Ultrabroadband Dispersive Radiation by Spatiotemporal Oscillation of Multimode Waves

In nonlinear dynamical systems, qualitatively distinct phenomena occur depending continuously on the size of the bounded domain containing the system. For nonlinear waves, a multimode waveguide is a bounded three-dimensional domain, allowing observation of dynamics impossible in open settings. Here we study radiation emitted by bounded nonlinear waves: the spatiotemporal oscillations of solitons in multimode fiber generate multimode dispersive waves over an ultrabroadband spectral range. This work suggests routes to sources of coherent electromagnetic waves with unprecedented spectral range.

Figure 1

Simulated (top) and example experimental (bottom) supercontinuum in multimode GRIN fiber. The pump pulse at 1550 nm creates a spectrum with a series of redshifted and blueshifted peaks. In the bottom panel, the $y$-axis reference (0 dB) is the maximum intensity of the 1550 nm pump peak.

Figure 2

Dynamics of dispersive wave formation in GRIN fiber. (a) Temporal and spatial breathing of the field (inset: zoom in near the onset of dispersive wave generation). (b) Evolution of the spectral intensity of the whole field through the same distance. (c) Energy in each dispersive wave band. The $x$-axis scales are normalized to the linear spatial oscillation period of the GRIN fiber, equal to $407\mu \mathrm{m}$. These dynamics are also shown in Movies 1 and 2 of Supplemental Material [51], which provide a considerably more complete representation of the complex spatiotemporal evolution.

Figure 3

(a) ODW from GMMNLSE simulations (GMMNLSE), Eq. (4) with $\gamma (z)$ as in text, 1D NEE simulations, and an experimental example spectrum. (b) Functions used in the quasi-1D approximation, along with the peak intensity variation of the field in GMMNLSE simulation. (c) Comparison of the periodic 1D phase-matching model with multimode simulations by the GMMNLSE and experiments in GRIN MMFs. Continuous curves are values of $m$ in Eq. (3), plotted with the best-fit parameter values.