Ributions of sodium atoms with recoil for I = 50 W/m2 , one hundred W/m2 , and 150 W/m2 for 0 MHz linewidth.Atmosphere 2021, 12,9 ofFigure 5. 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 four shows that higher intensity causes far more drastic recoil and aggravates the adverse situations. Simultaneously, the higher intensity makes sodium atoms drift to the higher Doppler frequency shifts. Figure five reveals that the linewidth broadening method can successfully alleviate the recoil effects for diverse laser intensities. 4.2. Option of Optimal Laser Linewidth In practice, if the recoil effects have to be dropped, and the laser is necessary to modulate the intensity distribution in Equation (5). The linewidth broadening on the laser intensity distribution aims at reaching the maximal excitation probability of mesospheric sodium atoms. The maximal Cyanine5 carboxylic acid Description average spontaneous emission rate is required. Consequently, we simulate the average spontaneous emission rates by the linewidth broadening from 0 to 1.0 GHz. In light of Equations (two)9), the average spontaneous emission rates together with the intensity from 0 to 1500 W/m2 are simulated in Figures six and 7.Figure 6. Typical spontaneous emission Tetraethylammonium References prices vs. linewidth and intensity from 5 to 150 W/m2 .Atmosphere 2021, 12,ten ofFigure 7. Average spontaneous emission prices vs. linewidth and intensity from 150 to 1500 W/m2 .Figures 6 and 7 show that the peak values of average spontaneous emission rates change with the laser linewidth and intensity. The high intensity enhances the peak values of average spontaneous emission prices. When the laser is broadened to a larger linewidth, the typical spontaneous emission prices as an alternative drop. Inside the case of reduce intensity, the laser linewidth broadening finitely gains the average spontaneous emission prices inside the array of l00 MHz. Nonetheless, it is actually not that the wider linewidth can get the most beneficial effect, but that the typical spontaneous emission prices have a maximum for the linewidth from 1 MHz to one hundred MHz. Even so, L the average spontaneous emission rate at v D = 0 MHz is reduce than the peak values. In Figures six and 7, the peak values of average spontaneous emission rates are the similar when it comes to linewidth. We hope that the linewidth broadening of laser intensity distributions makes the average spontaneous emission rate maximal. Figures 8 and 9 simulate the average spontaneous emission prices for laser linewidth from 1 to 103 MHz and laser intensity from 5 to 1500 W/m2 .Figure eight. Typical spontaneous emission prices for laser linewidth from 3 to 103 MHz and laser intensity I = five – 150 W/m2 .Atmosphere 2021, 12,11 ofFigure 9. Typical spontaneous emission rates for laser linewidth from three to 103 MHz and laser intensity I = 150 – 1500 W/m2 .Figures eight and 9 indicate that the peak values of typical spontaneous emission prices are in between 1 MHz and 100 MHz for an intensity from five W/m2 to 1500 W/m2 . Hence, the laser linewidth is taken as the value between 1 MHz and 100 MHz. Figure 10 demonstrates L the relation in between laser linewidth at v D = 0, 1, ten, one hundred MHz and average spontaneous emission rates. L By comparing typical spontaneous emission prices for every linewidth at v D = 0, 1, L =0 MHz and ap10, one hundred MHz, the typical spontaneous emission rates are lowest at v D L proximately equal for linewidth at v D = 1, 10, 100 MHz. This implies much more return photons L = 1, ten, 100 MHz. The laser linewidth at v L = 10 MHz i.