Spatiotemporal nonlinear optics in arrays of subwavelength waveguides

We report numerical and experimental investigations of spatiotemporal nonlinear optical effects leading to spectral broadening in an array of subwavelength silicon waveguides pumped with infrared femtosecond pulses. Adjusting an input pulse position across the array, we observe different patterns in the output spectra. We explain these observations using a theory of the resonant (Cherenkov) radiation emitted by temporal solitons belonging to different spatial supermodes of the array. We also demonstrate strong nonperturbative coupling of temporal dispersion and discrete diffraction in the subwavelength arrays.

Figure 1

(a) GVD of the three supermodes; positive and negative values correspond to anomalous and normal GVD, respectively. (b) Single-wire dispersion length $L_D$ (solid line) and coupling (discrete diffraction) length $L_C$ (dashed line).

Figure 2

(a,b) Experimentally measured and (c,d) numerically modeled transmission spectra of 120 fs pulses for the edge (left) and center (right) excitations as functions of the increasing averaged input power $P_{\mathrm{av}}$.

Figure 3

(a) Powers of the solitonic supermodes (solid lines) for $T_0=120$ fs and power threshold for nonlinearity-induced spatial symmetry breaking (dashed line). (b) Numerically modeled evolution of the pulse width times amplitude parameter for three supermodes generated by the edge excitation with $P_{\mathrm{av}}=70$ $\mu$W [cf. Figs. 4a, 4b, 4c].

Figure 4

(a–c) Temporal and (d–f) spectral evolution of the $S_1$(a,d), $S_2$(b,e), and $S_3$(c,f) supermodes along the array under the edge excitation with $P_{\mathrm{av}}=70$ $\mu$W. In order to simultaneously show formation of quasisolitons and dispersive radiation in the time domain, (a–c) are plotted on the linear scale in the soliton area ($t>-1$ ps) and on the log scale for $t<-1$ ps, where the radiation can be seen. In the spectral plots, $R_1$, $R_2$ ($\simeq 1.72$ $\mu$m), and $R_3$ correspond to the intramode resonances of the respectively numbered supermodes, while $R_{31}$ and $R_{13}$ correspond to the intermode ones.