Analysis and design optimization of electrooptic interferometric modulators for microphotonics applications

Scaling the electrode layout (electrode gap, electrode length) down to microscale dimensions extends the application of electrooptic (EO) modulators to microphotonics. In this paper, design criteria are set up to minimize the switching voltage of microscale EO Mach-Zehnder interferometric modulators. Mach-Zehnder interferometric modulators under different directions of electric field with respect to the optic axis are analyzed. Three expressions of the intensity output characteristics are presented for various crystal classes and compared in terms of conditions of validity and design applications. The analysis in this paper suggests that the switching voltage is strongly related with the direction of the electric field relative to the optic axis. For the 4-mm BaTiO₃ (r₃₃=28 pm/V,r₅₁=820 pm/V) Mach-Zehnder modulators, r₅₁ is utilized when the electric field is applied normal to the optic axis. In this configuration, the thermal stability and polarization insensitivity improve but the extinction ratio becomes a function of the electrode length. The phase-retardation expression is useful to find a suitable modulator length and maximize the extinction ratio. Some of the discussions also apply to Fabry-Pe´rot interferometric modulators.