The canonical equations of the optical cloaking proposed by Shurig, Pendry and Smith has been proved to be equivalent to the geodesic in a 3-dimensional curved space. Carrying out the argument we extend to the 4-dimensional Riemannian space where the extra time item appears as the potential term in the canonical equations. The physical meaning of the results is interpreted.

© 2009 Optical Society of America

1. J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science 312, 1780-1782 (2006). [CrossRef] [PubMed]
2. 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). [CrossRef] [PubMed]
3. U. Leonhardt, "Optical Conformal Mapping," Science 312(5781), 1777-1780 (2006). [CrossRef]
4. S. Cummer, B.-I. Popa, D. Schurig, D. Smith, and J. Pendry, "Full-wave simulations of electromagnetic cloaking structures," Phys. Rev. E 74, 036621 (2006). [CrossRef]
5. Z. Liang, P. Yao, X. Sun, and X. Jiang, "The physical picture and the essential elements of the dynamical process for dispersive cloaking structures," Appl. Phys. Lett. 92, 131118 (2008). [CrossRef]
6. Z. Ruan, M. Yan, C. Neff, and M. Qiu, "Ideal Cylindrical Cloak: Perfect but Sensitive to Tiny Perturbations," Phys. Rev. Lett. 99, 113903 (2007). [CrossRef]
7. H. Chen, B.-I. Wu, B. Zhang, and J. Kong, "ElectromagneticWave Interactions with a Metamaterial Cloak," Phys. Rev. Lett. 99, 063903 (2007).
8. D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, D. R. Smith, "Metamaterial Electromagnetic Cloak at Microwave Frequencies," Science 314, 977-980 (2006). [CrossRef] [PubMed]
9. L. D.  Landau and E. M. Lifshitz, The Classical Theory of Fields (Oxford: Butterworth-Heinemann, 1995).
10. J. Plebanski, "Electromagnetic Waves in Gravitational Fields," Phys. Rev. 118, 1396 (1960). [CrossRef]
11. Y. Kravtsov and Y. I. Orlov, Geometrical optics of inhomogeneous media (Springer-Verlag, Berlin, 1990).
12. G. T. del Castillo and C. P. Sánchez, "Uniformly accelerated observers in special relativity," Revista Mexicana De Físic 52, 70-73 (2006).

Appl. Phys. Lett.

• Z. Liang, P. Yao, X. Sun, and X. Jiang, "The physical picture and the essential elements of the dynamical process for dispersive cloaking structures," Appl. Phys. Lett. 92, 131118 (2008). [CrossRef]

Opt. Express

• 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). [CrossRef] [PubMed]

Phys. Rev.

• J. Plebanski, "Electromagnetic Waves in Gravitational Fields," Phys. Rev. 118, 1396 (1960). [CrossRef]

Phys. Rev. E

• S. Cummer, B.-I. Popa, D. Schurig, D. Smith, and J. Pendry, "Full-wave simulations of electromagnetic cloaking structures," Phys. Rev. E 74, 036621 (2006). [CrossRef]

Phys. Rev. Lett.

• Z. Ruan, M. Yan, C. Neff, and M. Qiu, "Ideal Cylindrical Cloak: Perfect but Sensitive to Tiny Perturbations," Phys. Rev. Lett. 99, 113903 (2007). [CrossRef]
• H. Chen, B.-I. Wu, B. Zhang, and J. Kong, "ElectromagneticWave Interactions with a Metamaterial Cloak," Phys. Rev. Lett. 99, 063903 (2007).

Revista Mexicana De Físic

• G. T. del Castillo and C. P. Sánchez, "Uniformly accelerated observers in special relativity," Revista Mexicana De Físic 52, 70-73 (2006).

Science

• D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, D. R. Smith, "Metamaterial Electromagnetic Cloak at Microwave Frequencies," Science 314, 977-980 (2006). [CrossRef] [PubMed]
• J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science 312, 1780-1782 (2006). [CrossRef] [PubMed]
• U. Leonhardt, "Optical Conformal Mapping," Science 312(5781), 1777-1780 (2006). [CrossRef]

Other

• L. D.  Landau and E. M. Lifshitz, The Classical Theory of Fields (Oxford: Butterworth-Heinemann, 1995).
• Y. Kravtsov and Y. I. Orlov, Geometrical optics of inhomogeneous media (Springer-Verlag, Berlin, 1990).

Click here to see a list of articles that cite this paper

Related Journal Articles

• Using rays better. I. Theory for smoothly varying media (JOSAA)
• Using rays better. II. Ray families to match prescribed wave fields (JOSAA)
• Using rays better. III. Error estimates and illustrative applications in smooth media (JOSAA)
• Using rays better. IV. Theory for refraction and reflection (JOSAA)
• Quadratic Cost Functional For Wave-Front Reconstruction (AO)

Related Conference Papers

• Applications of extreme anisotropy of two-dimensional photonic structures
• Is the photonic crystal in the butterflies T. imperialis and P. sesostris optimal?
• Third-Order Aberrations of an AGRIN Thin Lens as a Function of the Shape Factor and Conjugate Variable
• Numerical Integration of the Profile of Aspheric Surfaces
• Corrected Calculation of Star Trails Caused by Differential Atmospheric Refraction