Abstract
We derive the eigenvalue equation and the expressions for the field distribution for the TM modes of an anisotropic symmetric slab waveguide; the TE modes are identical to the isotropic case. It is assumed that the field components do not depend on the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">y</tex> coordinate and that the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</tex> axis of the uniaxial crystal lies in the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x-z</tex> plane. We find that, in spite of the symmetry of the waveguide, even and odd modes do not exist because the phase fronts of the modes are tilted with respect to the waveguide axis. However, the absolute magnitude of the H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">y</inf> component of the field has even or odd symmetry. The interesting case of an anisotropic slab waveguide with the optical axis located in the plane of the slab will be presented in Part II of this paper.
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