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

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.