Fig. 2: Ultra-broadband integrated parametric waveguides with hyper-dispersion engineering.

a, Theoretical conversion-efficiency spectral curves of 1-m-long χ⁽³⁾-base nonlinear integrated waveguides with various fourth-order dispersions. The waveguide loss was 1 dB m⁻¹, the nonlinear coefficient was 0.7 W⁻¹ m⁻¹ and the second-order dispersion was −1 ps² km⁻¹. The power at 1,550 nm wavelength was 35 dBm. The red, yellow, green, light blue and dark blue solid lines are for β₄ = 0.3, 0.4, 0.6, 0.8 and 1.2 fs⁴ μm⁻¹, respectively. The black dashed line corresponds to the case where fourth-order dispersion is not considered. b, Top, experimental set-up for the FWM characterization of the 0.56-m-long single-mode nonlinear rib Si₃N₄ integrated waveguide. Bottom, spectrum after the WDM coupler with a 1,551.1 nm pump and a 1,415 nm signal. c,d, Measured (red circles) on–off parametric gain (c) and on-chip conversion efficiency (d) of the single-mode nonlinear Si₃N₄ integrated waveguide with a 34-dBm on-chip pump power. The solid blue curves were calculated analytically with the assumption of a spectrally constant waveguide loss of 2.5 dB m⁻¹.