Presentation on theme: "Larmor-resonant Sodium Excitation for Laser Guide Stars"— Presentation transcript:
1 Larmor-resonant Sodium Excitation for Laser Guide Stars Ron HolzlöhnerS. Rochester 1D. Budker 2,1D. Bonaccini CaliaESO LGS Group1 Rochester Scientific LLC, Dept. of Physics, UC BerkeleyAO4ELT3Florence, 28 May 2013
2 Are E-ELT LGS lasers powerful enough? 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 complicatedE-ELT Project has expressed interest in exploring paths to raise the return fluxTwo avenues:Raise cw power Laser development (e.g., Raman fiber amplifiers)Raise coupling efficiency sce Explore new laser formatsWill focus on option 2
3 Sim. cw return flux on ground [106 ph/s/m2] ζ = 60°B3.6!Sky Maps ParanalBecoming more independent of field angle would be particularly beneficial in Paranal:Flux varies strongly with angle to B-fieldB-field inclination is only 21° most of the time this angle is large
4 What factors limit the return flux? 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)BmθvLaser+ 50 kHzspont.emissiontimeexcited (P3/2)ground (S1/2)
5 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.UnpolarizedSphere centeredat origin,equal probabilityin all directions.zxyOriented“Pumpkin” pointingin z-direction preferred direction.zxyAligned“Peanut” with axisalong z preferred axis.zxyCredit: D. Kimball, D. Budker et al., Physics 208a course at UC Berkeley
6 Precession in Magnetic Field torque causes polarized atoms to precess: BCredit: D. Kimball, D. Budker et al., Physics 208a course at UC BerkeleyCredit: E. Kibblewhite
7 Efficiency per Atom with Repumping Peak efficiencyModel narrow-line cw laser, circular polarizationψ : 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: BlochBlue curve peaks near 50 W/m2, close to Na saturation at 60 W/m2: Race to beat LarmorIrradiance (W/m2)20W cw laserin mesosphereTransitionsaturation62 W/m2Is there a way to harness the efficiency at peak of green curve?
8 Larmor Resonant Pulsing Pulse the laser resonantly with Larmor rotation: like stroboscope, Larmor period: 3 – 6.2 μs (Field in Paranal: G 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. powerParanal 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 angleIncreased irradiance also broadens the resonance*) PNAS /pnas (2011) (arXiv: )
9 Some Simulation Details B = 0.23 G, θ = 90°, q = 9%, 150 MHz linewidthReturn is fairly linear vs. irradianceSteady state reached after ca. 50 periods = 300μs (S- damping time)
10 Simulated Performance Can achieve 14 Mph/s/m2 at 10W, 28 Mph/s/m2 at 20W (D2a+D2b)Peak efficiency reached above 10WVery strong atomic polarization towards (F=m=2) of 60–70%F = m = 2F = m = 1582 W/m2Ground StatesExcited States
11 Larmor DetuningA small rep rate detuning shows up first at low peak irradianceReduces pumping efficiency, induces polarization oscillationsVariation in Paranal: –0.22%/year, –0.39%/10km altitudeOn resonance1% detuned2% detunedIp = 221 W/m2Ip = 27 W/m2
12 Best Laser Format?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 starsIn frequency: Chirp laser continuously, e.g. from – MHz (11 vel.c.)In frequency: Periodically address several discrete velocity classesOr 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 highNumerical 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
13 Prefer (F = 2, m = ±2) (F = 3, m = ±3) cycling transition Downpumping3S1/2 3P3/2 transitionF = I + J : Total angular momentumI = 3/2 : Nuclear spinJ = L + S : Total electronic angular momentum (sum of orbital and spin parts)40 MHz gridD2bExcitation from D2anarrow-band laserGraphic by UngerD2aPrefer (F = 2, m = ±2) (F = 3, m = ±3) cycling transition
14 Frequency Scanning Schemes Scan across >= 9 discrete velocity classesBlue-shift to achieve “snowplowing” via atomic recoilAvoid downpumping leave 40 MHz or >> 60 MHz gaps, but……without exceeding the sodium Doppler curve (1.05 GHz FWHM)9 × 40 MHz4 × 110 MHz
15 Hyperfine State Populations Excitation F = 1groundstatesPlot hyperfine state evolution for a selection of velocity classesVisualize Larmor precession, downpumping, excitationF = 2groundstatesTime excitedstatesLarmorperiodfirstpulse
17 Conclusions CW laser format is good, but leaves room for improvement Larmor precession reduces the return flux efficiency by factor 2; forces high irradiance to combat population mixingCan 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 buildFormat optimization is work in progressCW laser format is good, but leaves room for improvement
19 Frequency ShiftersWould like to frequency modulate over 100 MHz (or even 300 MHz) at >80% efficiencyEither sawtooth or step function with 160 kHz rep rate (Paranal)Need to maintain excellent beam quality and beam pointingOption1: 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+efficiencyOption 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?
