Unveiling the optical parameters of vanadium dioxide in the phase transition region: a hybrid modeling approach

The phase change behavior of vanadium dioxide (VO₂) has been widely explored in a variety of optical and photonic applications. Commonly, its optical parameters have been studied in two extreme regimes: hot (metallic) and cold (insulating) states. However, in the transition temperatures, VO₂ acts like an inherent metamaterial with mixed metallic-insulating character. In this range, the portions of metallic and insulating inclusions are tuned by temperature, and therefore a gradual change of optical parameters can be achieved. In this paper, a universal hybrid modeling approach is developed to model VO₂ in the intermediate region. For this aim, the measured reflectivity data, is analyzed and matched through the transfer matrix method (TMM) simulations where an effective medium theory (EMT) is employed. Based on the findings of this approach, not only the relative portions of inclusions are tailored but also their grain shapes are significantly altered in the transition range. Finally, the modeling approach is testified by experimental findings through dynamic device applications operating at short and mid infrared wavelengths. In addition, the hysteretic behaviors on electrical, optical, and structural parameters of the VO₂ film along the heating and cooling cycles are demonstrated by the experiments and scrutinized by the simulations.