Characteristics of return photons from the polychromatic laser guide star excited by a long pulse laser with 330 nm wavelength

Based on the solution to the rate equations of interactions between laser and sodium atoms, the excitation probability of sodium atoms is achieved. The return photons at 330 nm are numerically calculated for the 1 W laser power at the sodium layer in the mesosphere. Results show that a long pulse laser with a few microsecond durations and 1000 Hz repetition rates can well excite the polychromatic laser guide star to obtain no less return photons at 330 nm than that by the continuous-wave laser in a given condition. In order to obtain enough return photons to satisfy the requirement of tip-tilt detection, the parameters of linewidth, durations, repetition rates, polarization and launch diameters of the laser should be properly chosen. And effects of the laser launch diameters and the atmospheric turbulence on the return photons are slight. For the wonderful vertical atmospheric transmittance T0=0.5 at the Starfire Optical Range, Mauna Kea and Paranal, considering the effects of geomagnetic field, when the power of launch laser varies from 10 W to 25 W with the zenith angles from 0° to 40°, the return photons at 330 nm reach 10⁴ ph/m²/s.