Effects of spatial dispersion in wire medium formed by two mutually orthogonal wire lattices
Igor S. Nefedov, Ari J. Viitanen
Introduction
Electromagnetic waves in wire media formed by two mutually orthogonal wire lattices ( two-dimensional wire medium or 2D WM) are considered using the effective medium (EM) approach and the Integral Equation (IE) method. Effects of spatial dispersion are illustrated for spectra of propagating and evanescent waves as well as for reflection of a plane wave from 2D WM.
2D Wire medium
Effective medium approach
- Conventional (old) model
εh - permittivity of a host medium
Necessity to take into account spatial dispersion has been shown in [1].
Eigenvalue problem. Dispersion equation:
Integral Equation method
where 
, 
– 3D periodic scalar Green's function.
We neglect with azimuth currents under assumption r<< λ. Moment method is used for solution of IE.
Numerical and Effective Medium Simulations of WM
 |
 |
| Dispersion of the propagating modes. q t = 0.1 p, k y =q t cos φ, k z =q t sin φ, K p d= 1.38 |
Dispersion of the evanescent modes. q t = 0.1 p, k y =iq t cos φ, k z = iq t sin φ |
Near the plasma resonance range the results of numerical and EM theories practically coincide.
Wave reflection from 2D wire media
Eigenwaves in 2D WM (left) and Phase of reflection coefficient (right)
If k y is real, k z may be complex! k y =k sin φ, Θ =p/4, k p =1.9
Two extraordinary waves exist. Additional boundary conditions or other ideas are needed.
- reflection coefficient
where R α (k) is the residue of [ T(k z ,k) ] -1 at pole k zα
Approach proposed in [3] and applied to wire media in [4] is used
Conclusion
Comparison of the results demonstrates excellent agreement between the full-wave and effective medium theories both for propagating and evanescent modes for the frequencies close to the plasma resonance. Evanescent modes can be complex ones, if one of the components of the wavevector in WM is real at low frequencies.
References
- P.A. Belov, R. Marques, S.I. Maslovski, I.S. Nefedov, M. Silveirinha, C.R. Simovski, S.A. Tretyakov. Strong spatial dispersion in wire media in the very large wavelength limit. Phys. Rev. B , Vol. 63, p. 113103-1-113103-4, 2003.
- M.G. Silveirinha, and C.A. Fernandes. A Hybrid Method for the Efficient Calculation of the Band Structure of 3-D Metallic Crystals. IEEE Trans. Microwave Theory Tech , No 3, p. 889—902, 2004.
- K. Henneberger, "Additional Boundary Conditions: An Historical Mistake", Phys. Rev. Lett. , v.80, pp. 2889--2892, 1998.
- I.S. Nefedov, A.J. Viitanen. Electromagnetic Wave Reflection from the Wire Medium, Formed by Two Mutually Orthogonal Wire Lattices. 27th ESA Workshop. Antenna Technology on Innovative Periodic Antennas: Electromagnetic Bandgap, Left-handed Materials, Fractal and Frequency Selective Surfaces. 9-11 March 2004, Santiago de Compostela, Spain, pp. 265-271.