In the shadow theory, a new description and a physical mean at a low grazing limit of incidence on gratings in the two dimensional scattering problem have been discussed. In this paper, by applying the shadow theory to the three dimensional problem of multilayered dielectric periodic gratings, we formulate the oblique primary excitation and introduce the scattering factors through our analytical method, by use of the matrix eigenvalues. In terms of the scattering factors, the diffraction efficiencies are defined for propagating and evanescent waves with linearly and circularly polarized incident waves. Numerical examples show that when an incident angle becomes low grazing, only specular reflection occurs with the reflection coefficient -1, regardless of the incident polarization. It is newly found that in a circularly polarized incidence case, the same circularly polarized wave as the incident wave is specularly reflected at a low grazing limit.

Laser diodes in the (Al, Ga, In) N system are attractive for many applications. Due to the wurtzite crystal structure, cleaved facets are not easily produced. We have investigated distributed feedback (DFB) laser diodes employing embedded dielectric gratings with the grating located above the active region. The dielectric gratings are incorporated via epitaxial lateral overgrowth. The DFB laser diodes had reduced threshold current densities over the etched cavity devices, with a minimum of 15 kA/cm2. The spectral emission width was considerably reduced for the DFB devices. Voltages for the DFB devices were high due to the presence of the Si3N4 grating within the p-type material.