Comb-like Photonic Crystals With A One-dimensional Class Structure And The Defect Mode

numerous theoretical and experimental investigations have focused on photonic crystals. Due to existing photonic band gaps in the electromagnetic band structure of these artificial structures. In generally, photonic crystals are regular arrays of several materials with different refractive indices. In all these composite systems the contrast of dielectric properties among the constituent materials and the composition of the inhomogeneous material and the filling ratio as well as the periodicity are emerging as critical parameters in determining the existence of gaps. Based on the introduction of the optical properties of photonic crystals, by using interface response theory, the photonic band structures and the defect modes in one-dimensional comblike waveguide which made of dangling two different side branches grafted periodically along a infinite monomode waveguide were investigated in this paper. The dispersion relation of infinite comblike wave guide was obtained. Through calculating the transmission coefficient T of the wave guide when the side branches are grafted at a finite number of N sites. It was discovered that the photonic forbidden bands not only relate to the contrast in dielectric constants of side branch materials and the backbone, but also relate to the length and the number of the side branches, and to the periodicity. Relatively wide gaps still remain when the constituent materials are identical. In this case, the band gaps originate both from the periodicity of the system and the resonance states of the grafted branches, which playing the role of resonators, and the gap width is controlled by geometrical parameters of the structure. Based on these novel properties which being different from the usual photomc crystals, it provides a new way to fabricate new type photonic crystals. Numerical results show that the width of the gaps is related to the length and the number of the side branches, to theperiodicity, as well as to the numbers of the sites. The properties of defect modes by removing or inserting some defect branches in the comblike waveguide of finite N sites grafted branches were also investigated. It was found that the localized states appear in the transmission spectrum as very narrow peaks. The behavior of the localized states was analyzed as the function of the length, the position and the number of the defective branches. Such kind of waveguides could be very useful in making, for instants, filtering, or multiplexing devices.