volume | PIER Journals

Abstract

An optical impedance-matched medium with a gradient refractive index can resemble a geometrical analogy with an arbitrary curved space-time. In this paper, we show that a non-impedance-matched medium with a varying optical axis can also resemble the features of a space of non-trivial metric for light. The medium with a varying optical axis is an engineered stratified slab of material, in which the orientation of the optical axis in each layer slightly differs from the other layers, while the magnitude of refractive index remains constant. Instead of the change in refractive index, the inhomogeneity of such a medium is induced by the local anisotropy. Therefore, the propagation of light depends on the local optical axis. We study the conditions that make the analogy between curved space-time and a medium with a varying optical axis. Extension of the transformation optics to the media with optical axis profile might ease some fabrication difficulties of gradient refractive index materials for particular frequencies.

1. Leonhardt, U. and T. G. Philbin, "General relativity in electrical engineering," New J. Phys., Vol. 8, No. 10, 247, 2006.
doi:10.1088/1367-2630/8/10/247

2. Pendry, J. B., D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science, Vol. 312, No. 5781, 1780-1782, 2006.
doi:10.1126/science.1125907

3. Thompson, R. T., S. A. Cummer, and J. Frauendiener, "A completely covariant approach to transformation optics," J. Opt., Vol. 13, No. 2, 024008, 2011.
doi:10.1088/2040-8978/13/2/024008

4. Leonhardt, U. and T. Philbin, Geometry and Light: The Science of Invisibility, Dover, New York, 2012.

5. McCall, M., "Transformation optics and cloaking," Contem. Phys., Vol. 54, No. 6, 273-286, 2013.
doi:10.1080/00107514.2013.847678

6. Sarkissian, H., S. V. Serak, N. V. Tabiryan, L. B. Glebov, V. Rotar, and B. Y. Zeldovich, "Polarization-controlled switching between diffraction orders in transverse-periodically aligned nematic liquid crystals," Opt. Lett., Vol. 31, 2248-2250, 2006.
doi:10.1364/OL.31.002248

7. Nersisyan, S. R., N. V. Tabiryan, D. M. Steeves, and B. R. Kimball, "Optical axis gratings in liquid crystals and their use for polarization insensitive optical switching," Journal of Nonlinear Optical Physics and Materials, Vol. 18, No. 1, 1-47, 2009.
doi:10.1142/S0218863509004555

8. Liang, Z., X. Jiang, F. Miao, S. Guenneau, and J. Li, "Transformation media with variable optical axes," New J. of Phys., Vol. 14, No. 10, 103042, 2012.
doi:10.1088/1367-2630/14/10/103042

9. Sluijter, M., Ray-optics Analysis of Inhomogeneous Optically Anisotropic Media, Delft University of Technology, TU Delft, 2010.

10. Cai, W. and V. M. Shalaev, Optical Metamaterials, Springer, Berlin, Germany, 2010.
doi:10.1007/978-1-4419-1151-3

11. Born, M. and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference, and Diffraction of Light, Cambridge University Press, London, 1999.
doi:10.1017/CBO9781139644181

12. Neves, N. M., A. S. Pouzada, J. H. D. Voerman, and P. C. Powell, "The use of birefringence for predicting the stiffness of injection molded polycarbonate discs," Polym. Eng. Sci., Vol. 38, No. 10, 1770-1777, 1998.
doi:10.1002/pen.10347

13. Saleh, B. E. A., M. C. Teich, and B. E. Saleh, Fundamentals of Photonics, Vol. 22, Wiley, New York, 1991.
doi:10.1002/0471213748

14. Yariv, A. and P. Yeh, Optical Waves in Crystals, Vol. 10, Wiley, New York, 1984.

15. Jackson, J. D., Classical Electrodynamics, Wiley, New York, 1962.

16. Hao, J. and L. Zhou, "Electromagnetic wave scatterings by anisotropic metamaterials: Generalized 4 × 4 transfer-matrix method," Phy. Rev. B, Vol. 77, No. 094201, 2008.

17. Yeh, P., "Optics of anisotropic layered media: A new 4×4 matrix algebra," Surf. Science, Vol. 96, No. 1, 41-53, 1980.
doi:10.1016/0039-6028(80)90293-9

Dr. Sayed Alireza Mousavi

Dr. Rasoul Roknizadeh

Dr. Sahar Sahebdivan

Dr. Shahram Dehdashti