Temporal quadratic solitons and their interaction with dispersive waves in lithium niobate nanowaveguides

We present a model of soliton propagation in waveguides with quadratic nonlinearity. Criteria for solitons to exist in such waveguides are developed and two example nanowaveguide structures are simulated as proof of concept. Interactions between quadratic solitons and dispersive waves are analyzed, giving predictions closely matching soliton propagation simulations. The example structures are found to support five different regimes of soliton and quasisoliton existence. Pulse propagation in these example waveguides has been simulated confirming the possibility of soliton generation at experimentally accessible powers. Simulations of multisoliton generation, Cherenkov radiation, and quasisolitons with opposite signs of dispersion in the fundamental and second harmonic are also presented here.

Figure 1

Localization conditions, Eqs. (13) and (14), against soliton parameters $\mu$ and $\nu$. Conditions in Eqs. (13) and (14) are marked as shaded regions (in red and blue, respectively) and bounded by solid and dashed lines, respectively. Grey shaded regions bounded by dotted lines mark where constant amplitude solutions exist according to the condition in Eq. (17). Parameter $r_2=-1$ throughout, and (a) $s_2=-0.8,\kappa =4,s_1=-2$. (b) $s_2=-0.8,\kappa =2,s_1=-5$. (c) $s_2=0.8,\kappa =4,s_1=2$. (d) $s_2=-0.8,\kappa =-2,s_1=-1$. (e) $s_2=0.8,\kappa =-4,s_1=1$.

Figure 2

For a lithium niobate on insulator (LNOI), $n_{\mathrm{eff}}$ (a), $\kappa$ and $s_1$ (b), and ${\beta }_2$ (c) plotted against the FF wavelength ${\lambda }_f$. Insets in (a) show the FF (upper) and SH (lower) mode profiles. Inset in (b) shows the LNOI waveguide cross section, $h$ and $w$ label the height and width of the waveguide respectively. Data shown are for a LNOI structure with height of 350 nm and width of 500 nm. For free-standing LN and microfiber (hybrid) structure, $n_{\mathrm{eff}}$ (d), $\kappa$ and $s_1$ (e), and ${\beta }_2$ (f). Insets in (d) show the FF (upper) and SH (lower) mode profiles. Inset in (e) shows the cross section of the hybrid waveguide, $h$ and $w$ label the height and width of the waveguide respectively. Data shown are for a waveguide height of 300 nm, width of 470 nm, and a microfiber diameter of 1100 nm. Solid and dashed curves (red and blue) are for FF and SH modes respectively. Dotted black lines mark $\kappa =0,s_1=0$, and ${\beta }_2=0$. Shaded regions mark the different soliton supporting regimes labeled A–E.

Figure 3

XFROG plots of pulses after simulated propagation in nanowaveguide structures. Each panel consists of FF (right) and SH (left). Resonance predictions are included above XFROG plots for comparison. Wave vectors of dispersive waves are shown as solid lines (blue and red in color, truncated to third- and second-order dispersion respectively). Soliton wave vectors are shown as dot-dashed line (green). Resonances occur where these lines intersect and are marked by vertical dotted lines. (a), (c), and (e) are in the hybrid structure; (b) and (d) are in the LNOI structure. Input pulse parameters: (a) 1.1 kW peak power, 140 fs duration, central wavelength 1525 nm, propagation distance 20 mm. (b) 1.9 kW peak power, 560 fs duration, central wavelength 1530 nm, propagation distance 10 mm. (c) 760 W peak power, 180 fs duration, central wavelength 1460 nm, propagation distance 10 mm. (d) 14 kW peak power, 560 fs duration, central wavelength 1580 nm, propagation distance 30 mm. (e) 1.2 kW peak power, 120 fs duration, central wavelength 1430 nm, propagation distance 10 mm.

Figure 4

XFROG plots of pulses after simulated propagation in nanowaveguide structures. Each panel consists of FF (right) and SH (left). Resonance predictions are included above XFROG plots for comparison. Wave vectors of dispersive waves are shown as blue solid lines (truncated to third-order dispersion). Soliton wave vectors are shown as green dot-dashed lines. Dashed red lines show the wave vectors of solitons interacting with pump frequencies. Resonances occur where these lines intersect. Vertical dotted lines mark the resonance wavelengths. (b) and (c) are in the hybrid structure; (a) is in the LNOI structure. Initial pulse parameters: (a) 6.3 and 19 MW peak power in the FF and SH respectively, 16 fs duration, central wavelength 1580 nm, propagation distance 10 mm. (b) 17 and 21 kW peak power in the FF and SH respectively, 25 fs duration, central wavelength 1430 nm, propagation distance 15 mm. (c) 2.7 kW peak power, 390 fs duration, central wavelength 1530 nm, propagation distance 26 mm.