(c) Dr Paul Kinsler. [Acknowledgements & Feedback]
LOCATION: CLEO, Long Beach, USA, 2002: poster.
WORK DONE AT:
Physics Department,
Imperial College.
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AUTHORS: P Kinsler, G.H.C. New
We present a comprehensive framework for treating the nonlinear interaction of few-cycle pulses in which approximations are avoided until the final step. A wide range of numerical results are presented for an optical parametric oscillator.
Optical parametric oscillators (OPOs) based on aperiodically-poled
lithium niobate (APPLN) have generated 53 fs idler pulses at 3m
that are nearly transform limited, and contain only five optical
cycles[1]; laser pulses with less than three optical cycles have
been generated in other contexts[2]. Against this background, the
familiar slowly-varying envelope approximations (SVEAs)
traditionally used to model nonlinear optical processes are clearly
no longer satisfactory. New approaches are evidently needed that
will not only offer a more secure analysis of present problems, but
also provide a firm foundation for nonlinear optical experiments
with even shorter pulses in the future.
In this paper, 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 Krausz[3] (see also Porras[4]), 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. The application of the approach to other nonlinear optical processes is also addressed.
[1] T. Beddard, M. Ebrahimzadeh, T.D. Reid, W. Sibbett,
Opt.Lett. 25, 1052 (2000).
[2] A. Baltuska, Z. Wei, S. Pshenichnikov and D. Wiersma,
Opt.Lett. 22, 102 (1997).
[3] T. Brabec, F. Krausz,
Phys. Rev. Lett. 78, 3282 (1997).
[4] M.A. Porras,
Phys. Rev. A60, 5069 (1999).
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Date=20020619 Author=P.Kinsler