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Spectral overlap and off-resonant polarization terms in parametric interactions

STATUS: submitted, response not received
LOCATION: CLEO, Baltimore, USA, 2003.
WORK DONE AT: Physics Department, Imperial College.
SIZE: various

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AUTHORS: P Kinsler, G.H.C. New

Abstract (PDF 86k)

Multiple field descriptions of nonlinear interactions are usually restricted to non-overlapping spectra and on-resonance polarization terms. Since both approximations fail for wide bandwidth (few-cycle) pulses, we demonstrate here how to overcome these limitations.

Summary

In this paper we show how to treat the overlapping spectra that result from the interaction of fields whose carrier frequencies are close together compared with their bandwidths. We also examine the effect of including non-resonant polarisation terms and show that these have a significant effect in few-cycle pulse interactions.

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]. It is already well-known that in this regime the propagation of the pulse envelopes is modified (see e.g. [3,4]), but there are other effects that arise under these circumstances that also need to be considered.

Since the bandwidth of few-cycle pulses corresponds to a significant fraction of their carrier frequency, the situation where the spectra of different component frequencies overlap needs to be examined. In the parametric oscillator, for example, the signal and idler will overlap near degeneracy -- while, in the long-wavelength idler case (see e.g. [1]), the integrity of the pump and signal is under threat, unless the spectra are distiguished by polarization. In either case, the traditional coupled-wave equation approach must clearly be adapted to treat the new situation. For wide-bandwidth pulses, we must also ask how far the spectral wings extend. In the OPO case, for example, does the second harmonic of the signal or idler interact with the pump? Or does the sub-harmonic of the pump frequency interact with parts of the signal or idler spectrum? An sample case is shown in fig. 1. Of course the effect of overlapping spectra is commonly considered in engineering applications involving wavelength division multiplexing (see e.g. [5]), but here we aim to accurately model the significant interactions between fields, rather than ensuring that that cross-talk is negligible.

• 
• A sample spectrum for a 9fs pump pulse OPO system. The arrows A and B show the frequencies of the ``off-resonance'' polarization contributions which would usually be neglected. The horizontal lines with labels Idler, Signal, and Pump show the width of the arrays used to hold the numerical pulse envelopes, and clearly display overlap: the use of shorter pulses or inclusion of off-resonant polarization terms would cause an overlap in spectral amplitudes, not just array ranges.

We address all these issues, discussing different algorithms for handling overlapping spectra and presenting numerical simulations based on coupled-wave equation in which additional terms (not just the standard ``resonant'' terms) are included in the nonlinear polarisation. We show that, for pulses shorter than ~18 fs, off-resonant terms have a significant effect on the interaction, and that the increased spectral bandwidth requires the application of our spectral overlap procedure.

[1] T. Beddard, M. Ebrahimzadeh, T.D. Reid, W. Sibbett, ``Five-optical-cycle pulse generation in the mid infrared from an optical parametric oscillator based on aperiodically poled lithium niobate'', Opt.Lett. 25, 1052 (2000).
[2] A. Baltuska, Z. Wei, S. Pshenichnikov and D. Wiersma, ``Optical pulse compressionto 5fs at a 1-MHz repetition rate'', Opt.Lett. 22, 102 (1997).
[3] T. Brabec, F. Krausz, ``Nonlinear optical pulse propagation in the single-cycle regime'', Phys. Rev. Lett. 78, 3282 (1997).
[4] P. Kinsler, G.H.C. New, ``Few cycle pulse propagation'', to appear, Phys. Rev. A.
[5] Keang-Po Ho, Haitao Yu, Lian-Kuan Chen, and Frank Tong, ``High-Resolution Measurement and Spectral Overlap of Cross-Phase Modulation Induced Spectral Broadening'', IEEE Photonics Technol. Lett., 12, 1534 (2000).

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Date=20021125 Author=P.Kinsler