OSA's Digital Library

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)
http://dx.doi.org/10.1364/OE.22.018490


View Full Text Article

Enhanced HTML    Acrobat PDF (1136 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

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

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

Citation
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)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-15-18490


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. L. Ahlfors, “On quasi-conformal mappings,” J. Anal. Math.3(1), 1–58 (1953). [CrossRef]
  2. J. Li and J. B. Pendry, “Hiding under the carpet: A new strategy for cloaking,” Phys. Rev. Lett.101(20), 203901 (2008). [CrossRef] [PubMed]
  3. U. Leonhardt and T. G. Philbin, “Transformation optics and the geometry of light,” Prog. Opt.53, 69–152 (2009). [CrossRef]
  4. G. E. Shilov, Elementary Real and Complex Analysis (MIT, 1973).
  5. W. Yan, M. Yan, and M. Qiu, “Necessary and sufficient conditions for reflection less transformation media in an isotropic and homogenous background,” arXiv:0806.3231 (2008).
  6. U. Leonhardt, “Optical conformal mapping,” Science312(5781), 1777–1780 (2006). [CrossRef] [PubMed]
  7. Z. Chang, X. Zhou, J. Hu, and G. Hu, “Design method for quasi-isotropic transformation materials based on inverse Laplace’s equation with sliding boundaries,” Opt. Express18(6), 6089–6096 (2010). [CrossRef] [PubMed]
  8. N. I. Landy and W. J. Padilla, “Guiding light with conformal transformations,” Opt. Express17(17), 14872–14879 (2009). [CrossRef] [PubMed]
  9. Y. G. Ma, N. Wang, and C. K. Ong, “Application of inverse, strict conformal transformation to design waveguide devices,” J. Opt. Soc. Am. A27(5), 968–972 (2010). [CrossRef] [PubMed]
  10. N. Kundtz and D. R. Smith, “Extreme-angle broadband metamaterial lens,” Nat. Mater.9(2), 129–132 (2010). [CrossRef] [PubMed]
  11. H. F. Ma and T. J. Cui, “Three-dimensional broadband and broad-angle transformation-optics lens,” Nat. Commun.1, 124 (2010).
  12. Q. Wu, Z. H. Jiang, O. Quevedo-Teruel, J. P. Turpin, W. Tang, Y. Hao, and D. H. Werner, “Transformation optics inspired multibeam lens antennas for broadband directive radiation,” IEEE Trans. Antenn. Propag.61(12), 5910–5922 (2013). [CrossRef]
  13. D. Liu, L. H. Gabrielli, M. Lipson, and S. G. Johnson, “Transformation inverse design,” Opt. Express21(12), 14223–14243 (2013). [CrossRef] [PubMed]
  14. D. H. Spadoti, L. H. Gabrielli, C. B. Poitras, and M. Lipson, “Focusing light in a curved-space,” Opt. Express18(3), 3181–3186 (2010). [CrossRef] [PubMed]
  15. K. Astala, T. Iwaniec, and G. Martin, Elliptic Partial Differential Equations and Quasiconformal Mappings in the Plane (Princeton University, 2008).
  16. C. García-Meca, R. Ortuño, J. Martí, and A. Martínez, “Full three-dimensional isotropic transformation media,” New J. Phys.16(2), 023030 (2014). [CrossRef]
  17. D. E. Blair, Inversion Theory and Conformal Mapping (American Mathematical Society, 2000).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

Figures

Fig. 1 Fig. 2 Fig. 3
 
Fig. 4
 

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited