Theory of fundamental microwave absorption in sapphire (α-Al_2O_3)

摘要

An accurate model for intrinsic dielectric loss in sapphire (α-Al_2O_3) is presented. The proposed model is based on a theory of electromagnetic field absorption governed by multiphonon relaxation processes influenced by a finite lifetime of thermal phonons. Expressions for anisotropic sapphire dielectric loss tangent are derived utilizing sapphire dielectric function given in terms of the quasiharmonic approximation. The frequency-dependent two- and three-phonon damping constants of each fundamental transverse optical mode were determined numerically employing the accurate anharmonic coefficient computations based on sapphire lattice-dynamical data. The results of the dielectric loss tangent calculations in microwave and millimeter-wave regions are presented. The developed sapphire dielectric loss model offers excellent agreement between the experimental and calculated magnitudes of the tan δ components and also accurately reproduces their frequency and temperature dependencies.