Fig. 1. Variation of the third-order susceptibility tensorial components (χiiii,iijj) of YSZ 3.2% in Y2O3 as a function of the relative position between Y dopants (yellow spheres) and O vacancies (green spheres). The unit cells [25] of each configuration considered, representing symmetry in equivalent vacancy/dopant distributions, are schematically given at the right. Solid lines represent the corresponding susceptibility components of c-ZrO2. All values have been computed at the PBE0 level of theory.

Fig. 2. (a) Symmetry nonequivalent local crystal structures of YSZ 33% in Y2O3. Zirconium, oxygen, and yttrium atoms are in gray, red, and yellow, respectively, and the vacancy is in green. See Data File 1 and Data File 2 for the unit-cell fractional coordinates of YSZ-A and YSZ-B, respectively. (b) Total and projected density of states of c-ZrO2 and YSZ-A.

Fig. 3. (a) Unit cell of YSZ 7% considered in this study. (b) Evolution of χiiii(3) and χiijj(3) of YSZ as a function of the concentration in Y2O3 computed with the B3LYP and PBE0 functionals and the smallest ECP basis set used in this work. All local crystal structures have been optimized at the PBE0 level of theory. See Data File 3 and Data File 4 for the unit-cell fractional coordinates of YSZ 7% and YSZ 14%, respectively.

Fig. 4. (a) Schematic view of a YSZ-based rib waveguide, designed and fabricated for single-mode quasi-TE propagation in the H=300  nm YSZ thin film. (b) YSZ waveguide geometry is characterized by atomic-force microscopy (AFM). Dimensions of the waveguide are D=80  nm for the etching depth and W=760  nm for the width. (c) Simulation of fundamental TE mode under the experimental geometrical values of the YSZ waveguide. (d) X-ray diffraction (XRD) of the YSZ thin film studied on sapphire. The 2θ−ω XRD scan presents both (002) and (0006) diffraction peaks from YSZ and sapphire substrate, respectively, confirming the only one [001] YSZ growth direction. (e) The ω scan reveals the mosaïcity of the (001) YSZ plans with an FWHM=0.03°. (f) Propagation losses α=3.2  dB·cm−1 are estimated at λ=1550  nm thanks to the transmission level of different waveguides, long from 0.8 to 5.8 mm.

Fig. 5. (a) Pout versus Pin curve at λ=1580  nm revealing the absence of two-photon absorption (TPA), in agreement with the bandgap energy of Eg>5  eV. (b) Optical transmission at low (dashed orange) and high (solid blue) input powers. (c) Simulation (dashed red) of the spectrum transmitting through a YSZ-based waveguide calculated with the experimental parameters. (d) Experimental measurement of the power in the generated frequencies.

Fig. 6. Waveguides facets obtained with the two-step dicing procedure, including classical dicing technique and focus ion-beam (FIB) etching. (a) Top view of the sample edges with optical microscopy and (b) cross-section observation of a waveguide facet by SEM. Whereas the first classical technique allows to mechanically dice the whole sample, the FIB technique etches a small area, here the extremities of the waveguides, leaving highly transmissive facets.

Fig. 7. Most stable structures of Zr4O8Zr8O16 and Zr15O30.

Table 1. Cell Parameter a (Å), Bandgap Eg (eV), Electronic Contribution of the Dielectric Constant ϵ=ϵii, and Third-Order Susceptibility Components χiiii,iijj(3)(10−21m2·V−2) of c-ZrO2 Computed with the PBE, PBE0, and B3LYP Functionals

Table 2. Unit Cell Volume V (Å3), Bandgap Eg (eV), Electronic Contribution to the Dielectric ϵxx=ϵyy and ϵzz Components, and Kerr (IDRI) Effect Third-Order Susceptibility χxxxx(3)=χyyyy(3), χzzzz(3), and χxxyy(3), χxxzz(3)=χyyzz(3) Components (10−21m2·V−2) of Two Nonequivalent Local Crystal Structures of YSZ 33% in Y2O3 (see Fig. 2)^a

Table 3. Electronic Contribution to the Dielectric Susceptibilities (ϵxx), Third-Order Susceptibilities (χxxxx,xxyy(3)×10−21m2·V−2), Effective Third-Order Susceptibilities (χ^(3)×10−21m2·V−2), and Nonlinear Refractive Index (n^2×10−19m2·W−1) of YSZ 7% in Y2O3 [Fig. 3(a)] Computed at the PBE0 and B3LYP Levels of Theory on PBE0 Optimized Local Crystal Structures^a