5 Isat


Linear polarized light favors M = 0 state

Atoms concentrated in M = 0, ±1 states in ≈ 8 cyclesReturn increases from 5 to 6.2 ph/at/µs @ I =0.5 Isat

(2,0)

(2,±1)

(2,±2)


Optical Pumping #1• Assume single laser frequency of 508.848716213 THz(32S1/2-> 32P1/2)

•Atom moving in orthogonal direction after collision will beexcited with cross-section of 3λ2/2π m2

0 m/s35 m/s

55 m/s

F=3

F=2

F=2

F=1

Red shiftedatom


Atoms transitioning F=2 ->F = 1,2 are rapidly pumpedto lower ground state

F=0

F=1

F=2

F=3

F=2

F=1

245

2

15M=+2M=+0

M=+1

M=+1

M=+1

432

60

10 1525 15

2515

F=2 -> F=2

F=2 -> F=1

M=±2

M=±3

Lower ground

Lower ground

Upper ground

Upper ground

M±2 statedepopulated inmagnetic fields


Effect of optical pumping on upper ground levelpopulation

• Fractional loss of upper level population is 8/(8 + 5α)

Where α=rate of optical pumping depletion /collision lifetimerate of thermal repopulation/collision lifetime

• Rate of thermal repopulation/collision lifetime not known– Best guess ≈ 10%

• Depends on environment of mesosphere• Changes with height(collision lifetime changes by factor

10 across sodium layer)

16% loss/collision lifetime reduces number ofatoms in upper level by factor of 2


Upper level depopulation depends on pumping

• A single frequencydepopulates the upper level– 0.5 I sat ≈0.11/100 µs– 0.15 I sat ≈0.068/100 µs– 0.05 I sat ≈0.045/100 µs– 0.015 I sat ≈0.028/100 µs– 0.005 I sat ≈0.016/100 µs

• MUCH HIGHER LOSSES IFSMALL AMOUNT OF LINEARPOLARISATION– Bad news for fiber feeds (?)

Doppler Shift in MHz

0.5 Isat

0.15 Isat

0.05 Isat

0.015 Isat

0.005 Isat

Single frequency CW excitation


Chicago/CTI Lasers have number of single frequencymodes

Population ofupper ground level

Spectrum ofsodium beacon

Max loss at F=2->F=2 transition

Min loss at F=2->F=3 transition

Doppler shift

Spectrum and upperground level loss ofsodium atom I = 0.1Isat


Significant loss of atoms in upper state due tooptical pumping

1.300.274.390.4395.170.1 Isat10

1.800.621.040.1042.93Isat 1

Return/atom

Fractionleft inupperstate

α

Fractionlost/collision time

Return/Upperstate atom

LineIntensity

No ofLines

High wind speeds can replace some fraction (?)

Broadening line to reduce saturation increases this lossand can lower the overall return


Fiber lasers need broad lines to reduce SBS

50 MHz

50 MHz

50 MHz

Broad line lasers have additional ≈60% lossdue to simultaneous excitation of F=2 tohyperfine transitions [Hillman CfAO 03/07]


Broad line lasers can have significant return loss

NominalFlux/atom

Return/atom includingdepopulation effects

Spectral Bandwidth (MHz)

Decrease due tosaturation

Decrease due to loss inupper ground levelpopulation

“Hillman” effect

ALLLASERSARE NOTEQUAL


Larmor Precession (Classical model)

• Atom precesses in earthsmagnetic field

• If magnetic field orthogonalto photon direction the Mstate changes every ≈ µsec– For low cycle times(> 1 µs)

average oscillator strength is≈32 (half the return) (bad)

– Easier to optically pump tolower ground level (bad)

Magnetic

field

M=+2

M=-2

Oscillator strength =60

Oscillator strength =4

1.3µsec

Laser beam


Effect of Earths magnetic field• Magnetic precession reorders

populations in upper ground levelwith 2 - 3 µs cycle time– Depends on angle between laser

and magnetic field directions

• Cycle times of <0.5 µs keep atom in(2,2) state (good)

2,+/-2

2,+/-12,0

2,+/-2

2,02,+/-1

300

600

Lasers should be designed toproduce short cycle timestailored to spot size

Cycle times >few µs cansignificantly reduce photon return

0 2.3 µs


Factor of 2 in return at SOR depending on angle oflaser beam to magnetic field vector

