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The build-up of exciton populations in resonantly laser excitedsemiconductors is studied microscopically. For excitation at the $2s$-excitonresonance, it is shown that polarization with a strict $s$-type radial symmetrycan be efficiently converted into an incoherent $p$-type population. As aconsequence, inversion between the $2p$ and $1s$ exciton states can be obtainedleading to the appearance of significant terahertz gain.Comment: 4 pages, 3 figure

Exciton-Population Inversion and Terahertz Gain in Semiconductors Excited to Resonance