need help with lasers hw

1. Consider a Nd: YAG laser that is pumped with a diode laser. The configuration of this laser is shown below. Diode laser input Nd:YAG rod 1 cm 5 cm Back mirror Reflectivity=1 Curved mirror Radius of curvature = infinity Reflectivity=0.95 Radius of curvature=10 cm The internal loss is 5% per pass. a. Calculate the small signal threshold gain (Ym) for this laser. b. Now calculate the threshold power (Pth). Pan= 1 In( 1 ) (npd ) (hump ) (x (@. + w, 2)) 2 RIR2 T 1 20 where R1 and R2 are the radii of curvature. 6 = 2.8 x 10-2cm T= 230 us take Oo = 0p =130 um npd = nr nt na 17pq The energy of the upper laser level is 11417 cm". See Fig. 10.5 in the text. c. What is the reason for the external curved mirror instead of using the back end of the crystal as the second mirror?12840 12819 12623 12607 12575 12519 12432 12370 11507 (1 1512) 111423 (11417) 1.06415 pam 10% 10%% 10 1.0644 fam 4500 4440 40% 4035 4034 Energy in 10 cm- 3933 3924 4 150 5 2514 (2521) 2461 (2468) 2148 (2147) 21 10 (21 10) 2028 (2029) 2002 (2002) 808.7 nm 830 31 1 200 132 (a) (b) 300K (9) 77K FIGURE 10.5. Energy level for neodymium in YAG. (a) Structure of YAG showing the pumping routes with the percentages referring to a pump with a broad spectral output. (b) Details of the manifold at 300 K showing the dominam transitions, the semiconductor laser pumping route is also shown. (c) Energy levels at 77 K. [Data from Kaminski [25]. See also Koechner [241-1 360