Supercontinuum generation from Topological Edge Supermodes in a short SSH Photonic Crystal Fiber

Abstract

We introduce a topological photonic-crystal fiber that embeds a short Su-Schrieffer-Heeger (SSH) chain and supports two edge supermodes. Using full-vector modal analysis and a coupled generalized nonlinear Schroedinger equation, we show that each supermode provides an independent nonlinear channel with a distinct broadening mechanism: the even supermode features two zero-dispersion wavelengths and yields degenerate four-wave mixing sidebands, whereas the odd supermode is all-normal-dispersion and generates a smooth, flat ANDi-type continuum. Exciting a single core prepares a coherent superposition of the two supermodes; cross-phase modulation and inter-parity four-wave mixing then enable energy transfer across detunings inaccessible to either mode alone, producing the broadest and flattest spectrum with new short wavelengths components. Our results establish topology-enabled modal control as a scalable knob for engineering supercontinuum generation in short SSH topological fibers.

Figures (6)

• Figure 1: (a) Cross-section of the PCF embedding a four-core SSH chain. (b) SSH sketch with intracell coupling $t_{1}$ and intercell coupling $t_{2}$; edge states occur for $t_{1}<t_{2}$. (c) Representative normalized field maps (color: $|E|/\max|E|$) for bulk (left) and edge (right) supermodes in the even (top) and odd (bottom) parity sectors. The even/odd edge states are the hybridized end modes used throughout. All panels use the same spatial scale; maps shown at the pump wavelength $\lambda_{0}=1.064~\mu\mathrm{m}$ and one polarization.
• Figure 2: (a) Effective index, $n_\mathrm{eff}(\lambda)$, for bulk modes (black solid) and edge supermodes (odd, red dashed; even, blue dashed). (b) Corresponding dispersion, $D(\lambda)$. The even and odd edge supermodes exhibit distinct dispersion profiles, so each provides a different nonlinear channel for SCG.
• Figure 3: (a) Coupling coefficients extracted from the four-mode spectra: intracell $t_1(\lambda)$ (solid) and intercell $t_2(\lambda)$ (dashed). Across the band $t_2>t_1$, indicating the non-tivial SSH phase. (b) Robustness at the pump wavelength $\lambda_0 = 1.064~\mu$m, eigenvalue detunings $\Delta\beta$ (relative to the mid-gap $\beta_0$) under off-diagonal coupling disorder with r.m.s. 0.05 max$\{(t_1,t_2)\}$ (over 1000 realizations). Red circles: mean; red error bars: $\pm1~\sigma$. Solid gray lines mark the clean edge detunings $\pm\zeta_1$; dashed gray lines mark the clean bulk detunings $\pm\zeta_2$. Error bars for the two edge modes are not appreciable at this scale, while bulk modes show a larger (still visible) variance.
• Figure 4: SCG for eigenmode launches. Left: even edge supermode showing FWM sidebands and subsequent cascades. Right: odd edge supermode showing smooth SPM-dominated broadening. Top: output spectra (raw/thin and smoothed/bold); bottom: evolution maps (yellow-to-purple colormap).
• Figure 5: SCG for single-core launch, analyzed in the even (left panel)/odd (right panel) supermode basis. Both projected spectra inherit the hallmarks of their eigenmode analogs but extend further due to XPM and inter-parity FWM enabled by coherent co-propagation. Top: output spectra (raw/thin and smoothed/bold); bottom: evolution maps (yellow-to-purple colormap).