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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Calculation of returns from sodium beacons for different types of laser

E. J. Kibblewhite

Published Jul 12, 2008• 13 citations
Publisher

Abstract

We describe a Monte Carlo code that includes the effects and optical pumping, radiation pressure and magnetic fields on the interaction between a laser beam and a sodium atom in the mesosphere. The code is sufficiently general that it can calculate the return for different types of laser. We find that conventional theory overestimates saturation and does not include the effect of optical down-pumping, which significantly reduces the population of sodium atoms available for excitation. We compare the theoretical returns for two types of laser and predict significant enhancements to the photon return/watt can be achieved with tailored spectral and temporal formats.

DOI
10.1117/12.789601

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We describe a Monte Carlo code that includes the effects and optical pumping, radiation pressure and magnetic fields on the interaction between a laser beam and a sodium atom in the mesosphere. The code is sufficiently general that it can calculate the return for different types of laser. We find that conventional theory overestimates saturation and does not include the effect of optical down-pumping, which significantly reduces the population of sodium atoms available for excitation. We compare the theoretical returns for two types of laser and predict significant enhancements to the photon return/watt can be achieved with tailored spectral and temporal formats.
line by nanosecond time scale pulsed lasers is described. By numerically integrating transition rates in the sodium hyperfine structure, the return flux per sodium atom is predicted as a function of laser power. The simulation should be useful for studies of mesospheric sodium and adaptive optics. Applications include the estimation of sodium column density from lidar return flux, and of laser guide star brightness for different pulsed laser formats. The simulation assumes that the pulse repetition frequency is sufficiently low (smaller than a few kilohertz) that atomic collisions restore local thermodynamic equilibrium between pulses. It is also assumed that the pulse length is short compared to the Larmor precession time scale. The numerical results are well-approximated by a simple analytic model for a three-level atom. The number of emitted photons is found to be primarily dependent on the product of the length of the laser pulse and the energy density.
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.
We extend our previous analysis of the sodium beacon [J. Opt. Soc. Am. A15, 217 (1998)] to the case of continuous-wave excitation. Various effects that could be ignored in the case of pulsed excitation, such as the geomagnetic field, the recoil of the sodium atoms upon absorption and emission, and collisions of the sodium atoms with other mesospheric species, are included. Spin-relaxation collisions are among the most important of these effects for the cases considered. Analytical approximations to numerical results are presented, and using a semi-empirical estimate for Na-O2 spin relaxation, we compute photon returns in good agreement with recently reported measurements at the Steward Observatory.
We describe a two-level model for the mesospheric sodium resonance fluorescence excited by a train of pulses. For pulse durations that are short compared with the 16-ns natural lifetime, population-rate equations are inadequate and must be replaced by density-matrix (Bloch) equations. We briefly contrast these two approaches and discuss several issues associated with pulse-train excitation. Analytical approximations to averages over atomic velocities and the transverse spatial profile of the laser are described. Estimates of return photon numbers for trains of pulses, ranging in duration from tens of picoseconds to half a nanosecond, are made and these estimates are compared with those of more conventional long-pulse lidar schemes. Roughly similar photon numbers are predicted for both long and short pulses whenever their average intensities are comparable. For average intensities, less than ~ 10 W/cm(2), trains of asymptotically equal to 0.5-ns pulses yield greater photon returns than trains of asymptotically equal to 30-ps pulses. For larger intensities the reverse can be true.
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.
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.