Angular tuning of defect modes spectra for one dimensional photonic crystal filters with a liquid crystal layer

A tunable photonic crystal filter with a twisted nematic liquid crystal layer is proposed. The defect modes spectra with varying incident angles are discussed in detail by 4x4 matrix method. The results show that the defect modes are mainly decided by the applied voltage when the incident angle is smaller than 8o. As the incident angle further increases, the band gap and the defect modes shift toward the shorter wavelength side, and the changes of the two modes are different. In the lower voltage range, the defect modes can be tuned not only by the applied voltage but also by the incident angle. In the higher voltage range, the defect modes can be further tuned by varying incident angle and the different modes can be separated from each other by a big incident angle.