There have been several designs proposed for bimodal transmission resonators for use in EPR, Hall effect, and Faraday rotation measurements. Some of these are based on attempts to spatially define the field patterns of the normal modes of cylindrically symmetric resonators. Others try to separate the modes so that in some parts of the resonator, the radio frequency fields of predominantly one mode will be found. In this way, independent adjustment of the mode characteristics is attempted so that an adjustable null transmission resonator results. The property to be measured for a sample placed inside the resonator causes an imbalance and the resulting output appears in place of the null. This paper describes a different approach to the practical realization of such a resonator and gives the appropriate theory for its operation. In the resonator to be described the spatial position of the normal modes can be altered by a simple rotation control, and the input radio frequency field polarization direction can be rotated by another such control. There is a direct analogy between microwave propagation through this device and optical propagation through an anisotropic medium situated before an analyzer. The complete cavity resonator shows a minimum rejection in transmission which can be made arbitrarily large, and a tunable rejection notch whose attenuation has been observed to be greater than 100 dB, and which is theoretically infinite. A practical nonresonant device based on the same approach is also described.