Effect may be more significant for longer cycletimes

Flux =800

et al

Flux = 400

data from Denman et al


Mid-talk summary• Fully pumped return could be ≈ 300 ph/atom/cm2/watt

– SOR reaches 120 ph/at/cm2/watt @ 40 watt• Significant loss due to optical pumping from F=2 to F=1 ground

state and precession in earth’s magnetic field– Monte Carlo code correctly predicts return of laser guide stars for

SOR and Chicago lasers (I >0.1 I sat, cycle time < 0.3 µs)

CONCLUSIONS• Single frequency CW lasers should have significantly higher

return/watt than other types of laser ( for power < 20 watts)• High pumping rates (high power CW or pulsed lasers) are

important to reduce precession effects (cycle times ≈0.1-0.2 µsgoal in center of beacon)

CAN WE DO BETTER ?


OPTION #1 Backpumping

• Proposed by MIT/LL in 1980s

• Idea is to send a second freqencydisplaced by ≈ 1772- 60 MHzsimultaneously with primaryfrequency.

• For pumping with circular polarizedlight we can pump ALL atoms into(2,2) <-> (3,3) two level state (BIGEFFECT)

• Simulations show only 10% powerneeded to pump most atoms intoupper ground level.

1772 MHz

60 MHz


Two frequency experiment tried at SOR withdisplaced beam

50 w and 20 w lasers used tuned to different frequencies

photo from Denman et al


25% enhancement of return

• 250 ph/sec/cm2/watt return

• Loss in efficiency due to overlapnot being 100%

• Best frequency 1770 MHz (between (1,1) -> (2,1) and (2,2)transitions

data from Denman et al.


Chirping

• Radiation pressure usual considered a problem– Atom red-shifted 50 kHz/photon absorption

• Atom pushed out of laser line in 100 transitions

• MIT/LL proposed frequency shifting laser frequency totrack red shift- “Chirping”

• Sweeps up range of velocity groups

• Technique requires high intensity/natural line-width– Narrow laser line-widths << 10 MHz

• Broad-line lasers have difficulty chirping


Effect of radiation pressure on return

No radiationpressure Δν = -30MHz

Δν = 0 MHz Δν = + 10 MHz

Δν = -30 MHz

+ 0.5 MHz/µs chirp

Small initial doppler bin


Monte Carlo Simulations of Chirping

• Chirping single frequency lasermodes can provide significantenhancement for high pumpintensities.– Factor of 1.5 for I = 0.15 Isat– Factor of 2.4 for I = 0.5 Isat

• At high intensities chirpingsweeps up large Dopplerpopulation into a singlevelocity group

• Chirping improves loss ofupper level atoms.

No radpressure

No radpressure

No chirp

No chirp

Chirp

Chirp0.5 Isat

0.15 Isat

≈100 kHzFWHM


Optical pumping with backpumping and chirp

• Combined backpump and chirp maximizes number of atoms involvedin generating the sodium guide star.

Upper ground state loss

Upper ground state gain


Chirping + backpumping with pulsed multiline lasersaccesses ≈50% of total sodium population

Emission/unit velocitybin

Emission/unit frequency

bin

Most atomspumped up toupper groundlevel

Simulation of 10 modepulsed laser usingbackpumping and chirping


Chirping at high Intensity/linewidth + backpumpingmay be able to greatly increase return

Theory predicts 5 watt Chicago laserreturn of 136 ph/sec/cm2

– 150 ph/sec/cm2 typicalTheory predicts 40 watt SOR laser

return 2645 ph/sec/cm2

– 2600 ph/sec/cm2 fromDenman

Chirping + BackpumpingAn optimized 10 watt pulsed sum

frequency laser could produce5600/ph/sec/cm2 return(mv≈5)

Return

Intensity in units of Isat

Chirping +Backpump

Singlefrequency CW

Normal return

Normal laser operation


Conclusions

• Current generation of lasers only use a fraction of the availablesodium atoms in the mesosphere.

• Backpumping and chirping can in principle increase return/wattby an order of magnitude AT HIGH PUMPING RATES and gridof narrow lines– Requires careful optimization of spectral and temporal profiles– Not all laser technologies can produce high returns/watt– Requires experiments on sky to validate theory and optimize design

• Short pulse laser format for ELTs pose significant challenges– Not enough time to chirp– May not be necessary (?)

WE SHOULD UNDERSTAND WHAT THE BEST LASERSARE BEFORE INVESTING MORE MONEY IN NEWTECHNOLOGY

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