Theoretical investigation of ultracompact and athermal Si electro-optic modulator based on Cu-TiO2-Si hybrid plasmonic donut resonator.

An ultracompact silicon electro-optic modulator operating at 1550-nm telecom wavelengths is proposed and analyzed theoretically, which consists of a Cu-TiO(2)-Si hybrid plasmonic donut resonator evanescently coupled with a conventional Si channel waveguide. Owing to a negative thermo-optic coefficient of TiO(2) (~-1.8 × 10(-4) K(-1)), the real part of effective modal index of the curved Cu-TiO(2)-Si hybrid waveguide can be temperature-independent (i.e., athermal) if the TiO(2) interlayer and the beneath Si core have a certain thickness ratio. A voltage applied between the ring-shaped Cu cap and a cylinder metal electrode positioned at the center of the donut,--which makes Ohmic contact to Si, induces a ~1-nm-thick free-electron accumulation layer at the TiO(2)/Si interface. The optical field intensity in this thin accumulation layer is significantly enhanced if the accumulation concentration is sufficiently large (i.e., > ~6 × 10(20) cm(-3)), which in turn modulates both the resonance wavelengths and the extinction ratio of the donut resonator simultaneously. For a modulator with the total footprint inclusive electrodes of ~8.6 μm(2), 50-nm-thick TiO(2), and 160-nm-thick Si core, FDTD simulation predicts that it has an insertion loss of ~2 dB, a modulation depth of ~8 dB at a voltage swing of ~6 V, a speed-of-response of ~35 GHz, and a switching energy of ~0.45 pJ/bit, and it is athermal around room temperature. The modulator's performances can be further improved by optimization of the coupling strength between the bus waveguide and the donut resonator.