Efficient Analysis of Diffraction Grating with 10000 Random Grooves by Difference-Field Boundary Element Method

Jun-ichiro SUGISAKA  Takashi YASUI  Koichi HIRAYAMA  

IEICE TRANSACTIONS on Electronics   Vol.E100-C   No.1   pp.27-36
Publication Date: 2017/01/01
Online ISSN: 1745-1353
DOI: 10.1587/transele.E100.C.27
Type of Manuscript: Special Section PAPER (Special Section on Recent Progress in Electromagnetic Theory and Its Application)
diffraction grating,  random structure,  numerical method,  integral equation,  boundary element method,  

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A numerical investigation revealed the relation between the groove randomness of actual-size diffraction gratings and the diffraction efficiencies. The diffraction gratings we treat in this study have around 10000 grooves. When the illumination wavelength is 600 nm, the entire grating size becomes 16.2 mm. The simulation was performed using the difference-field boundary element method (DFBEM). The DFBEM treats the vectorial field with a small amount of memory resources as independent of the grating size. We firstly describe the applicability of DFBEM to a considerably large-sized structure; regularly aligned grooves and a random shallow-groove structure are calculated by DFBEM and compared with the results given by standard BEM and scalar-wave approximation, respectively. Finally we show the relation between the degree of randomness and the diffraction efficiencies for two orthogonal linear polarizations. The relation provides information for determining the tolerance of fabrication errors in the groove structure and measuring the structural randomness by acquiring the irradiance of the diffracted waves.