Ributions of sodium atoms with recoil for I = 50 W/m2 , 100 W/m2 , and 150 W/m2 for 0 MHz linewidth.Atmosphere 2021, 12,9 ofFigure five. Normalized distributions of sodium atoms with linewidth broadening for I = 50 W/m2 , 100 W/m2 , and 150 W/m2 for 0 MHz linewidth.Figure 4 shows that high intensity causes much more drastic recoil and aggravates the adverse conditions. Simultaneously, the greater intensity tends to make sodium atoms drift towards the 3-Hydroxybenzaldehyde Protocol larger Doppler frequency shifts. Figure five reveals that the linewidth broadening method can properly alleviate the recoil effects for different laser intensities. 4.2. Option of Optimal Laser Linewidth In practice, when the recoil effects need to be dropped, and the laser is required to modulate the intensity distribution in Equation (5). The linewidth broadening in the laser intensity distribution aims at reaching the 4′-Methoxyflavonol Technical Information maximal excitation probability of mesospheric sodium atoms. The maximal typical spontaneous emission rate is needed. Hence, we simulate the average spontaneous emission rates by the linewidth broadening from 0 to 1.0 GHz. In light of Equations (2)9), the typical spontaneous emission prices together with the intensity from 0 to 1500 W/m2 are simulated in Figures six and 7.Figure six. Typical spontaneous emission rates vs. linewidth and intensity from five to 150 W/m2 .Atmosphere 2021, 12,10 ofFigure 7. Average spontaneous emission rates vs. linewidth and intensity from 150 to 1500 W/m2 .Figures six and 7 show that the peak values of typical spontaneous emission prices adjust with the laser linewidth and intensity. The high intensity enhances the peak values of average spontaneous emission rates. When the laser is broadened to a bigger linewidth, the typical spontaneous emission rates as an alternative drop. Inside the case of lower intensity, the laser linewidth broadening finitely gains the average spontaneous emission prices inside the selection of l00 MHz. Nonetheless, it is actually not that the wider linewidth can acquire the very best impact, but that the average spontaneous emission prices possess a maximum for the linewidth from 1 MHz to one hundred MHz. However, L the typical spontaneous emission price at v D = 0 MHz is reduced than the peak values. In Figures 6 and 7, the peak values of average spontaneous emission rates will be the exact same in terms of linewidth. We hope that the linewidth broadening of laser intensity distributions makes the average spontaneous emission price maximal. Figures eight and 9 simulate the average spontaneous emission rates for laser linewidth from 1 to 103 MHz and laser intensity from 5 to 1500 W/m2 .Figure eight. Typical spontaneous emission rates for laser linewidth from 3 to 103 MHz and laser intensity I = five – 150 W/m2 .Atmosphere 2021, 12,11 ofFigure 9. Average spontaneous emission rates for laser linewidth from three to 103 MHz and laser intensity I = 150 – 1500 W/m2 .Figures 8 and 9 indicate that the peak values of typical spontaneous emission rates are between 1 MHz and 100 MHz for an intensity from 5 W/m2 to 1500 W/m2 . For that reason, the laser linewidth is taken because the worth among 1 MHz and one hundred MHz. Figure ten demonstrates L the relation between laser linewidth at v D = 0, 1, 10, 100 MHz and average spontaneous emission rates. L By comparing typical spontaneous emission prices for each linewidth at v D = 0, 1, L =0 MHz and ap10, one hundred MHz, the average spontaneous emission rates are lowest at v D L proximately equal for linewidth at v D = 1, ten, 100 MHz. This implies much more return photons L = 1, 10, one hundred MHz. The laser linewidth at v L = 10 MHz i.
