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2 August 2004 Transverse electromagnetic waves in periodic wire arrays
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Abstract
Periodic two-dimensional arrays of straight, conducting wires have been used to create structures with negative permittivity and have been incorporated into structures exhibiting a negative index of refraction or phase velocity. In these cases the electromagnetic wave propagating through the structure has its electric field parallel to the wires. Solutions to Maxwell's equations for transverse electromagnetic waves in these structures have been found previously using either an approximate permittivity appropriate to the long wavelength limit or been determined numerically using a finite element analysis. The calculation presented here is an exact solution of Maxwell's equations for a square wire array valid for wavelengths larger that the wire diameter. The permittivity calculated in the long wavelength limit predicts propagation constants which agree remarkably well with the exact solution down to wavelengths comparable to the lattice constant of the wire array, with the first serious discrepancy occurring at the first Bragg reflection. The exact solution shows that the gaps in the frequency versus propagation constant relation in the [10] direction decrease in size as the order of the Bragg reflection increases. Also the second, fourth, sixth, etc., Bragg reflections are complicated by the emergence of higher order grating modes which result in dispersion relation crossings near the Bragg reflection.
© (2004) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Graeme Dewar "Transverse electromagnetic waves in periodic wire arrays", Proc. SPIE 5508, Complex Mediums V: Light and Complexity, (2 August 2004); https://doi.org/10.1117/12.560651
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