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We combine inside a single noncentrosymmetric laser crystal, GdAl[sub 3](BO[sub 3])[sub 4]:Nd[sup 3+], a stimulated emission and two second-order nonlinearities in cascade. The first one self-doubles the 1062.8 nm Nd[sup 3+] laser emission corresponding to the [sup 4]F[sub 3/2]→[sup 4]I[sub 11/2] channel, despite the fact that it is not phase-matched. The second one can be phase-matched or not and mixes the laser wave and its second harmonic (SH) in order to produce the third harmonic (TH) at 354.3 nm. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]