Numerical techniques for excitation and analysis of defect modes in photonic crystals

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Abstract
Two numerical techniques for analysis of defect modes in photonic crystals are presented. Based on the finite-difference time-domain method (FDTD), we use plane wave incidences and point sources for excitation and analysis. Using a total-field/scattered-field scheme, an ideal plane wave incident at different angles is implemented; defect modes are selectively excited and mode symmetries are probed. All modes can be excited by an incident plane wave along a non-symmetric direction of the crystal. Degenerate modes can also be differentiated using this method. A proper arrangement of point sources with positive and negative amplitudes in the cavity flexibly excites any chosen modes. Numerical simulations have verified these claims. Evolution of each defect mode is studied using spectral filtering. The quality factor of the defect mode is estimated based on the field decay. The far-field patterns are calculated and the Q values are shown to affect strongly the sharpness of these patterns. Animations of the near-fields of the defect modes are presented to give an intuitive image of their oscillating features.
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