Analytical Modeling of Epsilon-Near-Zero Effect in Indium Tin Oxide and Its Application as an Optical Modulator

We present a theoretical model for the complex optical conductivity of a structure consisting of indium tin oxide (ITO) and hafnium oxide (HfO2). The model includes an analytical derivation of the electrostatic potential, electron concentration, and complex relative permittivity of the ITO thin film, which is then compared with a numerical model. Excellent agreement is observed between the analytical model and the numerical data, demonstrating its simplicity, accuracy, and ease of use for evaluating optical conductivity and designing ITO-based optical modulators. Exploiting plasma dispersion effect of ITO nanostructures, we have developed a novel vertical-cavity optical modulator. The modulator consists of ITO thin films and HfO2 dielectric layers positioned between two distributed Bragg reflectors (DBRs) mirrors. By utilizing the tunable property of the ultrathin layer at the ITO–dielectric interface, the modulator exhibits efficient optical modulation capabilities.