Generalized Conservation Of Complex Power Technique For Solving The Characteristics Of Periodic Dielectric Waveguide

Periodic structures are of considerable applications in the microwave, millimeter-wave and optic-wave regions. Although the general theory characterizing periodic waveguide has been rigorously established, theoretical analysis based on Floquet theorem involves matrixes of infinite order, and thus effective and efficient truncation in calculation of the Floquet propagation constants is still an active topic of current research. This is of important significance for many engineering applications, including distributed feedback lasers, optical filters, Bragg-feedback modulators, photonic bandgap materials, which involve operation near the stopbands region corresponding to Bragg reflection.In this paper, a novel approach based on generalized conservation of complex power (GCCPT) is presented for calculating waveguiding characteristics of one dimensional periodic structure having step discontinuity. Bounded approach, in which the structure is enclosed by perfectly conducting walls, is applied to facilitate discussion. Comparison among different matching techniques, including mode matching technique (MMT), conservation of complex power technique (CCPT), improper MMT with power decrement or increment (PD/PI-MMT), is taken to derive some properties for generalized scattering matrix (GSM) in conjunction with these techniques. It is shown that PD/PI-MMT, in contrast to the equivalence between MMT and CCPT in the context of closed waveguide, is in contradiction to principle of conservation of complex power, and cannot be employed to express GSM for discontinuity. Further analysis, however, suggests that PI-MMT and PD-MMT are in duality symmetry, and can, in combination, restore the continuity of complex power, which gives rise to GCCPT. GCCPT is employed to calculate the GSM for transverse discontinuity and, in turn, the transmission matrix of a unit cell.Regarding the periodic corrugations as consisting of step discontinuities connected via a length of waveguide, one may obtain the propagation constants of periodic structure of finite length by cascading algorithm, and propagation constants of infinite periodic corrugation from eigenvalues of matrix with the aid of solution selection rule. A number of numerical examples are shown to demonstrate the efficiency and accuracy of our approach.