Method for arbitrary phase transformation by a slab based on transformation optics and the principle of equal optical path

Y. Ke; W. Shu; H. Luo; S. Wen; D. Fan

doi:10.2971/jeos.2012.12013

Journal of the European Optical Society - Rapid publications, Vol 7 (2012)

Method for arbitrary phase transformation by a slab based on transformation optics and the principle of equal optical path

Y. Ke, W. Shu, H. Luo, S. Wen, D. Fan

Abstract

The optical path lengths travelled by rays across a wavefront essentially determine the resulting phase front irrespective of the shape of a medium according to the principle of equal optical path. Thereupon we propose a method for the transformation between two arbitrary wavefronts by a slab, i.e. the profile of the spatial separation between the two wavefronts is taken to be transformed to a plane surface. Interestingly, for the mutual conversion between planar and curved wavefronts, the method reduce to an inverse transformation method in which it is the reversed shape of the desired wavefront that is converted to a planar one. As an application, three kinds of phase transformation are realized and it is found that the transformation on phase is able to realize some important properties such as phase reversal or compensation, self focusing, and expanding or compressing beams, which are further confirmed by numerical simulations. The slab can be applied to realizing compact electromagnetic devices for which the values of the refractive index or the permittivity and permeability can be high or low, positive or negative, or near zero, depending on the choice of coordinate transformations.

Full Text: PDF

Citation Details

Cite this article

References

J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science 312, 1780-1782 (2006).

U. Leonhardt, "Optical conformal mapping," Science 312, 1777-1780 (2006).

D. Schurig, J. B. Pendry, and D. R. Smith, "Calculation of material properties and ray tracing in transformation media," Opt. Express 14, 9794-9804 (2006).

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial electromagnetic cloak at microwave frequencies," Science 314, 977-980 (2006).

B. L. Zhang, Y. Luo, X. G. Liu, and G. Barbastathis, "Macroscopic invisibility cloak for visible light," Phys. Rev. Lett. 106, 033901 (2011).

X. Z Chen, Y. Luo, J. J. Zhang, K. Jiang, J. B. Pendry, and S. Zhang, "Macroscopic invisibility cloaking of visible light," Nat. Commun. 2, 176 (2011).

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, "Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell's equations," Photonics Nanostruct: Fundam. Appl. 6, 87-95 (2008).

E. E. Narimanova and A. V. Kildishev, "Optical black hole: broadband omnidirectional light absorber," Appl. Phys. Lett. 95, 041106 (2009).

X. F. Xu, Y. J. Feng and T. Jiang, "Electromagnetic beam modulation through transformation optical structures," New J. Phys. 10, 115027 (2008).

C. García-Meca, M. M. Tung, J. V. Galán, R. Ortuño, F. J. Rodríguez- Fortuño, J. Martí and A. Martínez, "Squeezing and expanding light without reflections via transformation optics," Opt. Express 19, 3562-3575 (2011).

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, "Optical design of reflectionless complex media by finite embedded coordinate transformations," Phys. Rev. Lett. 100, 063903 (2008).

I. Gallina, G. Castaldi, V. Galdi, A. Alù, and N. Engheta, "General class of metamaterial transformation slabs," Phys. Rev. B 81, 125124 (2010).

M. Rahm, D. A. Roberts, J. B. Pendry, and D. R. Smith, "Transformation-optical design of adaptive beam bends and beam expanders," Opt. Express 16, 11555-11567 (2008).

Y. Liu, T. Zentgraf, G. Bartal, and X. Zhang, "Transformational plasmon optics," Nano Lett. 10, 1991-1997 (2010).

D. H. Kwon and D. H. Werner, "Polarization splitter and polarization rotator designs based on transformation optics," Opt. Express 16, 18731-18738 (2008).

Y. Luo, J. Zhang, L. Ran, H. Chen and J. A. Kong, "Controlling the emission of electromagnetic source," PIERS 4, 795-800 (2008).

N. Kundtz, D. A. Roberts, J. Allen, S. Cummer, and D. R. Smith, "Optical source transformations," Opt. Express 16, 21215-21222 (2008).

J. Li, S. Han, S Zhang, G. Bartal, and X. Zhang, "Designing the Fourier space with transformation optics," Opt. Lett. 34, 3128-3120 (2009).

