Fig. 2: Numerical analysis and classical measurements of nonlinear LPLN nanophotonic waveguides.

a Numerically calculated nonlinear coupling parameter (Γ) as a function of poling depth. The maximum Γ at a poling depth of ~290 nm (red dot) is more than two orders of magnitude higher than that of an unpoled LN waveguide (green dot). The inset illustrates that Γ is essentially determined by the overlap integral of the electric fields (E_z component) of the two involved modes and the χ⁽²⁾ polarity distribution in a TFLN waveguide. The gray dashed line indicates the 3 dB bandwidth (BW) of Γ, which corresponds to a poling depth range of 113 nm. b Measured SHG power as a function of pump power in a 2.5 mm long LPLN waveguide. A linear fitting reveals an on-chip conversion efficiency of 4615 ± 82% W⁻¹cm⁻². Inset: normalized SHG spectra of a LPLN waveguide (green) and a reference, unpoled waveguide (brown), showing a >20 dB difference. Both waveguides have the same width, are fabricated on the same chip, and are tested under the same conditions. c Simulated phase-matching wavelength shift (at FH) as a function of the TFLN thickness variation (nominal thickness = 600 nm) in a LPLN waveguide (blue) and a similar PPLN waveguide (red). Their thickness sensitivity is fitted to be 2.3 and −10.5 (in unit of nm wavelength shift per nm thickness change), respectively. d Phase-matching wavelength shift (at FH) as a function of waveguide width variation (nominal width = 1100 nm) for LPLN (blue) and PPLN (red) waveguides, showing a sensitivity of −0.32 and −1.5, respectively. Here, the data for the LPLN waveguide is based on the measurement, and data for PPLN is from simulation. Inset: Measured SHG spectra (x-axis: pump wavelength in nm) of LPLN waveguides with widths of 1200 nm (magenta), 1100 nm (green), and 1000 nm (yellow). e Measured phase-matching wavelength shift (at FH) as a function of temperature for LPLN (blue) and PPLN (red) waveguides, showing a fitted temperature sensitivity of 0.18 nm/^∘C and 0.77 nm/^∘C, respectively