Microwave transmissivity of a metamaterial–dielectric stack

Abstract

A metamaterial layer comprising of a conducting square mesh surrounding subwavelength holes has a largely pure imaginary effective refractive index. We explore the microwave transmissivity of a stack of such metamaterial layers separated by dielectric spacers. As expected, a family of high transmissivity bands is experimentally observed. It is found that the lowest frequency edge is independent of the number of unit cells making up the structure and is highly tunable by appropriate geometrical design of the metamaterial layers. © 2009 American Institute of Physics. ͓doi:10.1063/1.3253703͔Multilayer metal-dielectric structures have been extensively studied at visible frequencies, and their response utilized in areas such as electromagnetic shielding, nonlinear photonics and perfect lensing.1-3 Geffcken 4 in 1939 fabricated metal-dielectric thin film stacks that exhibited transmission features that were significantly narrower than those previously observed in conventional dielectric-dielectric multilayer arrangements. 5The spectral response of metal-dielectric stacks in the visible regime comprises of a series of photonic band gaps where the reflectivity is high ͑and the transmissivity is low͒, separated by a series of peaks of high transmissivity. These transmission peaks correspond to near-standing-wave resonances within each dielectric cavity, coupled together via exponential fields within the metal film. Near the high frequency band edge of the first transmission band, the electric fields are predominantly confined to the dielectric and pass through zero in the metal. In contrast, at the low frequency band edge a significant proportion of the field enhancement occurs inside the metal regions. [6][7][8] An equivalent study of a metal-dielectric layer stack in the microwave domain ͑10 9 -10 10 Hz͒ is at first sight impractical since the real and imaginary parts of the refractive index of metals are both large ͑Ͼ10 3 ͒ and almost equal ͑i.e., the metal is near-perfectly conducting͒. Even a metal film of thickness 20 nm will almost completely screen the incident field 9 because of the large impedance mismatch. Instead, a metal is structured on the subwavelength scale to create a metamaterial with effective electromagnetic properties which replicates the behavior of Drude-like ͑plasmonic͒ metals in the visible regime ͑Ag, Au, etc.͒. 10 The metamaterial layer consists of a non diffracting square metal mesh surrounding an array of identical square holes. At wavelengths greater than the size of the holes, the electromagnetic fields are exponential within the holes with a decay length that is primarily dictated by the metamaterial geometry. Consequently the metamaterial is equivalent to a thin layer with a pure imaginary refractive index. 12,13The sample shown in Fig. 1͑a͒ comprises of eight printed circuit board ͑PCB͒ layers that are originally clad with 18 m of copper on one face. The copper is removed from three of these substrates the remaining five being etched to leave a copper square mesh ͑Fig. 1͑b͒͒ with period...

Transmission through stacked 2D periodic distributions of square conducting patches

“…4(b) is compared with the spectra reported in Ref. 25 for the stacked grids, we can see that, in contrast with the bandpass behavior of the grid structure, the patch structure exhibits a low-pass band followed by a wide stopband (followed by another passband, and so on). This behavior is observed independently of the number of stacked layers.…”

“…At this point, it is worth mentioning that, in the same manner that the dense metal grid structures studied in Ref. 25 mimic the behavior of stacked dielectric slabs separated by negative-permittivity solid thin films (metals at optical frequencies have a negative real part of the permittivity), the response of the structure studied in this paper resembles the response of a system of dielectric slabs separated by thin dielectric foils of very high permittivity. In the structures with thin dielectric or metal films separating dielectric slabs, no evanescent TE/TM fields are excited.…”

“…30 (this method was also used in Ref. 25 to explain the existence of bands in a stacked-grids structure). Following the procedure described in Ref.…”

“…With these limitations, the analytical model 24 gives accurate results, and thus it has been used for the explanation of the experimental and numerical data previously reported in Ref. 25. It was discussed in Refs.…”

Topological modes in one-dimensional solids and photonic crystals

“…As with other experiments [27,28], modeling can also be used to visualize the electric field distribution in each mode. Plots of the norm of the electric field as a function of the distance through the sample are displayed in Fig.…”