In this study, we present an investigation of the optical properties and band structures for the photonic structures based on AIBIIICVI 2 with a Fibonacci sequence that can act as a multi-wavelength birefringent filter. The filtering wavelengths are analyzed by the indices concerning the quasi-periodicity of a Fibonacci sequence and the average lattice parameter. The transmittances of filtering wavelengths can be tuned by varying structure parameters such as the lengths of poled domains, filling factor, and dispersion relation. In our simulation, we employed the finite-difference time domain (FDTD) technique, which implies a solution from Maxwell equation.