Play all audios:
ABSTRACT Birefringence, from the very essence of the word itself, refers to the splitting of light rays into two parts. In natural birefringent materials, this splitting is a beautiful
phenomenon, resulting in the perception of a double image. In optical metamaterials, birefringence is often an unwanted side effect of forcing a device designed through transformation
optics1,2,3,4,5,6 to operate in dielectrics. One polarization is usually implemented in dielectrics, and the other is sacrificed7,8. Here we show, with techniques beyond transformation
optics, that this need not be the case, that both polarizations can be controlled to perform useful tasks in dielectrics, and that rays, at all incident angles, can even follow different
trajectories through a device and emerge together as if the birefringence did not exist at all. A number of examples are shown, including a combination Maxwell fisheye/Luneburg lens that
performs a useful task and is achievable with current fabrication materials. Access through your institution Buy or subscribe This is a preview of subscription content, access via your
institution ACCESS OPTIONS Access through your institution Subscribe to this journal Receive 12 print issues and online access $209.00 per year only $17.42 per issue Learn more Buy this
article * Purchase on SpringerLink * Instant access to full article PDF Buy now Prices may be subject to local taxes which are calculated during checkout ADDITIONAL ACCESS OPTIONS: * Log in
* Learn about institutional subscriptions * Read our FAQs * Contact customer support SIMILAR CONTENT BEING VIEWED BY OTHERS PTYCHOGRAPHIC LENS-LESS BIREFRINGENCE MICROSCOPY USING A
MASK-MODULATED POLARIZATION IMAGE SENSOR Article Open access 07 November 2023 FLAT OPTICS WITH DISPERSION-ENGINEERED METASURFACES Article 19 June 2020 MONOLITHIC FOCUS-TUNABLE LENS
TECHNOLOGY ENABLED BY DISK-TYPE DIELECTRIC-ELASTOMER ACTUATORS Article Open access 09 October 2020 REFERENCES * Service, R. F. & Cho, A. Strange new tricks with light. _Science_ 330,
1622 (2010). Article ADS Google Scholar * Leonhardt, U. Optical conformal mapping. _Science_ 312, 1777–1780 (2006). Article ADS MathSciNet Google Scholar * Pendry, J. B., Schurig, D.
& Smith, D. R. Controlling electromagnetic fields. _Science_ 312, 1780–1782 (2006). Article ADS MathSciNet Google Scholar * Shalaev, V. M. Transforming light. _Science_ 322, 384–386
(2008). Article Google Scholar * Chen, H. Y., Chan, C. T. & Sheng, P. Transformation optics and metamaterials. _Nature Mater._ 9, 387–396 (2010). Article ADS Google Scholar *
Leonhardt, U. & Philbin, T. G. _Geometry and Light: The Science of Invisibility_ (Dover, 2010). MATH Google Scholar * Schurig, D. et al. Metamaterial electromagnetic cloak at microwave
frequencies. _Science_ 314, 977–980 (2006). Article ADS MathSciNet Google Scholar * Ma, Y. G., Ong, C. K., Tyc, T. & Leonhardt, U. An omnidirectional retroreflector based on the
transmutation of dielectric singularities. _Nature Mater._ 8, 639–642 (2009). Article ADS Google Scholar * Pendry, J. B. Negative refraction makes a perfect lens. _Phys. Rev. Lett._ 85,
3966–3969 (2000). Article ADS Google Scholar * Cai, W. S., Chettiar, U. K., Kildishev, A. V. & Shalaev, V. M. Optical cloaking with metamaterials. _Nature Photon._ 1, 224–227 (2007).
Article ADS Google Scholar * Gabrielli, L. H., Cardenas, J., Poitras, C. B. & Lipson, M. Silicon nanostructure cloak operating at optical frequencies. _Nature Photon._ 3, 461–463
(2009). Article ADS Google Scholar * Leonhardt, U. & Tyc, T. Broadband invisibility by non-Euclidean cloaking. _Science_ 323, 110–112 (2009). Article ADS Google Scholar * Liu, R.
