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Using molecular hydrogen as a model system, we present the first calculation which demonstrates the feasibility of efficient third-harmonic and sum-frequency generation of ir laser radiation by diatomic molecular gases. A conversion efficiency of 10% without phase matching is achievable with a modest laser intensity of about 20 MW/cm2. In addition to a two-photon resonance, the efficient conversion depends on a mechanism which makes use of virtual vibronic transitions exclusively. Possible methods for phase matching are also suggested.

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