Numerical Analysis Of Multistep Dielectric Gratings

Yamakita, Jiro; Rokushima, Katsu; Mori, Shizuo

doi:10.1117/12.941747

Cited by 3 publications

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Analysis of anisotropic dielectric gratings using differential method

Yamakita

Matsumoto

Mori

et al. 1990

Electron Comm Jpn Pt II

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An analysis algorithm is presented for the scattered field from a surface relief‐type anisotropic dielectric grating with an arbitrary permittivity tensor. The method based on the differential equation known widely as an analysis for isotropic dielectric gratings is extended here to the case where a dielectric grating contains an anisotropic medium. Further, an algorithm is proposed which avoids, by means of reorthogonalization of the initial value vectors, the difficulty in numerical treatment encountered by the differential method when the groove in the grating is deep and the number of expansion terms is large. By means of numerical examples, it is shown that stable numerical solutions can be obtained regardless of the depth of the grating grooves or the size of the expansion terms.

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Analysis of anisotropic dielectric gratings using differential method

Yamakita

Matsumoto

Mori

et al. 1990

Electron Comm Jpn Pt II

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Analysis of lossy dielectric gratings using pseudo‐periodic green's function

Minami

Yamakita

Sawa

1993

Electron Comm Jpn Pt II

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Differential equation methods often are used for the analysis of the waves scattered by a dielectric grating. It is known that accurate numerical solutions can be obtained if the number of expansion terms of the spatial harmonics is increased. However, when the differential equation method is applied to a dielectric grating with an extremely large permittivity, the convergence speed of the solution becomes excessively slow in the TM wave analysis. Because of the increase of the computation time and the memory capacity, an analysis based on the differential equation method becomes difficult in practice. In this paper, it is shown that a boundary element method using Green's function satisfying the periodic condition is effective for the analysis. By introduction of pseudo‐periodic Green's function, the definition region for the integral equation is limited to the grating surface. In comparison to the boundary element method using the Hankel function, the number of linear equations is reduced. By means of numerical examples, it is shown that the convergence speed of the solution by the present method is faster and the computation time is significantly shorter than the solution by the differential equation method even in the TM wave analysis of a dielectric grating with a large loss.

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Numerical Simulation of Binary Lenses by Direct Solution of the Helmholtz Equation

Hadley

1998

Diffractive Optics and Micro-Optics

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Binary diffractive optics have become an important class of structures for use in optical interconnects and coupling into fibers1. Such structures have been successfully designed in the past using the techniques of Fourier analysis. These techniques are entirely adequate for near-paraxial optics such as occur with high-F-number lenses. The design of fast (F<1.5) lenses such as those required for coupling light into optical fibers, however, requires the use of more accurate techniques, most of which are based upon modal expansions2,3. In this paper we describe a new finite-difference method for modeling small-feature-size binary optical structures that involves the direct solution of the scalar Helmholtz in the vicinity of the structure, followed (in the case of lenses) by wide-angle beam propagation to predict the size of the focal spot. In this approach, the structure is described entirely by by its resulting dielectric function, allowing the treatment of aperiodic binary structures of arbitrary complexity. All reflections together with effects due to sub-wavelength feature sizes are automatically included. Polarization effects are treated approximately owing to the use of semivectorial boundary conditions at all dielectric interfaces. This technique has been shown previously4 to correctly model the behavior of first-and second-order diffraction gratings etched into waveguides. (The present method differs slightly from that described in reference 4 in that the solution method is direct matrix inversion instead of the iterative method described therein.) It involves no expansions or simplifying assumptions (aside from vectorial considerations) and is quite fast, requiring only a few minutes of workstation runtime.

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Numerical Analysis Of Multistep Dielectric Gratings

Cited by 3 publications

References 0 publications

Analysis of anisotropic dielectric gratings using differential method

Analysis of anisotropic dielectric gratings using differential method

Analysis of lossy dielectric gratings using pseudo‐periodic green's function

Numerical Simulation of Binary Lenses by Direct Solution of the Helmholtz Equation

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