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This study develops the scalar wave equations of auxiliary vector potentials for time harmonic electric and magnetic fields on transverse electric, transverse magnetic and transverse electromagnetic modes in an biaxial anisotropic medium. The concise scalar wave equations are achieved in both rectangular and cylindrical coordinates. Moreover, in an biaxial medium, it is identified that the decoupled TE, TM, and TEM modes can only exist under certain conditions for various modes respectively which clarify the suspect about the existence of these modes that was reported previously.

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