Theory of few-cycle pulses in an optical parametric oscillator

Summary form only given. We present a comprehensive theoretical framework for treating the interactions of few-cycle pulses that includes diffraction, dispersion, multiple fields, and a wide range of nonlinearities. Although the treatment builds upon the work of Brabec and Kraus (1997) and Porras (1999), a characteristic feature of our approach is that no approximations are made until the final stage when a particular problem is considered. The general result is naturally complicated, but it is left entirely to choice which terms in the exact solution to retain, and to what order these should be applied. A particular benefit of the technique is that a rigorous study can be undertaken to discover what combination of approximations affords the most efficient method for treating a given nonlinear interaction involving few-cycle pulses. We apply the approach to the case of an OPO, using its description of dispersion, multiple fields and the second-order nonlinearity. We present a wide range of numerical simulations involving pulses with different numbers of cycles, and including idler pulses containing as few as two cycles. The characteristic differences between the results under various levels of approximation are discussed in detail. The results are also compared to those based on an ad-hoc technique in which pump and signal pulses are described by envelopes while the idler is defined as a real signal with carrier excursions included.