Fig. 3: Phase-shifter orientation relative to crystal domains and the effective Pockels coefficient.
a, Schematic depicting the phase-shifter orientation relative to the domain orientations in the LN (left) and BTO (right) thin films. The orientation of the ferroelectric polarization domains is shown by the black arrows and denoted by angle φ. The LN thin film only has a single polarization direction of φ = 0°, whereas BTO has four possible orientations, namely, φ = 0°, 90°, 180° and 270°. The areas shaded in gold represent the signal and ground electrodes, which also serve as optical waveguides. The phase shifters are oriented such that the propagation direction (green arrow) is at an angle θ relative to the crystal c axis. The optical (red arrow) and RF (blue arrow) electric fields are both polarized perpendicular to the propagation direction. b,c, Analytically calculated effective Pockels coefficients according to equation (4) for LN (b) and BTO (c). The solid line shows the case in which all the domains are oriented in the same direction (νφ=0° = 1). The dashed and dotted lines show the case for films with domains oriented at 90° to each other, in which the domains are fully poled (dashed), partially poled (dot–dashed) or randomly distributed (dotted). d, Illustrations of the domain polarizations in BTO for the three cases of poling along with their domain fractions νφ. Domains with the preferred polarization direction are coloured in light green, and the antiparallel domains are coloured in dark green.
