  Birefringence phase-matching based \c{hi}(2) ZnGeP2 (ZGP) waveguide platform
has been recently reported for excellent mid-infrared laser generation. Here, a
detailed theoretical characterization of mode transmission taking waveguide
anisotropy and substrate material absorption into account in a micrometer ZGP
waveguide platform (ZGP-on-SiO2) is conducted. Benefited from high-index
contrast between ZGP and substrate (SiO2/Air), Transverse electric and magnetic
(TM and TE) mode transmission loss at interested wavelengths range of 2 - 12
{\mu}m is calculated to be less than 4 dB/cm and 1.5 dB/cm, respectively, in
the designed ZGP waveguide. Notably, non-obvious oscillation of mode
transmission loss versus phase-matching angles is observed, which is different
from that in the previously reported weakly guided anisotropic waveguide. A
vital phenomenon named mode crossing at some wavelengths in TM polarization is
also exhibited in our waveguide platforms, which jeopardizes waveguide
performances and could be avoided by changing the phase-matching angle in
practice. This work provides a significant indication of ZGP waveguide design
optimization in future and also exhibits extendibility to other birefringent
crystal waveguide platforms.
