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Journal of the Optical Society of America B

Pulse-train excitation of sodium for use as a synthetic beacon

Lee C. Bradley

Published Oct 1, 1992• 47 citations
Publisher

Abstract

The responses of two-level atoms and of sodium atoms to trains of repetitively pulsed resonance radiation are computed. It is found that the optimum backscatter from mesospheric sodium for a given irradiance is attained when the pulse trains are phase modulated and when the lengths of individual pulses are in the 500–700-ps range, corresponding to a transform-limited bandwidth somewhat smaller than the Doppler-broadened hyperfine-structure pattern of the D2 line.

DOI
10.1364/josab.9.001931

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Compared to a hypothetical two-level atom, the sodium atom has a more complex structure with both Zeeman and hyperfine levels. When an assembly of such atoms is illuminated by a pulse train, the excitation is made more complex by the phenomenon of optical pumping. It is well known that pro longed excitation of the 2S1/2 - 2P3/2 transition by circularly polarized light leads to a steady state in which the atoms oscillate exclusively between the F = 2, MF = 2 ground level and the F = 3, MF = 3 excited level. The pumping is comparatively slow, so the temporal behavior is important, and the steady state may not be attained in practice. The dynamics of this process will be explained.

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The responses of two-level atoms and of sodium atoms to trains of repetitively pulsed resonance radiation are computed. It is found that the optimum backscatter from mesospheric sodium for a given irradiance is attained when the pulse trains are phase modulated and when the lengths of individual pulses are in the 500–700-ps range, corresponding to a transform-limited bandwidth somewhat smaller than the Doppler-broadened hyperfine-structure pattern of the D2 line.
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 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.
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.
The steady-state absorption of a beam of sodium atoms irradiated by a train of pulses from a mode-locked dye laser has been measured. The sodium atoms were prepared as two-level systems by optical pumping with a two-mode laser. Absorption spectra on the 589.0-nm D2 line were recorded over 20 GHz with a frequency-stabilized, tunable, mode-locked dye laser having a bandwidth of 3.7 GHz and a mode spacing of 82 MHz. The laser-pulse profile was determined from the spectral profile assuming transform-limited pulses and was incorporated in theoretical calculations of excitation spectra obtained by numerical integration of the optical Bloch equations. By comparison of measured absorption spectra and theoretical excitation spectra the validity of the weak-field solution as well as the predicted saturation behavior were fully verified by the experimental results. For the highest level of irradiation applied, the laser pulses were identified as π pulses.
Compared to a hypothetical two-level atom, the sodium atom has a more complex structure with both Zeeman and hyperfine levels. When an assembly of such atoms is illuminated by a pulse train, the excitation is made more complex by the phenomenon of optical pumping. It is well known that pro longed excitation of the 2S1/2 - 2P3/2 transition by circularly polarized light leads to a steady state in which the atoms oscillate exclusively between the F = 2, MF = 2 ground level and the F = 3, MF = 3 excited level. The pumping is comparatively slow, so the temporal behavior is important, and the steady state may not be attained in practice. The dynamics of this process will be explained.