PROPAGATION CHARACTERISTICS OF DIELECTRIC WAVE-GUIDES WITH PERIODIC SURFACE-RELIEF

The Fourier series expansion method is applied to the problem of EM waves guided by a dielectric grating with periodic surface-relief. The periodic structures of dielectric gratings are divided into two types: (1) surface-relief type and (2) modulated refractive index type. For the modulated dielectric grating, the rigorous solution is obtained using the space-harmonics expansion method, but the usual method cannot be applied to the grating whose dielectric constant distribution has discontinuities. Previously, we pointed out this issue and gave an improved method which can be applied to those problems. This method can also be applied to the surface-relief grating by approximating it as an assembly of stratified thin modulated dielectric gratings. In this paper, numerical analysis is given for gratings with sinusoidal surface and triangular surface for both perpendicular polarization (TE waves) and parallel polarization (TM waves). The validity of our method has been checked by increasing the number of modal expansion terms and the number of multilayers. The results are compared with those obtained by other numerical methods. The differences in the propagation characteristics between the surface-relief grating and the modulated dielectric grating in Bragg region are also discussed.