Fig. 1. (a) Design of LPG waveguides. (b) Diagram of grating-induced phase matching. The soliton wave and dispersive wave are quasi-phase-matched and cause grating-induced phase matching. (c) Using LPG waveguides, the TE00 phase mismatch intersects the grating-induced phase mismatch, so the matching condition is achieved, and a spectrum with several peaks is generated.

Fig. 2. (a), (b) Dispersion and phase mismatch of uniform (δ=0) waveguides at different widths of W=525, 550, 575, 600, and 625 nm. (c), (d) Dispersion and phase mismatch of LPG waveguides at W=550nm and δ=100, 200, 300, and 400 nm. In all simulations, it is a strip waveguide with height = 220 nm.

Fig. 3. Measurement setup. OSA, optical spectrum analyzer. Inset: microscope image of the fabricated silicon photonic LPG waveguides.

Fig. 4. (a) Measured SCG output spectra of uniform (δ=0) waveguides, with different waveguide widths. (b) Measured SCG output spectra when varying δ, where W=550nm and Λ=0.5mm. (c) Measured SCG output spectra of LPG waveguides when varying Λ, where W=550nm and δ=200nm. In all experiments, we use 1550 nm, 100-MHz repetition rate, and 230-fs pulses with an average power of 0.01 W. Spectra are vertically offset by multiples of 50 dB for clarity. The arrows indicate the grating-induced dispersive waves.

Fig. 5. (a) Measured SCG output spectra of the LPG waveguides with different average pump powers, where W=550nm, δ=200nm, and Λ=0.3mm. (b) Measured SCG output spectra of 550-nm waveguide with different average pump powers. Spectra are vertically offset by multiples of 50 dB for clarity.

Fig. 6. (a) Simulated time and (b) spectral evolution on the LPG waveguides. (c) The output spectra of the SCG from the LPG waveguide and the uniform (δ=0) waveguide, respectively. Dashed lines: simulated results. Solid lines: experimental results. Spectra are vertically offset by 100 dB for clarity.