Covariant description of transformation optics in nonlinear media

Optics Express

Volumn 20, Issue 8, 2012, Pages 8982-8997

  Paul, Oliver ^a   Rahm, Marco ^a,b  

^a University of Koblenz Landau   (Germany)

^b FRAUNHOFER INSTITUTE FOR PHYSICAL MEASUREMENT TECHNIQUES IPM   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

OPTICAL CONSTANTS; OPTICS;

COVARIANT DESCRIPTION; COVARIANT FORMALISM; ELECTROMAGNETIC MEDIA; GENERAL COVARIANCE; MAGNETO-OPTICAL; MAGNETOELECTRIC COUPLINGS; MOVING MEDIA; NON-LINEAR MEDIA; SECOND HARMONIC WAVES; SPACE-TIME COORDINATES; TRANSFORMATION LAW; TRANSFORMATION OPTICS;

OPTICAL PROPERTIES;

EID: 84860144839     PISSN: None     EISSN: 10944087     Source Type: Journal    
DOI: 10.1364/OE.20.008982     Document Type: Article

References (43)

1. J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science 312, 1780-1782 (2006). (Pubitemid 43962892)
2. U. Leonhardt, "Optical conformal mapping," Science 312, 1777-1780 (2006). (Pubitemid 43962891)
3. G. W. Milton, M. Briane, and J. R. Willis, "On cloaking for elasticity and physical equations with a transformation invariant form," New J. Phys. 8, 248 (2006).
4. S. A. Cummer and D. Schurig, "One path to acoustic cloaking," New J. Phys. 9, 45 (2007).
5. A. V. Kildishev and V. M. Shalaev, "Engineering space for light via transformation optics," Opt. Lett. 33, 43-45 (2008). (Pubitemid 351328298)
6. 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).
7. N. Kundtz, D. Smith, and J. Pendry, "Electromagnetic design with transformation optics," Proc. IEEE 99, 1622-1633 (2011).
8. 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 312, 977-980 (2006). (Pubitemid 44749939)
9. W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, "Optical cloaking with metamaterials," Nat. Photonics 1, 224-227 (2007).
10. N. I. Landy, N. Kundtz, and D. R. Smith, "Designing three-dimensional transformation optical media using quasiconformal coordinate transformations," Phys. Rev. Lett. 105, 193902 (2010).
11. U. Leonhardt, "To invisibility and beyond," Nature 471, 292-293 (2011).
12. Y. A. Urzhumov, N. B. Kundtz, D. R. Smith, and J. B. Pendry, "Cross-section comparisons of cloaks designed by transformation optical and optical conformal mapping approaches," J. Opt. 13, 024002 (2011).
13. A. Novitsky, C.-W. Qiu, and S. Zouhdi, "Transformation-based spherical cloaks designed by an implicit transformation-independent method: theory and optimization," New J. Phys. 11, 113001 (2009).
14. D.-H. Kwon and D. H. Werner, "Two-dimensional eccentric elliptic electromagnetic cloaks," Appl. Phys. Lett. 92, 013505 (2008).
15. 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 maxwells equations," Photon. Nanostruct. Fundam. Appl. 6, 87-95 (2008). (Pubitemid 351389829)
16. T. Han, C. Qiu, and X. Tang, "An arbitrarily shaped cloak with nonsingular and homogeneous parameters designed using a twofold transformation," J. Opt. 12, 095103 (2010).
17. A. Nicolet, F. Zolla, and S. Guenneau, "Electromagnetic analysis of cylindrical cloaks of an arbitrary cross section," Opt. Lett. 33, 1584-1586 (2008).
18. X. Wang, S. Qu, S. Xia, B. Wang, Z. Xu, H. Ma, J. Wang, C. Gu, X. Wu, L. Lu, and H. Zhou, "Numerical method of designing three-dimensional open cloaks with arbitrary boundary shapes," Photon. Nanostruct. Fundam. Appl. 8, 205-208 (2010).
