Highly Noninstantaneous Solitons in Liquid-Core Photonic Crystal Fibers

The nonlinear propagation of pulses in liquid-filled photonic crystal fibers is considered. Because of the slow reorientational nonlinearity of some molecular liquids, the nonlinear modes propagating inside such structures can be approximated, for pulse durations much shorter than the molecular relaxation time, by temporally highly nonlocal solitons, analytical solutions of a linear Schrödinger equation. The physical relevance of these novel solitons is discussed.

Figure 1

(a) Localized solutions of Eq. (2) for $T=10$, $\mathcal{E}=30$, for $\beta =2.33614$ ($m=0$), 1.82551 ($m=1$), 1.45665 ($m=2$) and 1.16691 ($m=3$), calculated by using Eq. (5). (b) $\mathcal{N}$, $c_{\mathrm{AS}}$, $g$, $\beta$ as functions of $T$, for $\mathcal{E}=30$. (c) $\beta (T)$ for fixed $\mathcal{E}=10$. (d) $\beta (\mathcal{E})$ for fixed $T=10$.

Figure 2

(a) Propagation of 1-soliton in Eq. (1), $T=10$, $\mathcal{E}=30$, $\beta =2.33614$. (b) Same as (a) but for $T=250$, $\mathcal{E}=30$, $\beta =0.109846$. (c) Various final spectra showing reduction of RSFS ($\mathcal{E}=32$, $T=10$, 50, 100, 250). (d) Resonant radiation in reduced model for $\alpha =0.05$ (for $m=4$ state).

Figure 3

(a),(b) Soliton oscillations due to a small Kerr term [$r=0$ in (a) and $r=0.11$ in (b), $T=10$, input pulse $A=N\mathrm{sech}(t)$ with $N=5$], in Eq. (2). (c) GVD of the fundamental mode (${\mathrm{HE}}_{11}$) of a ${\mathrm{CS}}_2$-filled PCF. Fiber parameters are with $a=1.6\mu \mathrm{m}$, $b=1.2\mu \mathrm{m}$ (see inset). Each curve refers to different hole spacing $\Lambda$ expressed in $\mu \mathrm{m}$.