Equalization in photonic bandgap multiwavelength filters by the Newton binomial distribution

In this paper, the design criteria of a multiwavelength photonic bandgap (PBG) filter are shown. The spectral behavior of different defective structures, such as structures with a single defect and with multiple defects, is investigated. The filter behavior is analyzed in connection with the variation of different design parameters, i.e., the number of defects within the PBG structure, the defect length, and the defect position. In particular, the introduction of defects spatially distributed according to Newton binomial coefficients along the PBG structure allows the equalization of the transmission channels. The design and the electromagnetic simulations of the proposed structures were performed using proprietary codes based on the bidirectional beam propagation method with the method of the lines. The binomial distribution of multiple defects significantly increases the passband of each transmission channel with respect to the case of a single defect. For example, the PBG waveguide with a single centered defect having length L-d = 340 mu m exhibits 15 transmission channels in the PBG with free spectral range FSR = 1.6nm and 3 dB bandwidth Delta lambda(3) (dB) = 0.35 nm. Conversely, the PBG waveguide with four binomially spaced defects exhibits the same number of channels and the same free spectral range, whereas the 3 dB bandwidth of each channel is increased to Delta lambda(3 dB) = 0.9 nm.