Nonlinear transformation optics and engineering of the Kerr effect

@article{Bergamin2011NonlinearTO,
  title={Nonlinear transformation optics and engineering of the Kerr effect},
  author={Luzi Bergamin and Pekka Alitalo and Sergei A. Tretyakov},
  journal={Physical Review B},
  year={2011},
  volume={84},
  pages={205103}
}
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. 

Figures from this paper

Covariant description of transformation optics in nonlinear media.
TLDR
A general transformation law that holds for arbitrary materials including bianisotropic, magneto-optical, nonlinear and moving media is presented by using a complete covariant formalism.
A Unified Approach to Nonlinear Transformation Materials
TLDR
It is shown that nonlinearity can be incorporated into transformation optics in a consistent way, and used to illustrate a number of novel effects, including cloaking an optical soliton, modeling nonlinear solutions to Einstein’s field equations, controlling transport in a Debye solid, and developing a set of constitutive to relations for relativistic cloaks in arbitrary nonlinear backgrounds.
Dispersion engineering via nonlocal transformation optics
TLDR
This work introduced a framework of transformation media that can tailor the wave interaction in the reciprocal space of spatial wave-numbers, so as to induce desired nonlocal effects, and relies on the increased availability of nonlocal homogenization models.
Dispersion engineering via nonlocal transformation optics
Transformation optics (TO) has established itself as a powerful and versatile approach to the synthesis of metamaterials with prescribed field-manipulation capabilities, via suitable spatial
Nonlocal and Non-Hermitian Transformation Optics
  • M. Moccia, G. Castaldi, V. Galdi
  • Physics
    2019 Thirteenth International Congress on Artificial Materials for Novel Wave Phenomena (Metamaterials)
  • 2019
Conventional transformation optics is based on real-valued spatial coordinate transformations which cannot naturally handle nonlocal (spatial dispersion) and gain/loss effects. Here, we review some
Active control of electromagnetic radiation through an enhanced thermo-optic effect
TLDR
A structured planar cavity is used to enhance the thermo-optic effect in a transformation optical waveguide to provide a new approach toward development of transformation optical devices where active all-optical control of the impinging light can be achieved.
Beam steering based on coordinate transformation of Fermat spiral configurations
A two-dimensional transformational electromagnetic (T-E) device formed by configuring a circular disc with a Fermat spiral is realized. By tuning the phase of the emanating wave in the T-E medium,
Nonlinear Transformation Optics Techniques in the Design of Counter-Directed Energy Weapon Shields for Satellites
Abstract : The purpose of this thesis is to examine the feasibility of using an emerging technique, called transformation optics (TO), in designing materials to be used as a defense against directed
Surface second-harmonic generation from metallic-nanoparticle configurations: A transformation-optics approach
We study surface second-harmonic generation (SHG) from a singular plasmonic structure consisting of touching metallic wires. We use the technique of transformation optics and relate the structure to
...
1
2
3
...

References

SHOWING 1-10 OF 39 REFERENCES
Nonlinear optics.
TLDR
In this method, non-linear susceptibility tensors are introduced which relate the induced dipole moment to a power series expansion in field strengths and the various experimental observations are described and interpreted in terms of this formalism.
Frequency conversion by exploiting time in transformation optics
The fundamental framework of transformation optics describes how coordinate transformations on electromagnetic fields can be physically realized through complex material parameters. This approach
Optical design of reflectionless complex media by finite embedded coordinate transformations.
TLDR
This work applies finite, embedded coordinate transformations to the design of several devices, including a parallel beam shifter and a beam splitter, both of which are reflectionless and exhibit unusual electromagnetic behavior as confirmed by 2D full-wave simulations.
Transformation optics and metamaterials.
TLDR
The potential of transformation optics to create functionalities in which the optical properties can be designed almost at will is reviewed, which can be used to engineer various optical illusion effects, such as the invisibility cloak.
Transformation optics for the full dielectric electromagnetic cloak and metal-dielectric planar hyperlens
Full dielectric electromagnetic cloaks are studied in this paper for considering the possibility of achieving effective permeability gradients by taking advantage of a magnetic Mie resonance in
Generalized field-transforming metamaterials
In this paper, we introduce a generalized concept of field-transforming metamaterials, which perform field transformations defined as linear relations between the original and transformed fields.
Electromagnetic fields and boundary conditions at the interface of generalized transformation media
In this paper, the interface between two transformation media or between a transformation medium and vacuum is studied. Strictly from the transformation optics point of view, the consequences of the
Generalized transformation optics from triple spacetime metamaterials
In this paper various extensions of the design strategy of transformation media are proposed. We show that it is possible to assign different transformed spaces to the field strength tensor (electric
General relativity in electrical engineering
In electrical engineering metamaterials have been developed that offer unprecedented control over electromagnetic fields. Here, we show that general relativity provides the theoretical tools for
...
1
2
3
4
...