Tunable photonic defect modes in one-dimensional photonic crystals containing exponentially and linearly graded index defect

We present an analytical study of the defect modes in one-dimensional (1-D) photonic crystals with defect layer of exponentially and linearly graded index materials. The relative refractive index in the defect layer varies continuously along the direction perpendicular to the surface of layer. The transmission spectra demonstrate that there exist two defect modes inside the photonic band gap for the quarter-wave layers stacking photonic crystal structures with a defect layer of graded index material. The grading profiles of the defect layer affect the frequency and intensity of photonic defect modes. The intensity, frequency and number of defect modes have been changed with the thickness and gradation parameter of graded index defect layer. Moreover, results show that different incident angle in TE and TM polarizations can also be changed the frequency and intensity of the defect modes remarkably. This defect mode splitting and tuning phenomenon in 1-D photonic crystals containing defects of graded index materials can be used to design filters, sensors, and other photonic devices.