Electro-optical Amplitude and Phase Modulators Based on Tunable Guided-Mode Resonance Effect

摘要： Here, electrically tunable amplitude and phase modulators are designed by the hybridization of indium tin oxide (ITO) into a guided-mode resonance mirror (so-called GMRM) which consists of a high-index silicon (Si) nanograting placed on top of a Si guiding core followed by a silicon-dioxide optical buffer layer and a highly reflective substrate. The physical mechanism is based on the intriguing optical characteristics of GMRMs and integration of a dual-gated ITO with the capability of charge carrier modulation into the Si nanograting. A gate-tunable amplitude modulator with a modulation depth as high as ≈0.80 is realized by careful selection of structural parameters, excitation of a strongly coupled guided-mode resonance, and modifying the external bias voltage. This design can also be adjusted only by changing the thickness of its optical buffer layer and moderating the strength of the guided-mode resonance to serve as an efficient active phase modulator. The phase variation of ≈210° and relatively high reflection amplitude in 0.45-0.6 range are accomplished when the applied bias voltage alters from -15 V to +24 V. This reflection phase tuning mainly originates from the carrier depletion and accumulation inside the incorporated 5 nm-thick ITO layer. The accurate modeling and numerical calculation of optical response of the proposed unit cell for different applied external voltages are carried out through linking the electrostatics device physics model and rigorous coupled wave analysis (RCWA) optical simulation. The design rules and physical principles behind the dual-gated ITO-integrated GMRM unit cell are discussed in-depth by investigation of the structural parameters, the nature of supported resonances, and voltage-dependent effects of inhomogeneous carrier distributions in both ITO and Si layers. The electrical addressability and individual control over pixelated subwavelength unit cells provide the opportunity for realizing an actively reconfigurable metasurface with the desired gradient phase delay.