et al. Broadband ground-plane cloak. _Science_ 323, 366–369 (2009). Article ADS Google Scholar * Valentine, J., Li, J. S., Zentgraf, T., Bartal, G. & Zhang, X. An optical cloak made
of dielectrics. _Nature Mater._ 8, 568–571 (2009). Article ADS Google Scholar * Ergin, T., Stenger, N., Brenner, P., Pendry, J. B. & Wegener, M. Three-dimensional invisibility cloak
at optical wavelengths. _Science_ 328, 337–339 (2010). Article ADS Google Scholar * Landy, N. I., Sajuyigbe, S., Mock, J. J., Smith, D. R. & Padilla, W. J. Perfect metamaterial
absorber. _Phys. Rev. Lett._ 100, 207402 (2008). Article ADS Google Scholar * Luneburg, R. K. & Herzberger, M. _Mathematical Theory of Optics_ (Brown University Graduate School,
1944). MATH Google Scholar * Gutman, A. S. Modified Luneberg lens. _J. Appl. Phys._ 25, 855–859 (1954). Article ADS Google Scholar * Morgan, S. P. General solution of the Luneberg lens
problem. _J. Appl. Phys._ 29, 1358–1368 (1958). Article ADS MathSciNet Google Scholar * Kwon, D. H. & Werner, D. H. Polarization splitter and polarization rotator designs based on
transformation optics. _Opt. Express_ 16, 18731–18738 (2008). Article ADS Google Scholar * Hendi, A., Henn, J. & Leonhardt, U. Ambiguities in the scattering tomography for central
potentials. _Phys. Rev. Lett._ 97, 073902 (2006). Article ADS Google Scholar * Akbarzadeh, A. & Danner, A. J. Generalization of ray tracing in a linear inhomogeneous anisotropic
medium: a coordinate-free approach. _J. Opt. Soc. Am. A_ 27, 2558–2562 (2010). Article ADS Google Scholar * Danner, A. J. Visualizing invisibility: metamaterials-based optical devices in
natural environments. _Opt. Express_ 18, 3332–3337 (2010). Article ADS Google Scholar * Minano, J. C. Perfect imaging in a homogeneous three-dimensional region. _Opt. Express_ 14,
9627–9635 (2006). Article ADS Google Scholar * Leonhardt, U. Perfect imaging without negative refraction. _New J. Phys._ 11, 093040 (2009). Article ADS Google Scholar * Ma, Y. G.,
Sahebdivan, S., Ong, C. K., Tyc, T. & Leonhardt, U. Evidence for subwavelength imaging with positive refraction. _New J. Phys._ 13, 033016 (2011). Article Google Scholar Download
references ACKNOWLEDGEMENTS The authors acknowledge funding from the Singapore Ministy of Education Tier II Academic Research Fund (grant no. MOE2009-T2-1-086). U.L. was supported by the
Royal Society. T.T. acknowledges grants nos MSM0021622409 and MSM0021622419 from the Czech Ministry of Education. AUTHOR INFORMATION AUTHORS AND AFFILIATIONS * Department of Electrical and
Computer Engineering, National University of Singapore, Singapore, 117576 Aaron J. Danner * Faculty of Science and Faculty of Informatics, Masaryk University, Brno, 61137, Czech Republic
Tomáš Tyc * School of Physics and Astronomy, University of St Andrews, North Haugh, St Andrews, KY16 9SS, UK Ulf Leonhardt Authors * Aaron J. Danner View author publications You can also
search for this author inPubMed Google Scholar * Tomáš Tyc View author publications You can also search for this author inPubMed Google Scholar * Ulf Leonhardt View author publications You
can also search for this author inPubMed Google Scholar CONTRIBUTIONS A.D. devised the main theory presented in the text and created ray-traced images. T.T. contributed to designing the
interior focusing and multifocal length lenses. U.L. proposed the original problem and contributed to potential applications of the theory. CORRESPONDING AUTHOR Correspondence to Aaron J.
Danner. ETHICS DECLARATIONS COMPETING INTERESTS The authors declare no competing financial interests. SUPPLEMENTARY INFORMATION SUPPLEMENTARY INFORMATION (PDF 1157 KB) RIGHTS AND PERMISSIONS
Reprints and permissions ABOUT THIS ARTICLE CITE THIS ARTICLE Danner, A., Tyc, T. & Leonhardt, U. Controlling birefringence in dielectrics. _Nature Photon_ 5, 357–359 (2011).
https://doi.org/10.1038/nphoton.2011.53 Download citation * Received: 11 October 2010 * Accepted: 24 March 2011 * Published: 08 May 2011 * Issue Date: June 2011 * DOI:
https://doi.org/10.1038/nphoton.2011.53 SHARE THIS ARTICLE Anyone you share the following link with will be able to read this content: Get shareable link Sorry, a shareable link is not
currently available for this article. Copy to clipboard Provided by the Springer Nature SharedIt content-sharing initiative