It is shown theoretically that filamentation can lead to sizable second harmonic generation. The 2ω0 radiation is emitted into a forward-directed cone, its angle determined by the wavelength of the fundamental radiation in the plasma waveguide. Experimental observations confirm the theoretical predictions. Aside from the forward-directed emission cone, non-negligible 2ω0 power is detected over a broad angular range in the backward direction showing a broadened red-shifted spectrum.
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Meyer et al. (1987) studied this question.
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