Source: http://aoot.osa.org/josab/abstract.cfm?uri=josab-31-2-311
Timestamp: 2019-04-19 22:22:42+00:00

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We introduce a general full-field propagation equation for optical waveguides, including both fundamental and higher order modes, and apply it to the investigation of spatial nonlinear effects of ultrafast and extremely broadband nonlinear processes in hollow-core optical fibers. The model is used to describe pulse propagation in gas-filled hollow-core waveguides including the full dispersion, Kerr, and ionization effects. We study third-harmonic generation into higher order modes, soliton emission of resonant dispersive waves into higher order modes, intermodal four-wave mixing, and Kerr-driven transverse self-focusing and plasma-defocusing, all in a gas-filled kagomé photonic crystal fiber system. In the latter case a form of waveguide-based filamentation is numerically predicted.
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Fig. 1. Integration scheme for the waveguide mode propagation model.
Fig. 2. Calculated group velocity dispersion curves for the fundamental HE11 mode (blue) and the first two higher modes, HE12 (green) and HE13 (red). The calculations are based on a 27 μm core diameter kagomé-PCF filled with xenon at 2 bar (solid) and 7 bar (dashed). The inset shows a scanning electron micrograph of the fiber used for the experiments in Section 6.
Fig. 3. Tunable third-harmonic generation in the HE13 mode (linear scale). (a) Experimental spectra from . (b) Simulated spectra using the multimode model. In both cases a pulse with 1.3 μJ energy and 30 fs duration at 800 nm propagates through 20.5 cm of Ar-filled kagomé-PCF with 28 μm core diameter.
Fig. 4. Numerical simulations showing intermodal FWM in kagomé-PCF (core diameter 18 μm) filled with 25 bar of Xe. (a) Spectral evolution of the HE11 mode. (b) The temporal intensity evolution of the HE11 mode. MI indicates the breakup of the leading part of the pulse in the anomalous dispersion region. (c) Spectral evolution of the HE12 mode. The zero dispersion wavelengths are marked by dotted lines and anomalous and normal dispersion regions indicated by A and N. Also shown are the phase-matched FWM pump and Stokes wavelengths in the HE11 mode and anti-Stokes wavelength in the HE12 mode.
Fig. 5. Simulation of the propagation of a 40 fs, 0.7 μJ pulse in a kagomé-PCF (core diameter 27 μm) filled with 2.7 bar of Xe. (a) Temporal and (b) spectral evolution. A and N indicate anomalous and normal dispersion. Three modes were included in the calculation.
Fig. 6. (a) Experimental spectra (blue curve) and corresponding simulations (gray curve) at the output of a 17 cm long kagomé-PCF (core diameter 27 μm) filled with 2.7 bar of Xe. (b) Simulated spectrum decomposed into its individual modes. Pulses of duration 40 fs and energy 0.7 μJ were used in both the experiment and the simulations.
Fig. 7. Pressure dependence of the phase-match wavelength for dispersive waves in the HE11, HE12, and HE13 modes (solid lines), together with the central wavelengths at which the peaks appear in the experiments (points). Also shown are the near-field mode patterns measured at the fiber endface for the HE12 and HE13 modes.
Fig. 8. Simulations of MI dynamics in the fundamental mode. A pulse with energy 5 μJ, duration 500 fs and wavelength 800 nm propagates along a kagomé-PCF (core diameter 18 μm) filled with 10 bar of Xe. (a) Temporal and (b) spectral evolution. A and N indicate anomalous and normal dispersion. (c) Magnified image of the boxed-in region in (a), showing the fine details of the “soliton shower”.
Fig. 9. Beam radius against propagation distance, with and without ionization, in a kagomé-PCF (core diameter 18 μm) filled with 10 bar Xe and pumped with 5 μJ, 500 fs pulses at 800 nm.

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