Defect modes in two-dimensional parallelogram lattice photonic crystals

Using plane wave method (PWM) combined with supercell method, Fourier extension coefficient of dielectric function for arbitrary defects in parallelogram lattice PC are derived, then the point and line defect modes of TM mode for 5×5 supercell PC with lattice angle 70° are calculated. These results would provide theoretical instruction for designing vacuum electron devices using PC with parallelogram lattice.