  Planar Orthomode Transducers (OMTs) are commonly used for polarization
measurements at millimeter wavelengths. We present an optical coupling study of
an octave bandwidth planar OMT in circular waveguide based on 3D
electromagnetic simulations. We quantify results through metrics such as co-
and cross- polar coupling, reflection, and waveguide leakage as a function of
the OMT construction geometry. We evaluate the tolerance of these metrics to
the waveguide backshort distance, probe impedance, waveguide gap size, and
waveguide-to-probe misalignment. Two probe geometries are studied: the
`classic' shape used in several previous experiments, and a new `wineglass'
geometry. The bandwidth ratio of both optimized OMTs is 2.0:1, defined where
co-polar coupling exceeds 80%. The average co-polar coupling, cross-polar
coupling, reflection, and waveguide leakage of the classic probe is
approximately 93%, $<$-50 dB, 5% and 2%, respectively and depends slightly on
the exact frequency range. The wineglass probe co-polar coupling is $\sim$ 2%
larger. Radial waveguide misalignment at the level of 4% of the waveguide
radius can result in up to a 10% reduction in co-polar coupling and -20 dB
cross-polar coupling in one polarization. These results may be used to guide
the detector module designs of future Cosmic Microwave Background experiments
and beyond
