Nonlinear transformation optics and engineering of the Kerr effect

The concept of transformation optics is extended to nonlinear electrodynamics. It is shown that transformation optics favors implicit constitutive relations in terms of energy densities D.E and B.H rather than E^2 and H^2. The Kerr nonlinearity is studied in detail and the transformation optics based engineering of self-interaction effects is discussed. As a specific example we introduce transformation optics applied on a self-focusing field configuration.

[1]  F. Hehl,et al.  Foundations of classical electrodynamics : charge, flux, and metric , 2003 .

[2]  D. Genov,et al.  Mimicking celestial mechanics in metamaterials , 2009 .

[3]  Steven A. Cummer,et al.  Frequency conversion by exploiting time in transformation optics , 2011 .

[4]  Shuang Zhang,et al.  Cloaking of matter waves. , 2008, Physical review letters.

[5]  J. Pendry,et al.  Hiding under the carpet: a new strategy for cloaking. , 2008, Physical review letters.

[6]  A. Favaro,et al.  The non‐birefringent limit of all linear, skewonless media and its unique light‐cone structure , 2010, 1008.2343.

[7]  P. Sheng,et al.  Transformation optics and metamaterials. , 2010, Nature materials.

[8]  C. C. Wang,et al.  Nonlinear optics. , 1966, Applied optics.

[9]  David R. Smith,et al.  Optical design of reflectionless complex media by finite embedded coordinate transformations. , 2007, Physical review letters.

[10]  T. Tyc,et al.  Broadband Invisibility by Non-Euclidean Cloaking , 2009, Science.

[11]  K. Stetson,et al.  Progress in optics , 1980, IEEE Journal of Quantum Electronics.

[12]  Huanyang Chen,et al.  Acoustic cloaking in three dimensions using acoustic metamaterials , 2007 .

[13]  Andrew G. Glen,et al.  APPL , 2001 .

[14]  David R. Smith,et al.  Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations , 2007, 0706.2452.

[15]  U. Leonhardt,et al.  General relativity in electrical engineering , 2006, SPIE Optics + Optoelectronics.

[16]  U. Leonhardt.  Optical Conformal Mapping , 2006, Science.

[17]  L. Bergamin,et al.  Generalized transformation optics from triple spacetime metamaterials , 2008, 0807.0186.

[18]  S. Tretyakov,et al.  Generalized field-transforming metamaterials , 2008, 0806.0489.

[19]  D. Gaillot,et al.  Transformation optics for the full dielectric electromagnetic cloak and metal–dielectric planar hyperlens , 2008 .

[20]  S. Cummer,et al.  One path to acoustic cloaking , 2007 .

[21]  L. Bergamin,et al.  Electromagnetic fields and boundary conditions at the interface of generalized transformation media , 2009, 0903.1821.

[22]  David R. Smith,et al.  Controlling Electromagnetic Fields , 2006, Science.