23 Some Commercial Frequency Shifters 2 Brimrose Corp.
24 Some Commercial Frequency Shifters 3 A.AREFERENCEMaterialWavelength (nm)Aperture(mm²)Frequency(MHz)PolarDeflection angle (mrd)EfficiencyMQ200-B30A BrSiO20.7 x 3200 +/- 15Lin> 60MQ110-B30A1-UV1 x 2110 +/- 15MCQ110-B30A2-VISQuartz2 x 2532nm> 70MT350-B120-A0.12-VIS TeO2-L0.12 x 2350 +/- 50MT250-B100-A0.5-VISTeO2-L0.5 x 2250 +/- 50MT250-B100-A0.2-VIS0.2 x 1MT200-B100A0.5-VIS200 +/- 50MT200-B100A0.2-VISMT110-B50A1-VIS110 +/- 25MT110-B50A1.5-VIS1.5 x 2MT80-B30A1-VIS80 +/- 15> 65MT80-B30A1.5-VIS
25 To Frequency Shift, or not? 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 enoughCould be done after seed laser with fiber-coupled AOM and thus also shift the PDH sidebandsWould 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?Egg-laying wool milk swine:Broadband, highly efficient,high power, no aberrations,constant pointing.And cheap!
26 Bloch Equation Simulation Schrödinger equation of density matrix, first quantizationdρ/dt = Aρ + b = 0Models ensemble of sodium atoms, 100–300 velocity groupsTakes into account all 24 Na states, Doppler broadening, spontaneous and stimulated emission, saturation, collisional relaxation, Larmor precession, recoil, finite linewidth lasersCollisions change velocity and spin (“v-damping,S-damping”)More rigorous and faster than Monte Carlo rate equationsBased on AtomicDensityMatrix package,Written in Mathematica v.6+, publicly available[“Optimization of cw sodium laser guide star efficiency”, Astronomy & Astrophysics 520, A20]
27 EOMs for Repumping Affordable way to retrofit pulsed lasers Vendors: New Focus, QubigUsed free-space EOM in “Wendelstein” transportable LGS systemIssues with peak power (photodarkening, coatings, cooling)Taken fromAffordable way to retrofit pulsed lasers
28 What is crucial for good return flux? Most Important:Laser power, sodium abundance (seasonal)Circular polarization state ☼D2b repumping (power fraction q≈12%, GHz spacing) ☼(Peak) power per velocity class ☼Overlap with sodium Doppler curve (but: implicit repumping) ☼For return flux on ground: zenith angle, atmospheric transmission2Somewhat 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)Could improve on the crucial parameters (☼)
29 Light linearly polarized along z can create alignment along z-axis. Optical pumpingLight linearly polarized along z can create alignment along z-axis.zF’ = 0F = 1MF = -1MF = 0MF = 1Credit: D. Kimball, D. Budker et al., Physics 208a course at UC Berkeley
30 Optical pumpingLight linearly polarized along z can create alignment along z-axis.zF’ = 0F = 1MF = -1MF = 0MF = 1Medium is now transparent to lightwith linear polarization along z !Credit: D. Kimball, D. Budker et al., Physics 208a course at UC Berkeley
31 Optical pumpingLight linearly polarized along z can create alignment along z-axis.zF’ = 0.F = 1MF = -1MF = 0MF = 1Medium strongly absorbs lightpolarized in orthogonal direction!Credit: D. Kimball, D. Budker et al., Physics 208a course at UC Berkeley
32 Optical pumping Optical pumping process polarizes atoms. Optical pumping is most efficient whenlaser frequency (l) is tuned toatomic resonance frequency (0).
33 Precession in Magnetic Field Interaction of the magnetic dipole momentwith a magnetic field causes the angular momentumto precess – just like a gyroscope! = BB =dFdt, FgF B F BdFdt B=L = gF B B