Source: http://aoot.osa.org/josab/abstract.cfm?uri=josab-36-4-1117
Timestamp: 2019-04-22 22:47:28+00:00

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In this paper, we introduce the concept of spatial and spectral control of nonlinear parametric sidebands in multimode optical fibers by tailoring their linear refractive index profile. In all cases, the pump experiences Kerr self-cleaning, leading to a bell-shaped beam profile. Geometric parametric instability, owing to quasi-phase matching from the dynamic grating generated via the Kerr effect by pump self-imaging, leads to frequency multicasting of beam self-cleaning across a wideband array of sidebands. Our experiments show that introducing a Gaussian dip into the refractive index profile of a graded index fiber permits us to dramatically change the spatial content of spectral sidebands into higher-order modes. This is due to the breaking of the oscillation synchronism among low-order and higher-order modes. Hence, the inter-modal four-wave mixing approach should be used to describe the sideband generation mechanism. Observations agree well with theoretical predictions based on a perturbative analysis and with full numerical solutions of the (3+1)D nonlinear Schrödinger equation.
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Fig. 1. Iso-intensity surfaces identifying the local variation of the refractive index induced by the Kerr effect and obtained for δn=0 (a) and δn=−0.004 (b).
Fig. 2. Numerical simulation of sideband generation for an input intensity of 10 GW/cm2, pulse duration of 9 ps, input beam diameter of 40 μm, and propagation distance of 0.16 m. First (a) and second (b) anti-Stokes sidebands obtained for δn=0 (green), δn=−0.002 (orange), and δn=−0.004 (violet). The lower frames show the corresponding beam shapes integrated over a 10 THz bandwidth, for the two extreme cases of δn=0 (green frame) and δn=−0.004 (violet frame).
Fig. 3. (a) Beam diameter versus input (guided) peak power (Pp−p) measured at the FWHMI, emerging from a 10-m-long GRIN dip MMF. The blue fitting curve is a guide for the eye. Insets: output near-field patterns for different Pp−p. (b) Measured index profile of the dip fiber (red filled curve). Parabolic profile used in the simulations (black curve) and Gaussian approximation of the dip (yellow curve).
Fig. 4. Experimental output two-dimensional near-field shapes (normalized intensity in the linear scale) as a function of input guided power Pp−p measured at the pump wavelength of 1064 nm in 10-m-long GRIN dip MMF. Panels (a) and (b) show the results obtained for slightly different input conditions. Asterisk (*): results for the Pp−p at which frequency conversion into sidebands was also observed.
Fig. 5. Experimental spectra obtained from a 10-m-long GRIN MMF without (top, red curve) and with (bottom, blue curve) a central dip in the refractive index profile. The input guided power was Pp−p=36 kW. The vertical dashed lines indicate the analytically calculated sideband frequencies. The blue spectrum was down-shifted by 50 dB for better visualization.
Fig. 6. Experimental output two-dimensional near-field shapes (normalized intensity in linear scale) of a series of selected spectral components measured from 10-m-long GRIN MMF with a dip in their index profile at Pp−p=36 kW including the first four-orders anti-Stokes parametric sidebands (upper panel). Asterisk (*): near-field shape at the pump wavelength (1064 nm) in the linear regime with Pp−p=18 W.
Fig. 7. Measured refractive index profiles of two types of GRIN fibers: (a) fiber with a nearly parabolic profile—the black curve shows the parabolic profile used in the numerical simulations; (b) fiber with a parabolic profile with a dip on the top—the black curves and the yellow curve represent the parabolic profiles and the Gaussian approximation of the dip, respectively, as used in the numerical simulations.
Fig. 8. Low-order mode profiles for a GRIN fiber with a Gaussian dip with δn=−4×10−3. Since these modes have intensity profiles similar to the linearly polarized modes of a step-index fiber, we adopted the same numbering.
Fig. 9. Calculated shift of the sideband positions upon barrier depth.
Fig. 10. Experimental evolutions of two-dimensional near-field shape at 1064 nm (normalized intensity in linear scale) (a) and spectrum (b) as a function of input guided power Pp−p measured at the output of a 10-m-long GRIN MMF with perturbed index profile.
Fig. 11. Supercontinuum generation in the GRIN fiber with dip: fiber length of 10 m and average power of 36 kW. We used a series of 10-nm-wide bandpass filters with center wavelengths of 550, 650, 750, 900, 1000, 1200, 1300, 1500, and 1600, and a 3-nm-wide bandpass filter at 1064 nm.
Fig. 12. Experimental output two-dimensional near-field shapes (normalized intensity in linear scale) as a function of input guided power Pp−p measured at the pump wavelength of (a) 1064 nm and (b) 532 nm in a 30-m-long GRIN dip MMF. Asterisk (*): results for the Pp−p at which frequency conversion into sidebands was also observed.

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