H. Y. Chen, B. Hou, S. Y. Chen, X. Y. Ao, W. J. Wen, and C. T. Chan, "Design and experimental realization of a broadband transformation media field rotator at microwave frequencies," Phys. Rev. Lett. 102, 183903 (2009).

W. X. Jiang, T. J. Cui, H. F. Ma, X. Y. Zhou, and Q. Cheng, "Cylindrical-to-plane-wave conversion via embedded optical transformation," Appl. Phys. Lett. 92, 261903 (2008).

G. X. Yu, W. X. Jiang and T. J. Cui, "Beam deflection and splitting using transformation optics," Cent. Eur. J. Phys. 9, 183-188 (2011).

H. Ma, S. B. Qu, Z. Xu, and J. F. Wang, "General method for designing wave shape transformers," Opt. Express 16, 22072-22082 (2008).

N. Kundtz and D. R. Smith, "Extreme-angle broadband metamaterial lens," Nat. Mater. 9, 129-132 (2010).

J. J. Zhang, Y. Luo, S. Xi, H. S. Chen, L. X. Ran, B. I. Wu, and J. A. Kong, "Directive emission obtained by coordinate transformation," PIERS 81, 437-446 (2008).

D.-H. Kwon and D. H. Werner, "Transformation optical designs for wave collimators, flat lenses and right-angle bends," New J. Phys. 10, 115023 (2008).

L. Lin, W. Wang, J. Cui, C. L Du, and X. G. Luo, "Design of electromagnetic refractor and phase transformer using coordinate transformation," Opt. Express 16, 6815-6821 (2008).

P.-H. Tichit, S. N. Burokur, D. Germain, and A. de Lustrac, "Design and experimental demonstration of a high-directive emission with transformation optics," Phys. Rev. B 83, 155108 (2011).

F. Kong, B. Wu, J. A. Kong, J. Huangfu, and S. Xi, "Planar focusing antenna design by using coordinate transformation technology," Appl. Phys. Lett. 91, 253509 (2007).

Y. Luo, L. X. He, S. Z. Zhu, H. L. W. Chan, and Y. Wang, "Flattening of conic reflectors via a transformation method," Phys. Rev. A 84, 023843 (2011).

E. Hecht, Optics (Addison-Wesley, San Francisco, 2002).

M. Born and E. Wolf, Principles of Optics (Cambridge University Press, Cambridge, 1999).

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (John Wiley & Sons, New Jersey, 2007).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill Companies, San Francisco, 1996).

D. A. Roberts, N. Kundtz, and D. R. Smith, "Optical lens compression via transformation optics," Opt. Express 17, 16535-16542 (2009).

R. Yang, W. X. Tang, Y. Hao, and I. Youngs, "A coordiante transformation based broadband flat lens via microstrip array," IEEE Antenn. Wirel. Pr. 10, 99-102 (2011).

R. W. Ziolkowski, "Propagation in and scattering from a matched metamaterial having a zero index of refraction," Phys. Rev. E 70, 046608 (2004).

J. Li, and J. B. Pendry, "Hiding under the carpet: a new strategy for cloaking," Phys. Rev. Lett. 101, 203901 (2008).

W. X. Tang, C. Argyropoulos, E. Kallos, W. Song, and Y. Hao, "Discrete coordinate transformation for designing all-dielectric flat antennas," IEEE Trans. Antennas Propag. 58, 3795-3804 (2010).

T. J. Cui, D. R. Smith, and R. P. Liu, Metamaterials (Springer, New York, 2010).

Z. H. Jiang, M. D. Gregory, and D. H. Werner, "Experimental demonstration of a broadband transformation optics lens for highly directive multibeam emission," Phys. Rev. B 84, 165111 (2011).

T. C. Han and C.-W. Qiu, "Isotropic nonmagnetic flat cloaks degenerated from homogeneous anisotropic trapeziform cloaks," Opt. Express 18, 13038-13043 (2010).

M. Gharghi, C. Gladden, T. Zentgraf, Y. Liu, X. Yin, J. Valentine, and X. Zhang, "A Carpet Cloak for Visible Light," Nano Lett. 11, 2825-2828 (2011).

A. M. Yao and M. J. Padgett, "Orbital angular momentum: origins, behavior and applications," Adv. Opt. Photon. 3, 161-204 (2011).