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We report on the generation of 7.6 ns, $162~\mu \text{J}$ and 21.3 kW (peak power) single-frequency optical pulses at 780 nm with near-diffraction limited beam quality (M2 < 1.1) from a frequency-doubled all-fiber MOPA system for a 87 Rb based dating application. Frequency doubling is performed in 4-cm long non-critically-phase-matched (NCPM) LBO crystal with a measured conversion efficiency of ~50%. The same technology has also been used to build another similar pulsed laser at 776nm. To the best of our knowledge, this is the highest pulse energy and peak power in a single-frequency laser near 780nm with near-Gaussian beam quality obtained from a frequency-doubled all-fiber MOPA system. The use of the all-fiber MOPA configuration allowed us to develop compact and rugged laser systems at both 780nm and 776nm for 87Rb dating applications. [ABSTRACT FROM AUTHOR]