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Journal of the Optical Society of America A

Theory of continuous-wave excitation of the sodium beacon

Peter W. Milonni, H. Fearn, John M. Telle, Robert Quentin Fugate

Published Oct 1, 1999• 62 citations
Publisher

Abstract

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.

DOI
10.1364/josaa.16.002555

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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.
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.
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.
We report experimental on-sky observations of atomic spin precession of mesospheric sodium driven by polarization modulation of a continuous-wave laser. A magnetic resonance was remotely detected from the ground by observing the enhancement of induced fluorescence when the driving frequency approached the precession frequency of sodium in the mesosphere, between 85 and 100 km altitude. The experiment was performed at La Palma, and the uncertainty (0.2 kHz) in the measured Larmor frequency (≈260 kHz) corresponded to an error in the geomagnetic field of 0.3 mG. The results are consistent with geomagnetic field models and with the theory of light-atom interaction in the mesosphere.
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.
We report experimental results on the first on-sky observation of atomic spin precession of mesospheric sodium driven by polarization modulation of a continuous-wave laser. The magnetic resonance was remotely detected from the ground by observing the enhancement of induced fluorescence when the driving frequency approached the precession frequency of sodium in the mesosphere, between 85 km and 100 km altitude. The experiment was performed at La Palma, and the uncertainty in the measured Larmor frequency ($\approx$260 kHz) corresponded to an error in the geomagnetic field of 0.4 mG. The results are consistent with geomagnetic field models and with the theory of light-atom interaction in the mesosphere.
Directed mirrorless lasing from the mesospheric sodium layer has been proposed as a way to overcome the isotropy of laser guide star fluorescence, with demonstrated cell-scale analogues and a demonstrated stand-off magnetometry application. Several transition paths on the Na ladder compete for the same pump photons. We build a ten-level rate-equation model of the ladder from NIST transition probabilities and evaluate every electric-dipole line under four continuous-wave pumping schemes, both in a Doppler-averaged treatment and in a velocity-selective treatment appropriate for the collision-poor mesosphere. Three design-relevant results emerge. At practically accessible continuous-wave irradiances the column-gain exponents remain far below unity, consistent with published feasibility estimates; the value of the classification is to identify which lines, schemes, and pulse formats merit further study.