Band-reject infrared metallic photonic band gap filters on flexible polyimide substrate
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183 Mat. Res. Soc. Symp. Proc. Vol. 484 © 1998 Materials Research Society
can also lead to fundamentally different PBG characteristic. For an interconnected mesh structure, the stop band extends from zero frequency up to some cutoff frequency, determined by the periodicity of the structure[4]. On the other hand, isolated metal patches show a bandstop behavior very similar to a dielectric PBG characteristic[5]. In this paper, we describe an MPBG structure which shows both these behaviors, a lower order bandgap extending from zero to cutoff frequency and another bandstop region at higher frequency. The fabrication technique and the transmission behavior of this mechanically flexible MPBG structure in the far infrared are discussed in detail. The MPBG structure described in this paper are related to frequency selective surfaces (FSSs), which are two dimensional arrays of metallic patches or aperture elements with frequency filtering properties. Frequency selective surfaces have been studied in great detail because of their application in the microwave region.[6] Most of the FSS work has focused on single layer metal structures. THEORETICAL CALCULATION We calculated the expected transmission spectrum of the three-layer MPBG structure before fabricating it. The transfer matrix method (TMM) originally introduced by Pendry and MacKinnon has been used for the theoretical calculations.[7] In the TMM technique, the total volume is divided into small cells, and the fields associated with each cell are coupled to neighboring cells. The final transfer matrix relates the incident wave on the PBG from one side to the outgoing wave on the other side. The TMM can be used to calculate the band structure of an infinite periodic system. However, for these studies, we used the TMM to determine the electromagnetic transmission and reflection coefficients as functions for frequency for waves incident on a PBG of finite thickness. The transfer matrix method has previously been applied in studies of defects in 2D PBG structures, of 3D layer-by-layer PBG structure, and of 2D and 3D metallic structure. In all those previous investigations, the theoretical results matched very well with experimental measurements.[8]-[10] EXPERIMENT The metallic photonic bandgap structures were fabricated in a layer-by-layer fashion using alternating layers of polyimide for the dielectric and aluminum for metal grids, as depicted in figure l(a). The MPBG structures covers an area of 2cm x 2cm. The lattice constant of the metal grid is 321tm and the width of the metal lines is 2.5gtm as shown in figure 1(b). Halfway between each intersection, a short perpendicular cross-arm defect has been added. The cross-arm is 2.5gm wide and has lengths(L) of 10.5gjm, 18.5gjm and 22.5pgm for three different samples. The
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thickness of the dielectric separation layer is 11 gim in all the samples. Standard spin-on polyimide supplied by DuPont Pyralin® SP series PI-1111 with a dielectric constant Cr = 2.8 was used for dielectric.
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Polyimide
encapsulating -" the PBG
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