1. 4 Nov 2012 1 Paths to a Brighter Sodium Laser Guide Star Paul Hillman, Tom Kane, and Craig Denman CfAO Fall Science Retreat - Laser Workshop FASORtronics LLC

2. 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

3. 4 Nov 20122012 CfAO Fall Science Retreat - Laser Workshop 3 History of Laser Guide Star returns FacilityYear Return (ph/cm 2 /sec/W) Average Power (W) Spot Size, 2/e 2 (arcsec) ~ ψ (ph/atom/sr/sec/( W/m 2 )) UofA1997120013274 Lick19961012221 Keck20011012 - 151.8 x 2.321 Palomar200560 - 806 - 83169 SOR200510040 - 504 x 3.4212 Gemini North2007276 @ meas1.3114 VLT200654101.25114 SOR200620040a + 10b4 x 3.4423

4. 4 Nov 20122012 CfAO Fall Science Retreat - Laser Workshop 4 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.

5. 4 Nov 20122012 CfAO Fall Science Retreat - Laser Workshop 5 Sodium D 2 Transitions Using circular polarization, ∆m F = 1 for each absorption. ∆m F = 1, 0, -1 for each spontaneous emission. Driven to m F = 2 in the ground state, atoms become optically trapped and the F=2, m F =2F’=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.

6. 4 Nov 20122012 CfAO Fall Science Retreat - Laser Workshop 6 Method 1: increasing the repump ratio Promotes atoms out of the lower ground so they don’t accumulate there. Assumed D 2 b 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 D 2 b slightly dependent intensity. Intensity 47 W/m 2 Linewidth: 9 MHz B = 0.5 g and 90° to beam in this and all following examples unless noted

7. 4 Nov 20122012 CfAO Fall Science Retreat - Laser Workshop 7 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.

8. 4 Nov 20122012 CfAO Fall Science Retreat - Laser Workshop 8 Method 2: Increasing the Linewidth Intensity: 500 W/m 2 D 2 b 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/m 2 ) Optimal Linewidth (MHz) 207 479 10012 20020 50030 100050 2000100

9. 4 Nov 20122012 CfAO Fall Science Retreat - Laser Workshop 9 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.

10. 4 Nov 20122012 CfAO Fall Science Retreat - Laser Workshop 10 Method 3: Chirp Demonstration Average Return: ψ = 592 ph/atom/sr/sec/(W/m 2 )*. No chirp Return: ψ = 330 ph/atom/sr/sec /(W/m 2 )*. 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 Velocity Group Population (a.u.) Intensity: 47 W/m 2 Chirp Rate: 0.75 MHz/µs Linewidth: 0 MHz Repump ratio: 10% total ground states total excited states

11. 4 Nov 20122012 CfAO Fall Science Retreat - Laser Workshop 11 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, f L, is proportional to the B field; at B= 0.5 G, f L = 350 kHz, or τ = 2.8 µs.

12. 4 Nov 20122012 CfAO Fall Science Retreat - Laser Workshop 12 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 beam LineWidth = 9 MHz Repump = 15% B field = 0.5 Gauss Intensity for CW beam = 47 W/m 2

13. 4 Nov 20122012 CfAO Fall Science Retreat - Laser Workshop 13 Method 4: SOLUTION, Pulse Resonantly at Larmor Use a pulsed beam with a frequency equal to the Larmor frequency, f L. 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.

14. 4 Nov 20122012 CfAO Fall Science Retreat - Laser Workshop 14 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 beam LineWidth = 9 MHz Repump = 15% B field = 0.5 Gauss Intensity for CW beam = 47 W/m 2 Avg. Intensity = 47 W/m 2, Peak Intensity for pulsed beam = 522 W/m 2 Pulse Frequency = 350 kHz

15. 4 Nov 20122012 CfAO Fall Science Retreat - Laser Workshop 15 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

16. 4 Nov 20122012 CfAO Fall Science Retreat - Laser Workshop 16 Summary of Results - Pulsed at Larmor Frequency Pulsed at Larmor Frequency Average Intensity (W/m 2 ) Flux (ph/atom/sr/sec) ψ = Flux/Intensity ph/atom/sr/sec (W/m 2 ) RepumpDuty cycleLinewidth (MHz) 207,311365.60.0980.08882 4717,220366.40.0920.09150 10034,160341.60.0880.1220 20060,540302.70.0960.12275 500117,750235.50.110.15370 1,000184,908184.90.100.17490 2,000281,180140.60.110.22550 Angle between beam and B field is 90° B = 0.5 G

17. 4 Nov 20122012 CfAO Fall Science Retreat - Laser Workshop 17 Summary of Results - CW CW Average Intensity (W/m 2 ) Flux (ph/atom/sr/sec) ψ = Flux/Intensity ph/atom/sr/sec (W/m 2 ) RepumpDuty cycleLinewidth (MHz) 2034871740.1517 4778471670.1519 10016,3341630.14112 20032,6001630.14120 50078,9461580.12130 1,000160,2171600.14150 2,000314,0341570.121100 Angle between beam and B field is 90° B = 0.5 G

18. 4 Nov 20122012 CfAO Fall Science Retreat - Laser Workshop 18 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 f L CW Angle between beam and B field is 90° B = 0.5 G

19. 4 Nov 20122012 CfAO Fall Science Retreat - Laser Workshop 19 Photon Flux at Telescope, 0.6 - 1 arcsec seeing Pulsed at f L CW Average Intensity (W/m 2 ) laser Power (W) Flux (ph/cm 2 /sec) Stellar Magnitude Flux (ph/cm 2 /sec) Stellar Magnitude 208.71,0377.14957.9 4720.42,4436.21,1137.0 10043.54,8475.42,3176.2 20087.08,5904.84,6255.5 500217.416,7064.111,2014.5 1000434.826,2353.622,7323.8 2000869.639,8943.144,5563.0 LGS size similar to Holzlöhner (2009), equivalent Gaussian FWHM = 40.4 cm. Magnitude V = 4.7 for a flux of 10,000; Drummond (2004).

20. 4 Nov 20122012 CfAO Fall Science Retreat - Laser Workshop 20 Various values used spin relation rate250 µs Sodium column density 4 x 10 13 atoms/m 2 velocity changing collision rate50 µs Mean sodium layer height 92 km rate atoms enter and leave the beam 100 sec -1 Mesosphere Temperature185 K Geomagnetic Field0.5 G Angle between beam and B field, unless noted 90°

21. 4 Nov 20122012 CfAO Fall Science Retreat - Laser Workshop 21 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 f L / 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/m 2 frequency = 29.2 kHz Intensity = 3.7 W/m 2 frequency = 30.4 kHz For both plots: Peak Intensity = 500 W/m 2 Pulse length = 0.26 µs Linewidth = 150 MHz, Repump = 9% (Parameters were not optimized)

22. 4 Nov 20122012 CfAO Fall Science Retreat - Laser Workshop 22 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

23. 4 Nov 20122012 CfAO Fall Science Retreat - Laser Workshop 23 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 f L /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.