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Thanks for the explanation. I figured you could, but there are clearly far more efficient items to use.You're talking about optical pumping. The decay rate (which results in spontaneous emission, not stimulated emission)of a given lasing medium is very short, which means you need a LOT of optical energy in a small area to achieve population inversion. That is why only ultra-high intensity light sources are used for pumping. Flash lamps, arc lamps, or other lasers are common devices for this purpose.
Also, even if an LED could somehow be modified for ultra-high power, it would not necessarily have the emission spectra to align properly with the lasing medium's absorption bands, resulting in huge amounts of wasted energy.