Electrical modeling of single defect in Photonic Crystal Waveguide

A planar photonic crystal waveguide (PCW) is an essential component of a photonic integrated circuit. For a given guided mode, a PCW can be modeled by an equivalent transmission line. Electrical modeling of a PCW and its defect can help using circuit theory for designing photonic crystal circuits. The ratio of electric and magnetic field (called the wave impedance), weighted by the Poynting vector for an infinitely long PCW, can serve the purpose of the characteristic impedance of the transmission line. FDTD method is employed to compute the wave impedance of PCW. The characteristics of a square lattice PCW with dielectric pillars of refractive index 3.4, placed in two different dielectric substrates of refractive indices 1 and 1.45 respectively are investigated here. Investigation of a point defect created by placing a rod in the waveguide shows that depending upon the size and location, a point defect can be inductive or capacitive.