© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

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

Simple model, including recoil, for the brightness of sodium guide stars created from CW single frequency fasors and comparison to measurements

Paul D. Hillman, J. Drummond, Craig A. Denman, Robert Quentin Fugate

Published Jun 30, 2008• 13 citations

Abstract

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.

DOI: 10.1117/12.790650

Related papers

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

Felipe Pedreros Bustos, Ronald Holzlöhner, Simon Rochester +3 more

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.

Journal of the Optical Society of America B•Mar 6, 2020•15 citations

Frequency chirped continuous-wave sodium laser guide stars

Felipe Pedreros Bustos, Ronald Holzlöhner, Simon Rochester +3 more

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/$μ$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.

arXiv:2001.02717•Jan 8, 2020•0 citations

Efficient excitation of a mesospheric sodium laser guide star by intermediate-duration pulses

J. R. Morris

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.

Journal of the Optical Society of America A•Feb 1, 1994•53 citations

Fluorescence enhancing mechanism of optical repumping in sodium atoms for brighter laser guide star

Lihang Li, Hongyan Wang, Weihong Hua +2 more

With quantum Bloch equations and sodium cell based experiment, we systematically resolved optical repumping mechanism of sodium atoms, a path to brighter sodium laser guide star (SLGS) that would be accepted by worldwide observatories. Besides the former studies, we detailed the population distribution of sodium atoms with and without repumping, which makes the repumping mechanism easy to understand. Experimental results based on a buffer gas free sodium cell and a single frequency laser implies that the optimum repumping frequency offset is 1712 MHz, and the repumping power fraction should be 10-18%. The light intensity depended character of repumping is also carried out. We learned that future SLGS pumped by higher effective light intensity would benefit more from repumping. To the best of our knowledge, this is the first systematic investigation of repumping mechanism using a single mode sum-frequency laser, which gives thorough support for previous numerical work and shows that the lab bench experiment could be used as an intermediate link between theoretical modeling and on-sky test.

Optics Express•Mar 22, 2016•10 citations

Simulations of return flux of polychromatic laser guide stars based on Bloch equations

Wang Gong-Chang, Kai Wei, Yan Li

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.

Acta Physica Sinica•Jan 1, 2018•1 citation

Modeling the response of mesospheric sodium to pulsed-laser excitation

Joschua Hellemeier, Paul Hickson, Lucas Labadie

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.

Journal of the Optical Society of America A•Jul 19, 2017•2 citations

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.

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/

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.

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.

With quantum Bloch equations and sodium cell based experiment, we systematically resolved optical repumping mechanism of sodium atoms, a path to brighter sodium laser guide star (SLGS) that would be accepted by worldwide observatories. Besides the former studies, we detailed the population distribution of sodium atoms with and without repumping, which makes the repumping mechanism easy to understand. Experimental results based on a buffer gas free sodium cell and a single frequency laser implies that the optimum repumping frequency offset is 1712 MHz, and the repumping power fraction should be 10-18%. The light intensity depended character of repumping is also carried out. We learned that future SLGS pumped by higher effective light intensity would benefit more from repumping. To the best of our knowledge, this is the first systematic investigation of repumping mechanism using a single mode sum-frequency laser, which gives thorough support for previous numerical work and shows that the lab bench experiment could be used as an intermediate link between theoretical modeling and on-sky test.

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.

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.