Phase matching in cascaded third-order processes

We present an analytical, computational, and experimental study of frequency mixing and propagation that takes place in the guided-wave nonlinear frequency conversion of ultrashort pulses from the near infrared to the far and the vacuum ultraviolet. In addition to the standard phase-matching conditions for frequency mixing, we observe that cascaded frequency conversion, in which one of the input frequency components is generated simultaneously, is subject to two additional phase-matching conditions, In cascaded quasi-phase matching, one of the input fields oscillates in strength with a period that matches the phase mismatch. In gain-assisted phase matching, the growth of one of the input fields results in growth of the signal, in spite of a phase mismatch for the final mixing process. (C) 2002 Optical Society of America.