VO ₂ as a statistically correlated disordered random metasurface: a complex-valued mixing parameter model for correlated phase transitions

The description of the permittivity phase transition in vanadium dioxide (VO 2 ) is commonly based on effective medium theories that modulate a real-valued volume fraction between the dielectric and metal. Such approaches cannot reproduce all complex interactions arising in the VO 2 matrix during this transition. In this work, we introduce what is believed to be a new modeling framework based on a complex-valued interpolating parameter, whose real and imaginary components jointly govern the thermal evolution of the complex permittivity of VO 2 . Within this formulation, the real part of the mixing parameter primarily reflects the progressive change in metallic volume fraction, while its imaginary part captures correlation-driven effects associated with the spatial organization and coherence of metallic inclusions. By combining numerical simulations with experimental measurements, we demonstrate that this complex mixing model provides an accurate and physically consistent description of the VO 2 phase transition across a broad spectral range. The results show excellent agreement between theory and experiment, highlighting the importance of correlation-induced contributions that are neglected in conventional real-valued mixing models. Beyond improving the physical understanding of the VO 2 phase transition, the proposed approach offers a compact and flexible framework that is well suited for the modeling and optimization of tunable photonic devices and metasurfaces based on phase-change materials.