Analysis of photonic crystal waveguide bends by a plane-wave transfer-matrix method

We have developed a plane- wave transfer- matrix method ( PWTMM ) to analyze light propagation through sharp photonic crystal bend structures. With the aid of the supercell technique, the original aperiodic waveguide bend can be modeled by a periodic scattering problem of two semi- infinite photonic crystal waveguide arrays face to face or two semi- infinite photonic crystal waveguide arrays separated by a sandwiched slab of bend region. The proposed approach has been applied to several sharp bend structures in two- dimensional photonic crystals. The calculated transmission and reflection spectra of the waveguide mode are in good agreement with existing results made by other numerical methods, even at the frequency close to the waveguide cutoff frequency. The developed PWTMM only needs to handle a single unit- cell layer domain and is therefore numerically friendly. The proposed approach can become an efficient and accurate numerical tool to understand and design high performance sharp waveguide bends in different two- dimensional and three-dimensional photonic crystals with complex geometries.