Generally when anisotropic material such as liquid crystals are confined in a Fabry-Perot cavity, the transmission through the device becomes sensitive to the input polarization. While continuous tunability of the refractive index is possible by applying a small electric field across the liquid crystal, It is found that under certain circumstances a forbidden gap in transmission wavelength is observed. It is shown that this occurs because of mode mixing brought by slightly twisted uniaxial structure disposed between the Fabry-Perot structure. A theoretical model is presented to explain the experimentally observed data with excellent agreement.