Article

Circuit modeling of the transmissivity of stacked two-dimensional metallic meshes

Dept. of Electrical Engineering, University of Mississippi, University, MS 38677-1848, USA.
Optics Express (Impact Factor: 3.49). 06/2010; 18(13):13309-20. DOI: 10.1364/OE.18.013309
Source: PubMed

ABSTRACT

This paper presents a simple analytical circuit-like model to study the transmission of electromagnetic waves through stacked two-dimensional (2-D) conducting meshes. When possible the application of this methodology is very convenient since it provides a straightforward rationale to understand the physical mechanisms behind measured and computed transmission spectra of complex geometries. Also, the disposal of closed-form expressions for the circuit parameters makes the computation effort required by this approach almost negligible. The model is tested by proper comparison with previously obtained numerical and experimental results. The experimental results are explained in terms of the behavior of a finite number of strongly coupled Fabry-Pérot resonators. The number of transmission peaks within a transmission band is equal to the number of resonators. The approximate resonance frequencies of the first and last transmission peaks are obtained from the analysis of an infinite structure of periodically stacked resonators, along with the analytical expressions for the lower and upper limits of the pass-band based on the circuit model.

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    • "the inductive nature of the sub-wavelength apertures [40]. Several other EC models can be found in the literature dealing with problems involving stacked perforated metal layers [41]–[46]. However, most of these works are of heuristic nature and do not provide closed-form expressions for the circuit elements [43], [44] or their scope is limited to certain configurations and structural parameters (small unit cells, large longitudinal period and so on). "
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    ABSTRACT: Metallic plates with a two-dimensional (2D) periodic distribution of sub-wavelength apertures are known to exhibit extraordinary transmission of electromagnetic waves. Stacking two or more of such plates gives place to the so-called fishnet structures, which constitute a popular way of achieving an effective negative index medium at frequencies ranging from microwaves to optics. Unfortunately, a general wideband equivalent circuit has not yet been proposed to facilitate its understanding and design. This work presents this circuit model with closed-form expressions for the circuit elements, thus making it possible to obtain the electrical response for this class of structures in a very efficient way. This procedure is much faster than alternative numerical methods at the same time that it retains a high level of accuracy when compared with some other oversimplified models. The circuit model also provides a simple rationale as well as a good physical insight in order to explain the qualitative behavior of such structures, independently of the number of stacked layers.
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    • "Another 2-D representation of a metasurface is in terms of homogenized surface impedances [19], [20]. Here also, most attention has been given to the plane wave problem [21]–[24], although homogenized Green's functions for linesource excitations were presented in [25], and previously for one-dimensional (1-D) periodic structures, in [26]. Thus, all previous works on homogenized Green's functions, either using susceptibility dyadics or surface impedances, have been done assuming a line-source excitation. "

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    • "Another two-dimensional representation of a metasurface is in terms of homogenized surface impedances [19], [20]. Here also, most attention has been given to the plane wave problem [21]–[24], although homogenized Green's functions for linesource excitations were presented in [25], and previously for one-dimensional periodic structures, in [26]. Thus, all previous work on homogenized Green's functions, either using susceptibility dyadics or surface impedances, have been done assuming a line-source excitation. "
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