Theory of fundamental microwave absorption in sapphire (alpha-Al_(2)O_(3))

摘要

An accurate model for intrinsic dielectric loss in sapphire (alpha-Al_(2)O_(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 delta components and also accurately reproduces their frequency and temperature dependencies.