Open AccessAnisotropy minimization via least squares method for transformation optics
Author(s) -
Mateus A. F. C. Junqueira,
Lucas H. Gabrielli,
Danilo H. Spadoti
Publication year - 2014
Publication title -
optics express
Language(s) - Uncategorized
Resource type - Journals
SCImago Journal Rank - 1.394
H-Index - 271
ISSN - 1094-4087
DOI - 10.1364/oe.22.018490
Subject(s) - optics , transformation optics , transformation (genetics) , anisotropy , coordinate system , isotropy , geometrical optics , conformal map , power series , cauchy distribution , least squares function approximation , photomask , minification , physics , mathematical analysis , mathematics , mathematical optimization , materials science , geometry , biochemistry , chemistry , metamaterial , statistics , layer (electronics) , estimator , resist , composite material , gene
In this work the least squares method is used to reduce anisotropy in transformation optics technique. To apply the least squares method a power series is added on the coordinate transformation functions. The series coefficients were calculated to reduce the deviations in Cauchy-Riemann equations, which, when satisfied, result in both conformal transformations and isotropic media. We also present a mathematical treatment for the special case of transformation optics to design waveguides. To demonstrate the proposed technique a waveguide with a 30° of bend and with a 50% of increase in its output width was designed. The results show that our technique is simultaneously straightforward to be implement and effective in reducing the anisotropy of the transformation for an extremely low value close to zero.