Light bullets in nonlinear waveguide arrays under the influence of dispersion and the Raman effect

We study the formation and the dynamics of spatially broad light bullets generated in silica waveguide arrays. We show that these bullets are metastable even in the presence of high-order dispersion, coupling dispersion, and the Raman effect and can be approximated by the hyperbolic secant function with a high degree of accuracy. We also investigate the formation of narrow light bullets which are spatially localized in only a few adjacent waveguides and short in time. We reveal that the latter are extremely robust even in the presence of the Raman effect.

Figure 1

(a) Coupling coefficient $\kappa$ as a function of the wavelength. Inset in (a): Zoomed version of (a) in the region of shorter wavelengths. (b) The solid (blue) curve represents the dispersion parameter $D$ of each individual waveguide as a function of the wavelength, whereas the dotted (red) vertical line indicates the position of the cutoff wavelength at 1.3308 $\mu \text{m}$. Inset in (b): Zoomed version of (b) in the region around the cutoff wavelength. The parameters of the WA are given in the text.

Figure 2

(a,b) Generation of a broad light bullet in the ($n,\tau ,\xi$) and ($k,\lambda ,\xi$) spaces, respectively, when $b_0$ = 0.302. The first and last frames in (a) are shown in (c) and (d), respectively, in the ($n,\tau$) plane.

Figure 3

(a,b) Pulse propagation in the central waveguide $n$ = 0 and with the delay $\tau$ = 0, respectively. (c,d) The dashed black curves represent the input signal with the sech profile; solid blue curves represent the output profiles; solid red curves represent the curves fitted by the sech function, which are practically on top of the solid blue curves.

Figure 4

(a,b) Evolution of a pulse in the ($n,\tau ,\xi$) space when $b_0$ = 0.28 and 0.32, respectively.

Figure 5

(a,b) Evolution of a pulse in the ($n,\tau ,\xi$) space when $b_0$ = 0.56 and 0.84, respectively.

Figure 6

(a,b) Evolution of a broad light bullet in the ($n,\tau ,\xi$) space when the Raman effect and coupling dispersion are considered, respectively. The initial peak amplitude $b_0$ = 0.302 and 0.3 in (a) and (b), respectively. All other parameters are the same as in Fig. 2.

Figure 7

(a,b) Evolution of a pulse with Raman effect and $b_0$ = 0.32 in the ($n,\tau ,\xi$) space and in the ($\tau ,\xi$) plane for the central waveguide ($n=0$), respectively. (c,d) The pulse profile at the final frame in (a) at the central waveguide and at the delay $\tau$ = 18.37, respectively. The dashed (blue) curves in (c,d) are the results obtained through direct pulse propagation simulation, whereas the solid (red) curves are fitted with sech functions. The first and last frames in (a) are shown in (e) and (f), respectively, in the ($k,\lambda$) plane and on a logarithmic scale.