Masamitsu Asai

Numerical method of applying shadow theory to all regions of multilayered dielectric gratings in conical mounting

Nakayamas shadow theory first discussed the diffraction by a perfectly conducting grating in a planar mounting. In the theory, a new formulation by use of a scattering factor was proposed. This paper focuses on the middle regions of a multilayered dielectric grating placed in conical mounting. Applying the shadow theory to the matrix eigenvalues method, we compose new transformation and improved propagation matrices of the shadow theory for conical mounting. Using these matrices and scattering factors, being the basic quantity of diffraction amplitudes, we formulate a new description of three-dimensional scattering fields which is available even for cases where the eigenvalues are degenerate in any region. Some numerical examples are given for cases where the eigenvalues are degenerate in the middle regions.

Reciprocity theorem and accuracy evaluation on scattering fields by dielectric gratings

In the theory of gratings, a diffraction solution must satisfy the energy balance and the reciprocity. This paper examines the diffraction by multilayered dielectric gratings, including lossy layers of which the solutions do not satisfy the energy balance. Applying the shadow theory to the matrix eigenvalues method, the symmetry of scattering factors in the theory and that of diffraction efficiencies are shown in some formulae and then are validated numerically. In addition, the reciprocity errors for diffraction efficiencies and scattering factors are newly considered as an accuracy criterion. It is shown that, on numerical calculations, the reciprocity errors for diffraction efficiencies have only to be checked.

Numerical evaluation by reciprocity in dielectric gratings

In the theory of gratings, a numerical diffraction solution must be satisfy the energy balance and the reciprocity. The matrix eigenvalues method has been presented to study the diffraction by dielectric gratings. In the method, the error of energy balance always becomes zero except for rounding error. An accuracy criterion of a solution is left as a difficult problem. This paper shows the reciprocity for the diffraction efficiencies of the reflected and transmitted waves, numericaffy. It is suggested that the reciprocity can be used the criterion.