Propagation Characteristics of Periodic Arrays of Dielectric Slabs

Modeling of Glide-Symmetric Dielectric Structures

“…In order to determine the Floquet coefficients A m and the propagation constant k x,0 of the propagating wave inside the parallel-plate waveguide we need to match the tangential EM components with the ones in the corrugated walls. The wave propagating in the corrugated region can be modeled as a wave propagating along a periodic array of dielectric slabs [18,20] with the following EM field distribution (N corr denotes the highest-order considered mode).…”

“…The reported analysis methods were often based on the assumption that periodic variation acts only as a small perturbation of a planar multilayer waveguide [15][16][17], which may produce erroneous results in many cases, e.g., if the corrugated grating is thick. The proposed rigorous solution is based on the Floquet mode decomposition and a mode matching (MM) technique [18,19] in which the corrugated layer is modeled as a periodic array of infinite dielectric slabs [20]. All previously considered structures contained one layer of corrugations, except in Reference [21] where two layers of corrugations with different periodicities were investigated.…”

Analysis of dielectric grating waveguides for the design of dichroic structures

“…The characteristic equation for calculating y, , for an array of NP dielectric slabs per cell was later obtained [8,11,12] and given by where MPii are elements of an M, matrix, resulting from the product of the transmission matrices of each Lth dielectric slab. This matrix is obtained by applying the boundaly conditions, at the interfaces between slabs e and e+ 1, on the fie'3 colALponents transverse to the x axis, propagating along this axis, in each one of the Lth slab, with a phase constant given by and expressed by [ll, 121 (10) is the admittance of each mode propagating along the x direction, equal to ( m , E r i ) / k i n or kin/Wpo for the 'I'M or TE modes, respectively, and u,, = k,,d, is the phase constant, normalized with respect to the dielectric slab thickness. After obtaining the values of y, , from eq.…”

Electromagnetic wave propagation in a periodic array of rectangular dielectric waveguides

“…ExceIlent agreement is again observed when compared with the results obtained by Costa and Giarola [4] for their TE modes, which corresponds to our group 2, for the particular case of d=b. A rigorous modal approach was used in both formulations of Lewys and Hessel [3] and Costa and Giarola [4]. As in Fig.3, Fig4 also shows that P / k o decreases as d is decreased.…”

“…~=2.56, k0=176 m-', a=2.142 cm, b=1.0 cm and 1=0.926cm. Also shown with dark marks are results from Lewys and Hessel[3].…”