## 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.

© 2010 Optical Society of America

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### Equations (6)

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(1)
$${\beta}_{0}=\frac{\omega}{c}\phantom{\rule{.2em}{0ex}}\phantom{\rule{.2em}{0ex}};{\beta}_{d}=\sqrt{{\epsilon}_{r}(1-j\mathrm{tan}\delta )}{\beta}_{0}$$
(2)
$${Z}_{0}=\sqrt{\frac{{\mu}_{0}}{{\epsilon}_{0}}}\phantom{\rule{.2em}{0ex}}\phantom{\rule{.2em}{0ex}};\phantom{\rule{.2em}{0ex}}{Z}_{d}=\sqrt{\frac{{\mu}_{0}}{{\epsilon}_{0}}}\frac{1}{\sqrt{{\epsilon}_{r}(1-j\mathrm{tan}\delta )}}$$
(3)
$${Z}_{g}=j\omega {L}_{g}\phantom{\rule{.2em}{0ex}}\phantom{\rule{.2em}{0ex}};\phantom{\rule{.2em}{0ex}}{L}_{g}=\frac{{\eta}_{0}{\lambda}_{g}}{2\pi c}\mathrm{ln}\left[\mathrm{csc}\left(\frac{\pi {w}_{m}}{2{\lambda}_{g}}\right)\right]$$
(4)
$$\mathrm{cosh}\left(\gamma {t}_{d}\right)=\mathrm{cos}\left({k}_{d}{t}_{d}\right)+j\frac{{Z}_{d}}{2{Z}_{g}}\mathrm{sin}\left({k}_{d}{t}_{d}\right)$$
(5)
$$\mathrm{cosh}\left(\gamma {t}_{d}\right)=-1$$
(6)
$$\mathrm{cosh}\left(\gamma {t}_{d}\right)\equiv \mathrm{cos}\left({k}_{d}{t}_{d}\right)+j\frac{{Z}_{d}}{2{Z}_{g}}\mathrm{sin}\left({k}_{d}{t}_{d}\right)=1.$$