Fig. 1. (a) Rotation of the optical axes under applied y-direction external electric field. (b) Schematic of achieving cascaded linear EO effects and SHG simultaneously in a single PPLN. The periodically inverted optical axes of PPLN lead to the periodic alteration of the sign of electro-optic coefficients (±γij). (c) Illustration of cascaded linear EO effects. (d) Changes of refractive indices caused by linear, Kerr, and cascaded linear EO effects, respectively. (e) Part of etched poling surface of the sample, with domain inversion period of 20.3 μm.

Fig. 2. Calculated transmission spectrum and the effective EO nonlinear refractive index as a function of ΔβL. Δβ=0 corresponds to the central wavelength λc of the transmission spectrum.

Fig. 3. (a) Measured transmission and SHG spectra fully overlapped at T=26.3°C. SHG spectra with varied external electric fields at (b) 26.3°C; (c) 24.1°C; (d) 27.6°C. The intensity of SHG was modulated by the enhanced Kerr EO nonlinearity.

Fig. 4. (a) Index variations caused by the linear and intrinsic Kerr EO effects as a function of the external electric field. (b) Nonlinear refractive index caused by cascaded linear EO effects versus the external electric field for the specific case of λ=1581.9  nm (Δn2eff<0) in Fig. 3(c) and λ=1582.6  nm (Δn2eff>0) in Fig. 3(d). Points A, B, and C mark the index changes at 0.1 V/μm.

Fig. 5. Measured normalized transmission (a) and SHG intensity (b) at two selected wavelengths [1581.8 and 1582.3 nm in Fig. 3(c)] as a function of the external electric fields. At Ey=0.32  V/μm, the two wavelengths have the same transmittances but quite different SHG intensities.

Fig. 6. Calculated inversion domain periods for achieving SHG (solid) and the cascading effects (dashed) as a function of fundamental wavelengths at different temperatures. Points a, b, and c correspond to the three inversion domain periods we performed in our experiment. Inset figure shows the relationship among the three parameters to realize the cascading process and SHG simultaneously.