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Acta Physica Sinica

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

Wang Gong-Chang, Kai Wei, Yan Li

Published Jan 1, 2018• 1 citation

Abstract

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.

DOI: 10.7498/aps.67.20171940

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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.

Abstract The efficiency of ten sodium atom excitation schemes that can potentially be used to generate a sodium polychromatic laser guide star (PLGS) and a monochromatic laser guide star (LGS) is compared. It is shown that for creating an LGS in sodium vapor using the cascade fluorescence effect with single-photon excitation, the most suitable is the 42P3/2 ← 32S1/2 transition excited at a wavelength of 330.237 nm and demonstrating the highest LGS characteristics, while the efficiency decreases by two orders of magnitude compared to a monochromatic LGS at a wavelength of 588.995 nm.

Seven possible variants of the sodium atom excitation are considered for creating a polychromatic laser guide star (LGS). It has been shown that the 42P3/2 ← 32S1/2 transition excited at a wavelength of 330.237 nm is most suitable for creating a polychromatic LGS in sodium vapor using the effect of cascade fluorescence at one-photon excitation. In this case, the excitation efficiency will be 2 orders of magnitude lower compared to the efficiency of creating a monochromatic LGS at a wavelength of 589 nm.

Sodium laser guide star (LGS) is the key for the success of modern adaptive optics (AO) supported large ground based telescopes, however, for many field applications, Sodium LGS’s brightness is still a limited factor. Large amounts of theoretical efforts have been paid to optimize Sodium LGS exciting parameters, that is, to fully discover potential of harsh environment surrounding mesospheric extreme thin sodium atoms under resonant excitation, whether quantum or Monte Carlo based. But till to now, only limited proposals are demonstrated with on-sky test due to the high cost and engineering complexities. To bridge the gap between theoretical modeling and on-sky test, we built a magnetic field controllable sodium cell based lab-bench, which includes a small scale sum-frequency single mode 589nm laser, with added amplitude, polarization, and phase modulators. We could perform quantitative resonant fluorescence study under single, multi-frequency, side-band optical re-pumping exciting with different polarization, also we could perform optical field modulation to study Larmor precession which is considered as one of devils of Sodium LGS, and we have the ability to generate beams contain orbital angular moment. Our preliminary sodium cell based optical re-pumping experiments have shown excellent consistence with Bloch equation predicted results, other experimental results will also be presented in the report, and these results will give a direct support that sodium cell based lab-bench study could help a Sodium LGS scientists a lot before their on-sky test.

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.