Fig. 1. (a) Schematic of the waveguide cross section. (b) Dominant electric field component ($E_z$) of the ${\mathrm{TE}}_{00}$ mode at the fundamental wavelength. (c) Dominant electric field component ($E_z$) of the ${\mathrm{TE}}_{01}$ mode at the SH wavelength. Both $d_{33}$ and $E_z$ of the ${\mathrm{TE}}_{01}$ mode have the opposite signs across the polarization-reversed double-layer LN. (d) Dependence of the effective refractive indices of the interacting waveguide modes on wavelength, with PM at 1552.2 nm. (e) Calculated ${\eta }_{\text{norm}}$ of the double-layer LNOI waveguide as a function of $h_1$. (f) Black: ${\eta }_{\text{norm}}$ versus the total thickness ($H$) of the waveguide. Red: ${\eta }_{\text{norm}}$ versus the waveguide loss. (g) Effective refractive indices of the interacting waveguide modes versus the width of the waveguide when $H$ is 450 nm. (h) Scanning electron microscopy (SEM) image of the waveguide sidewall.

Fig. 2. Experimental setup for device characterization. PC, polarization controller; EDFA, erbium-doped fiber amplifier; WG, waveguide; AL, aspherical lens.

Fig. 3. (a) Measured ${\eta }_{\text{norm}}$ (black) as a function of wavelength. Maximum ${\eta }_{\text{norm}}$ of $9600\%{\mathrm{W}}^{-1}{\mathrm{cm}}^{-2}$ at 1485.7 nm is observed. The red dotted and blue dashed curves correspond to simulations with ideal and corrected models, respectively. The inset shows the top-view optical micrograph of the scattered SH signal at the waveguide facet. (b) The transmission spectrum of a microring resonator is used to extract waveguide loss, with experimental data shown in black and a fitting curve shown in red. (c) PM wavelength versus the top width of the waveguide.

Fig. 4. (a) Measured (green) and simulated dependence of SHG power (at the output facet of the waveguide) on the pump power (at the input facet of the waveguide). Red dashed line: simulation without considering pump depletion and waveguide loss. Black dashed line: simulation with considering pump depletion only. Blue dashed line: simulation with considering both pump depletion and waveguide loss. The inset shows the input–output power relation in the low-power regime. (b) Measured and simulated ${\eta }_{\mathrm{abs}}$ (${\eta }_{\mathrm{abs}}=P_{2\omega }/P_{\omega }$) of SHG as a function of the pump power extracted from (a).

Fig. 5. Measured and simulated PM wavelengths as a function of temperature, in good agreement. Also, this exhibits a desirable thermal tunability.

Table 1. Comparison of SHG waveguides in LNOI working at telecommunication band.