2. (Problem 6.4.1) A laser comprises a cylindrical rod of Nd:YAG in an optical cavity consisting of two mirrors, which h

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2 Problem 6 4 1 A Laser Comprises A Cylindrical Rod Of Nd Yag In An Optical Cavity Consisting Of Two Mirrors Which H 1 (126.61 KiB) Viewed 18 times

2. (Problem 6.4.1) A laser comprises a cylindrical rod of Nd:YAG in an optical cavity consisting of two mirrors, which have reflectances of R₁ = 1 and R₂ = 0.92. The rod is 5 cm long and 0.5 cm in diameter and each end is anti-reflection coated so that reflection from the Nd:YAG/air interface is negligible. • Taking losses from the cavity other than transmission through the mirror to be negligible, calculate the threshold gain coefficient and population inversion density. • If the total density of Nd³+ ions, Ntotal = 1.4 × 1020 cm-³, what fraction are in the upper laser level at threshold? • Assuming uniform pumping of the whole rod, what excitation rate, R, is required for this laser to reach threshold? • How much power is emitted as spontaneous emission at threshold? Take the stimulated emission cross-section, o, and fluorescence lifetime, 7, of Nd:YAG to be 2.8 x 10-¹9 cm² and 230 µs, respectively. The Nd:YAG wavelength is 1064 nm.