Temperature-Dependent Anisotropic Refractive Index in β-Ga₂O₃: Application in Interferometric Thermometers

An accurate knowledge of the optical properties of β-Ga₂O₃ is key to developing the full potential of this oxide for photonics applications. In particular, the dependence of these properties on temperature is still being studied. Optical micro- and nanocavities are promising for a wide range of applications. They can be created within microwires and nanowires via distributed Bragg reflectors (DBR), i.e., periodic patterns of the refractive index in dielectric materials, acting as tunable mirrors. In this work, the effect of temperature on the anisotropic refractive index of β-Ga₂O₃n(λ,T) was analyzed with ellipsometry in a bulk crystal, and temperature-dependent dispersion relations were obtained, with them being fitted to Sellmeier formalism in the visible range. Micro-photoluminescence (μ-PL) spectroscopy of microcavities that developed within Cr-doped β-Ga₂O₃ nanowires shows the characteristic thermal shift of red-infrared Fabry-Perot optical resonances when excited with different laser powers. The origin of this shift is mainly related to the variation in the temperature of the refractive index. A comparison of these two experimental results was performed by finite-difference time-domain (FDTD) simulations, considering the exact morphology of the wires and the temperature-dependent, anisotropic refractive index. The shifts caused by temperature variations observed by μ-PL are similar, though slightly larger than those obtained with FDTD when implementing the n(λ,T) obtained with ellipsometry. The thermo-optic coefficient was calculated.