And: glass amplifier material has peak emission cross section 4 × 10–20 cm2 at the amplifier wavelength = 1054 nm, and fluorescence lifetime 290 s. the nd ion density is 3 × 1020 cm–3, and the pump rate for one nd ion is 170 s–1. (a) determine the number of nd ions pumped to the excited state per unit volume per unit time. (b) if there is no signal light, determine the steady-state, upper-level population (number of excited ions per unit volume). (c) what fraction of nd ions are in the excited state? (d) determine the gain coefficient at 1054 nm.