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Journal of the Optical Society of America B

Frequency chirped continuous-wave sodium laser guide stars: modeling and optimization

Felipe Pedreros Bustos, Ronald Holzlöhner, Simon Rochester, Domenico Bonaccini Calia, Joschua Hellemeier, Dmitry Budker

Published Mar 6, 2020• 15 citations
Publisher

Abstract

We numerically study a method to increase the photon return flux of continuous-wave laser guide stars using one-dimensional atomic cooling principles. The method relies on chirping the laser towards higher frequencies following the change in velocity of sodium atoms due to recoil, which raises atomic populations available for laser excitation within the Doppler distribution. The efficiency of this effect grows with the average number of atomic excitations between two atomic collisions in the mesosphere. We find the parameters for maximizing the return flux and evaluate the performance of chirping for operation at La Palma. According to our simulations, the optimal chirp rate lies between 0.8 − 1.0 M H z / µ s , and an increase in the fluorescence of the sodium guide star up to 60% can be achieved with current 20-W-class guide star lasers.

DOI
10.1364/josab.389007

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Frontiers in Optics•Jan 1, 2009•0 citations
We numerically study a method to increase the photon return flux of continuous-wave laser guide stars using one-dimensional atomic cooling principles. The method relies on chirping the laser towards higher frequencies following the change in velocity of sodium atoms due to recoil, which raises atomic populations available for laser excitation within the Doppler distribution. The efficiency of this effect grows with the average number of atomic excitations between two atomic collisions in the mesosphere. We find the parameters for maximizing the return flux and evaluate the performance of chirping for operation at La Palma. According to our simulations, the optimal chirp rate lies between 0.8 − 1.0 M H z / µ s , and an increase in the fluorescence of the sodium guide star up to 60% can be achieved with current 20-W-class guide star lasers.
We numerically study a method to increase the photon return flux of continuous-wave laser guide stars using one-dimensional atomic cooling principles. The method relies on chirping the laser towards higher frequencies following the change in velocity of sodium atoms due to recoil, which raises atomic populations available for laser excitation within the Doppler distribution. The efficiency of this effect grows with the average number of atomic excitations between two atomic collisions in the mesosphere. We find the parameters for maximizing the return flux and evaluate the performance of chirping for operation at La Palma. According to our simulations, the optimal chirp rate lies between 0.8-1.0 MHz/μμμs and an increase in the fluorescence of the sodium guide star up to 60% can be achieved with current 20 W-class guide star lasers.
Mesospheric sodium magnetometry with a laser guide star measures the geomagnetic field near 90~km. Its sensitivity hinges on laser linewidth and chirp, yet prior work optimized these two parameters only separately. We use velocity-resolved density-matrix simulations of Larmor-synchronous pulsed Na D2_22​ pumping to scan both parameters jointly. Linewidth and chirp exhibit a synergy: when chirping carries the recoil-mitigation role, the return flux stays within 1\% of its peak across linewidths of 2--10~MHz. The flux-optimal chirp is $0.19~\mathrm{MHz/\upmu s}$, one fifth of the continuous-wave rate; this synergy guides high-sensitivity mesospheric magnetometer design.
Sodium laser guide star (LGS) becomes an essential part in modern astronomical adaptive optics system, especially for the next generation extremely large ground based telescope. The LGS technology has experienced the developmental stages as natural guide star, Rayleigh LGS, sodium LGS and constellation of LGS. The sky coverage is still limited in that the LGS cannot not be used to detect the tip/tilt aberrations. While the polychromatic laser guide star (PLGS) is one of the most effective ways to enlarge the sky coverage to 100%. Previous simulation models are insufficient for the accurate calculation of the return flux, especially for the simulation model of PLGS which is generated by one-photon excitation of mesospheric sodium atoms. The simulation model based on Bloch equations proposed in this paper can be used to compute the return flux of one-photon excited PLGS precisely. Doppler broadening, beam atom exchanging, collisions and recoil are taken into account in the model. The return flux is validated by the return efficiency. The simulation results indicate that with one-photon excitation of sodium atoms, a return efficiency of 330 nm is minimum compared with those of other wavelengths; the saturation power density will decrease with recoil increasing and increase with collision rate increasing; an optimal line-width exists up to maximum the photon return efficiency. In the best case, when the power density is 10 W/m2 at the sodium layer, the maximum return efficiency at 330 nm is 0.907 photons/s/sr/atom/(W/m2) with an optimal laser line-width of 18 MHz.
Calculations of backscatter emission of mesospheric sodium atoms in a laser guide star that is excited by pulses ranging from 30-ns to 0.9-μs duration are described. The efficient use of such pulses at saturating irradiance values is shown to require ~3 GHz of spectral broadening to provide access to the full absorption spectrum of the D2 line. The broadening is provided by frequency modulation. A set of density matrices was used to account for all 24 hyperfine states and inhomogeneous Doppler broadening. At the broadband (3-GHz) saturation irradiance of 4 W/cm2, both linearly and circularly polarized laser beams are shown to produce emission rates exceeding 60% of the maximum possible rate-equation rate for the 0.9-μs pulses. As expected, circular polarization produced more backscatter than did linear polarization, but the enhancement never exceeded 1/3 in the calculations that are reported. A brief estimate of state precession in the Earth’s magnetic field suggests that achieving even this enhancement will require that the time scale for optical pumping be held to less than 1 μs, which will require the use of irradiances greater than 0.7 W/cm2 and spectral coverage of the full 3-GHz hyperfine-plus-Doppler absorption profile, at least until most of the population is pumped out of the F = 1 ground states.
Using a stable single frequency (Δυ < 1 MHz) cw fasor we have characterized the guide star radiance under several conditions, including routinely measuring the radiance at various launch powers and simultaneously illuminating the same spot with a second fasor with a range of different frequency separations. Making use of sodium's hyperfine energy diagram and allowed transitions it is shown that some transitions do not contribute to the radiance after a short time period thus greatly reducing the number of states whose populations need to be tracked in a simple rate equation model. An offshoot of this view is the importance of the pump source's spectral content for efficient sodium scattering. Accounting for atomic recoil, which causes atoms to be Doppler shifted out of resonance, we obtain model curves for photon return flux versus launch power for both linear and circular polarization, both agree with measurements; the only free parameter being the sodium column density on the single night both sets of data were taken. We attempted to measure the sodium velocity distribution due to recoil using two Fasors in a pump-probe arrangement. We have measured some subtle phenomena that this simple model does not explain and these will be discussed. These may imply the importance of understanding the collision rates for sodium atoms to re-equilibrate through velocity changing collisions, spin relaxation and coherent beam propagation under various atmospheric conditions.