Fig. 1. Ultrathin Mie-based free-space electro-optic modulators.

a Free-space electro-optic modulators change the properties of a beam that is incident from free space. Sub-wavelength Mie resonators impart an intensity modulation to the incident light that propagates through the thin film via the electro-optic effect that occurs in an organic electro-optic coating that covers the nanoresonators; the interaction length is typically a few hundred nanometers long, shorter than a single wavelength, commensurate with the thickness of the organic electro-optic coating. b Resonant electro-optic modulators work on the principle that their resonant frequency ${\omega }_{\mathrm{res}}$ is tuned by Δω_eo(t) linearly by an applied bias, due to the phase shift induced by the electro-optic effect. A radio-frequency bias V_RF(t) = V_eo × sin(2πf_RFt) is applied across two interdigitated electrodes (signal is shown in yellow and GND is shown in orange) displacing the resonance frequency around its zero bias value. Narrowband resonances that satisfy $\mathrm{\Delta }{\omega }_{\mathrm{eo}}>\delta {\omega }_{\mathrm{res}}$ are preferred for full intensity modulation at low switching voltages. Dashed black arrows indicate the applied tuning field that introduces the electro-optic effect. Red arrows indicate the propagating optical field. EO electro-optic, GND ground.