The propagation characteristics of dielectric waveguides with slanted grating structure are analyzed by using the combination of the improved Fourier series expansion method and the approximated multilayer method. The slanted grating region is appoximated by a structure with stratified thin modulated index layers. This method is effective to the guiding problems of the planar slanted grating, because the electromagnetic fields in each layer can be expressed by shifting the phase of the solution in the first layer. In this paper, numerical results are given for the grating with the rectangular and the sinusoidal profile for arbitrary slant angle. The radiation efficiencies for the grating with negative and positive slant angle are also discussed.

The scattering of electromagnetic waves by a dielectric grating with planar slanted-fringe is analyzed using the improved Fourier series expansion method. In the analysis, the slanted grating region is divided into layers to make an assembly of stratified thin modulated index layers. This method can be applied to a wide range of periodic structures and is especially effective in the case of planar slanted grating, because the electromagnetic fields in the each layer can easily be obtained by shifting the solution in the first layer. In this paper, the numerical results are given for grating with rectangular and sinusoidal dielectric profiles, and for TM and TE cases of arbitrary incident angle. The diffraction efficiencies obtained by the presented method are compared with the results by the coupled-wave approach; the influences of the slant angle on the diffraction efficiencies at the Wood's anomaly and at the coupling resonance frequency are also discussed.