19. W. X. Jiang, J. Y. Chin, Z. Li, Q. Cheng, R. Liu, and T. J. Cui, "Analytical design of conformally invisible cloaks for arbitrarily shaped objects," Phys. Rev. E 77, 066607 (2008).
20. H. Chen and C. T. Chan, "Transformation media that rotate electromagnetic fields," Appl. Phys. Lett. 90, 241105 (2007).
21. N. Kundtz and D. R. Smith, "Extreme-angle broadband metamaterial lens," Nat. Mater. 9, 129-132 (2010).
22. Y. G. Ma, C. K. Ong, T. Tyc, and U. Leonhardt, "An omnidirectional retroreflector based on the transmutation of dielectric singularities," Nat. Mater. 8, 639-642 (2009).
23. D. A. Genov, S. Zhang, and X. Zhang, "Mimicking celestial mechanics in metamaterials," Nat. Phys. 5, 687-692 (2009).
24. E. E. Narimanov and A. V. Kildishev, "Optical black hole: Broadband omnidirectional light absorber," Appl. Phys. Lett. 95, 041106 (2009).
25. P. L. Kelley, "Self-focusing of optical beams," Phys. Rev. Lett. 15, 1005-1008 (1965).
26. W. L. Faust and C. H. Henry, "Mixing of visible and near-resonance infrared light in gap," Phys. Rev. Lett. 17, 1265-1268 (1966).
27. N. Bloembergen, "The stimulated raman effect," Am. J. Phys. 35, 989-1023 (1967).
28. J. T. Manassah, P. L. Baldeck, and R. R. Alfano, "Self-focusing, self-phase modulation, and diffraction in bulk homogeneous material," Opt. Lett. 13, 1090-1092 (1988).
29. Y. R. Shen, "Surface properties probed by second-harmonic and sum-frequency generation," Nature 337, 519-525 (1989).
30. G. Agrawal and N. Olsson, "Self-phase modulation and spectral broadening of optical pulses in semiconductor laser amplifiers," IEEE J. Quantum Electron. 25, 2297-2306 (1989). (Pubitemid 20653113)
31. J. J. Macklin, J. D. Kmetec, and C. L. Gordon, "High-order harmonic generation using intense femtosecond pulses," Phys. Rev. Lett. 70, 766-769 (1993).
32. 3," J. Opt. Soc. Am. B 12, 2102-2116 (1995).
33. A. Dubietis, R. Butkus, and A. Piskarskas, "Trends in chirped pulse optical parametric amplification," IEEE J. Sel. Top. Quantum Electron. 12, 163-172 (2006). (Pubitemid 43742745)
34. Y. R. Shen, "Recent advances in nonlinear optics," Rev. Mod. Phys. 48, 1-32 (1976).
35. M. Evans and S. Kielich, Modern Nonlinear Optics (Wiley, 1997).
36. R. W. Boyd, Nonlinear Optics (Academic Press, 2008).
37. L. Bergamin, P. Alitalo, and S. A. Tretyakov, "Nonlinear transformation optics and engineering of the kerr effect," Phys. Rev. B 84, 205103 (2011).
38. E. J. Post, Formal Structure of Electromagnetics: General Covariance and Electromagnetics (Dover Publications, 1997).
39. R. T. Thompson, "Transformation optics in nonvacuum initial dielectric media," Phys. Rev. A 82, 053801 (2010).
40. R. T. Thompson, S. A. Cummer, and J. Frauendiener, "A completely covariant approach to transformation optics," J. Opt. 13, 024008 (2011).
41. D. Cheng and J.-A. Kong, "Covariant descriptions of bianisotropic media," Proc. IEEE 56, 248-251 (1968).
42. L. Landau, E. Lifshitz, and L. Pitaevskii, Electrodynamics of Continuous Media (Butterworth-Heinemann, 1984).
43. G. Rousseaux, "On the electrodynamics of minkowski at low velocities," Europhys. Lett. 84, 20002 (2008).