# Complex k band diagrams of 3D metamaterial/photonic crystals.

@article{Fietz2011ComplexKB, title={Complex k band diagrams of 3D metamaterial/photonic crystals.}, author={Chris R Fietz and Yaroslav A. Urzhumov and Gennady Shvets}, journal={Optics express}, year={2011}, volume={19 20}, pages={ 19027-41 } }

A finite element method (FEM) for solving a complex valued k(ω) vs. ω dispersion curve of a 3D metamaterial/photonic crystal system is presented. This 3D method is a generalization of a previously reported 2D eigenvalue method [Opt. Express 15, 9681 (2007)]. This method is particularly convenient for analyzing periodic systems containing dispersive (e.g., plasmonic) materials, for computing isofrequency surfaces in the k-space, and for calculating the decay length of the evanescent waves. Two… Expand

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#### References

SHOWING 1-10 OF 56 REFERENCES

The complex Bloch bands of a 2D plasmonic crystal displaying isotropic negative refraction.

- Physics, Medicine
- Optics express
- 2007

A wave interference effect that leads to transmission resonances similar to Fano resonances, as well as on the isotropy of the crystal's negative index band, indicate that effective propagation constants obtained from scattering simulations may not always be directly related to individual crystal Bloch bands. Expand

Computations of lossy Bloch waves in two-dimensional photonic crystals

- Mathematics
- 2009

In this article we compute lossy Bloch waves in two-dimensional photonic crystals with dispersion and material loss. For given frequencies these waves are determined from non-linear eigenvalue… Expand

Tunneling in photonic band structures

- Physics
- 1995

The plane-wave method is modified for tunneling evanescent solutions of Maxwell’s equations with complex k vectors (tunneling modes). In our formulation the imaginary part of the k vectors is not… Expand

Photonic band structures solved by a plane-wave-based transfer-matrix method.

- Physics, Medicine
- Physical review. E, Statistical, nonlinear, and soft matter physics
- 2003

Application of the transfer-matrix technique to an important class of 3D layer-by-layer photonic crystals reveals the superior convergency of this different approach over the conventional plane-wave expansion method. Expand

Fishnet metamaterials--rules for refraction and limits of homogenization.

- Physics, Medicine
- Optics express
- 2010

The perfectly conducting stacked fishnet metamaterial is studied, showing that only for small angles of incidence and in the immediate vicinity of Wood's anomaly can the fishnet be seen as homogenizable uniaxial medium. Expand

Effective Constitutive Parameters of Plasmonic Metamaterials: A Direct Approach

- Physics
- 2011

We introduce a general implementation of the recently proposed homogenization theory [Tsukerman, J. Opt. Soc. Am. B 28, 577 (2011)] allowing one to retrieve all 36 linear constitutive parameters of… Expand

Behavior of light at photonic crystal interfaces

- Materials Science
- 2005

Band structures and Bloch modes give a generalized description of light in infinite photonic crystals. We show that the band structure and Bloch modes also contain the information necessary to find… Expand

Spatial dispersion in metamaterials with negative dielectric permittivity and its effect on surface waves.

- Materials Science, Medicine
- Optics letters
- 2006

Spatial dispersion is found to have the most dramatic effect on the surface waves that exist at the wire mesh-vacuum interface. Expand

Three-dimensional optical metamaterial with a negative refractive index

- Chemistry, Medicine
- Nature
- 2008

Bulk optical metamaterials open up prospects for studies of 3D optical effects and applications associated with NIMs and zero-index materials such as reversed Doppler effect, superlenses, optical tunnelling devices, compact resonators and highly directional sources. Expand

Bloch material parameters of magneto-dielectric metamaterials and the concept of Bloch lattices

- Physics
- 2007

Abstract Metamaterials comprising lattices of small resonant scatterers and (optionally) infinite wires are considered. The crystal planes of these lattices contain magnetic dipoles and electric… Expand