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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 22, Iss. 15 — Jul. 28, 2014
  • pp: 18490–18498

Anisotropy minimization via least squares method for transformation optics

Mateus A. F. C. Junqueira, Lucas H. Gabrielli, and Danilo H. Spadoti  »View Author Affiliations

Optics Express, Vol. 22, Issue 15, pp. 18490-18498 (2014)

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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.

© 2014 Optical Society of America

OCIS Codes
(000.3860) General : Mathematical methods in physics
(130.2790) Integrated optics : Guided waves
(230.0230) Optical devices : Optical devices
(160.3918) Materials : Metamaterials

ToC Category:
Physical Optics

Original Manuscript: May 14, 2014
Revised Manuscript: June 21, 2014
Manuscript Accepted: June 24, 2014
Published: July 23, 2014

Mateus A. F. C. Junqueira, Lucas H. Gabrielli, and Danilo H. Spadoti, "Anisotropy minimization via least squares method for transformation optics," Opt. Express 22, 18490-18498 (2014)

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