EM Performance Analysis of Multilayered Metamaterial Frequency Selective Surfaces Shiv Narayan, Gopinath R., R.U. Nair, and R.M. Jha Computational Electromagnetics Lab. Aerospace Electronics and Systems Division CSIR-National Aerospace Laboratories Bangalore-560017, India e-mail: shivnarayan@nal.res.in, jha@nal.res.in Abstract— This paper presents EM performance analysis of the multilayered metamaterial FSS using TLTM method. It is shown that a multilayered metamaterial structure reveals the FSS properties. For efficacy of the method, the computed results are validated for metamaterial FSS structure such as tri-layer radome with the reported results in the open literature. Excellent matching is found between the computed and reported results. Further, a five-layer metamaterial FSS radome is investigated for TE and TM polarizations at incidence angles 0°, 30°, 45°, and 60°. It is observed that a multilayer metamaterial FSS radome exhibit multi resonance properties with proper tuning of thickness of the layers. Keywords-Metamaterial; MTM-FSS; Frequency Selective Surfaces; Transmission Line Transfer Matrix Method; Radome I. INTRODUCTION The response of the system in presence of electromagnetic (EM) field is determined by the macroscopic parameters such as permittivity and permeability of the material. Several numerical and analytical methods have been discussed in open literature for the analysis of multilayered metamaterial (MTM) structures such as Transfer Matrix Method (TMM) [1], Iterative Method [2], and Propagation Matrix Method [3]. In the present work, the EM performance analysis of five-layer metamaterial FSS has been carried out using transmission line transfer matrix (TLTM) method. It is shown that multilayer metamaterial structures exhibit frequency selective properties in various applications, which are not observed in common materials. II. THEORITICAL ASPECTS The transmission line transfer matrix method is the combination of transmission line method (TLM) and transfer matrix method [1]. This method is applicable for both TE and TM polarizations at both normal and oblique angle of incidence. In TLTM method, an equivalent transmission line represents a multilayered planar structure. The transmission line section is described by a characteristic impedance and propagation constant in the z- direction, which depends on the incidence angle, frequency, and polarization. The tangential components at the consecutive layers are related and the reflection and transmission coefficients of the total structure can be calculated for different polarizations. The side view of a five-layer metamaterial FSS radome is shown in Figure 1. Figure 1. Side view of five-layer metamaterial FSS radome. By using Snell’s law the relationship between the two adjacent layers l and (l+1) can be expressed as, ߛ ௟ ݏ ߠ ௟ ൌ ߛ ሺ௟ାଵሻ ݏ ߠ ሺ௟ାଵሻ ሺͳሻ where ߛ ௟ is the propagation constant. It can be written as ߛ ௟௭ ൌ ඥ ߤ ௟ ߝ ௟ ݋ ߠݏ ௟ ሺʹሻ where ߝ ௟ and ߤ ௟ are permittivity and permeability of the l th layer respectively. ൌʹߨ is the angular frequency. ߠ ௟ Incident wave Reflected wave Refracted wave ݖൌͲ ݖൌ ଵ ݖൌ ହ y ߠ ௜௡௖ ߠ ௥௘௙௟ z ߠ ௥௘௙௥ ߝ ଴ ߤ, ଴ ߝ ଵ ߤ, ଵ ߝ ௢ ߤ, ௢ ߝ ଶ ߤ, ଶ MTM layers  ଵ  ଶ ߝ ସ ߤ, ସ  ସ ݖൌ ଷ ߝ ଷ ߤ, ଷ ߝ ହ ߤ, ହ ݖൌ ଶ ݖൌ ସ  ଷ  ହ 978-1-4577-1099-5/11/$26.00 ©2011 IEEE