(c) Dr Paul Kinsler. [Acknowledgements & Feedback]
STATUS: postdeadline presentation
LOCATION: ECLEO, Munich, 2003.
WORK DONE AT:
Physics Department,
Imperial College.
SIZE: various
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AUTHORS: P Kinsler, G.H.C. New
We show how to handle an important problem in few-cycle nonlinear optics: what to do when the spectra of interacting few-cycle pulses overlap.
We treat the case where the spectra of non-linearly interacting few-cycle pulses overlap: this is important for both near-degenerate sum-frequency generation ($\omega_1 + \omega_2 \Rightarrow \omega_3$) as well as sub-harmonic generation ($\omega_3 \Rightarrow \omega_1 + \omega_2 $). Such scenarios are of great interest since near transform limited 5-cycle idler pulses at 3$\mu$m have been generated in OPOs based on aperiodically-poled lithium niobate (APPLN). Full consideration of the effects of spectral overlap are rarely addressed, {\em even when applying pulse envelope techniques to cases where there are wide and/or overlapping spectra} (see e.g. the recent [1]).
In modelling few-cycle pulses in an OPO with a near-IR idler[2], we found that few-cycle effects both modified the output pulse shapes {\em and} superposed an extra pulse-to-pulse phase shift. This was interesting in itself, but in a near-degenerate few-cycle OPO, there is the additional complication that the signal and idler spectra almost completely overlap! If these fields are not distinguished by polarization, the ambiguity between different field components that share the same frequency needs to be managed.
One option is to resort to a combined signal+idler field -- but the two sub-components would interfere to give a pulse shape with an oscillating envelope, a feature that could violate the usual ``smooth envelope'' requirements of standard theoretical models. Alternatively, we can retain separate field components with overlapping spectra, but carefully manage the ambiguous spectral components and the additional complications of extra, near-resonant nonlinear polarization terms (e.g. oscillating at the normally off-resonant frequency $2\omega_1$, etc).
We address all these issues in this paper, 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 OPO pulses shorter than $\sim$18fs, 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] Xiaojun Fang, N. Karasawa, R. Morita, R.S. Windeler, M. Yamashita,
IEEE Photonics Techn. Lett. 12, 233 (2003).
[2] P. Kinsler, G.H.C. New,
"Few cycle pulse propagation",
Phys. Rev. A67, 023813 (2003).
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Date=20030630 Author=P.Kinsler