Special Issue on Metamaterials EBG Combinations of low/high permittivity and/or permeability substrates for highly directive planar metamaterial antennas G. Lovat, P. Burghignoli, F. Capolino and D.R. Jackson Abstract: An investigation of planar metamaterial antennas consisting of grounded metamaterial substrates with low and/or high values of the electric permittivity and/or the magnetic permeability excited by dipole sources is presented. Their performances are characterised in terms of their capa- bility to radiate high levels of power density in the broadside direction and to produce narrow pencil beams pointing at broadside with high directivity. To achieve a high directivity, a pair of weakly attenuated cylindrical leaky waves is excited along the metamaterial substrate; sufficient conditions are established for the existence of such leaky waves in terms of the values of the substrate permit- tivity and permeability. Approximate closed-form expressions are derived for the phase and attenu- ation constants of the leaky waves. Numerical results are given in order to illustrate the radiative features of this class of antennas and to validate the theoretical analysis. 1 Introduction medium with parameters mr, 1r excited by a horizontal elec- tric or magnetic dipole placed inside the slab or on the Periodic structures made of metallic and/or dielectric ground plane, respectively. The goal is to design planar inclusions in a uniform host medium may be represented, antennas with a simple single-dipole feed featuring enhanced in suitable frequency ranges, as homogeneous artificial broadside radiation and/or very high directivity at broadside. materials (metamaterials) that show novel and interesting Metamaterials are not usually isotropic when practically electromagnetic features. One of these features is the implemented, but the general properties discussed in this creation of highly directive radiation beams from simple paper for the isotropic case, assumed for simplicity, have sources such as dipoles or slots placed inside such materials, also been found assuming specific anisotropic models. as was obtained in the pioneering work of Gupta [1], In this contribution, we focus on a comparison among Poilasne et al. [2] and Enoch et al. [3] For a detailed antennas based on different realisations of substrates with historical overview of such enhanced-directivity antennas, high/low values of permittivity and/or permeability. The we address the reader to the Introduction of Lovat et al. possibility of achieving high levels of radiated power [4]. The structures considered here consist of a grounded density at broadside is ascertained, in connection with the metamaterial layer that may have either high or low values of the constitutive parameters of the substrate and values of permittivity and/or permeability, excited by of the electric or magnetic type of the source. Conditions either an electric or a magnetic dipole source. Such struc- for achieving the excitation of a pair of TEz and TMz tures are different from those where a cavity is created leaky modes (where z is the direction orthogonal to the under a partially reflective surface that is formed by high- air–slab interface) with small and equal values of the permittivity dielectrics [5–7], metallic FSS layers [8, 9] phase and attenuation constants are then derived, which is or other periodic dielectric structures [10, 11]. Although a requirement for the radiation of a highly directive pencil different in structure, the metamaterial antennas considered beam pointing at broadside with a circular cross-section in this work are similar in terms of the mechanism of [12]. The conclusions given in this paper provide guidelines radiation: in fact, all the antennas in [1–11] radiate a for a more comprehensive investigation assuming a more narrow beam because the feed excites slowly attenuating realistic homogeneous anisotropic model, or even the still leaky waves, as demonstrated in the work of Lovat et al. further realistic case of a metamaterial made of actual per- [4] and Jackson and Oliner [6]. iodic inclusions. Their importance rely also on the fact that The theory behind a grounded slab made of such metama- no other studies have been carried out so far on this topic, terials is revisited here, assuming a homogeneous isotropic and that the example seen in the literature represents just one of the possible choices (a low-permittivity metamater- ial) that can be adopted in order to realise a planar radiator # The Institution of Engineering and Technology 2007 with enhanced directivity or broadside radiation. doi:10.1049/iet-map:20050353 For convenience of the reader, the terminology adopted Paper first received 15th December 2005 and in revised form 20th July 2006 throughout the paper for describing the various considered G. Lovat and P. Burghignoli are with the Electronic Engineering Department, ‘La Sapienza’ University of Rome, Via Eudossiana 18, Roma 00184, Italy metamaterial media is reported here. F. Capolino is with the Information Engineering Department, University of Siena, Via Roma 56, Siena 53100, Italy MNZ – mu near zero, that is, jmrj1; D.R. Jackson is with the Department of Electrical and Computer Engineering, ENZ – epsilon near zero, that is, j1rj1; University of Houston, Houston, TX 77204-4005, USA MENZ – mu and epsilon near zero, that is, jmrj1, and E-mail: [email protected] j1rj1; IET Microw. Antennas Propag., 2007, 1, (1), pp. 177–183 177 Authorized licensed use limited to: Univ of Calif Irvine. Downloaded on April 4, 2009 at 15:36 from IEEE Xplore. Restrictions apply. MVL – mu very large, that is, jmrj1; as the ratio EP,J ¼ PJ(0)/PJ,0(0) between the broadside EVL – epsilon very large, that is,pj1rj1; power density radiated in the presence of the grounded Low-impedance material – hr ¼ (mr/1r) 1; slab PJ(0) and that radiated in free space PJ,0(0): the latter p 2 2 High-impedance material – phr ¼ (mr/1r) 1; is equal to PJ,0(0) ¼ k0h0/(32p )W/steradian [13],so Low-index material – nr ¼ p(mr1r) 1; that in this case High-index material – n ¼ (m 1 ) 1. r r r 2 EP;J ¼ 4hr ð3Þ 2 Maximisation of broadside radiation In contrast, for a magnetic dipole (whose broadside power 2 density radiated in free space is equal to PM,0(0) ¼ k0/ Let us consider a grounded slab as in Fig. 1, with constitu- 2 (32p h0)W/steradian), (1b) yields tive parameters mr, 1r, and thickness h, excited by a y-directed horizontal electric or magnetic dipole source k2 P ð0Þ¼ 0 ð4Þ placed at z ¼ hs or on the ground plane, respectively. The M 8p2h electric far field radiated by the electric dipole source at 0 broadside can be found by means of a simple application that is independent of hr. Hence a fixed enhancement factor of the reciprocity theorem [5]. This is done by letting a EP,M ¼ PM(0)/PM,0(0) ¼ 4 is obtained, which is the same y-polarised incident plane wave, having an amplitude of as that due to the ground plane alone, and therefore no the electric field equal to 2jk0h0 exp(2jk0r)/(4pr) at the power enhancement at broadside is obtained from the meta- origin, impinge on the structure from broadside, and then material. It can be concluded that, for high-impedance slabs, calculating the reaction between the dipole source and the electric sources must be employed in order to enhance electric field inside the structure due to the incident plane broadside radiation. wave. A similar analysis holds for the magnetic dipole source, using an x-polarised incident plane wave and Case 2: Materials with low intrinsic impedance. taking the reaction between the dipole source and the Conversely, considering metamaterial slabs with very low resulting magnetic field inside the structure. The resulting values of intrinsic impedance, that is, with hr 1, it can broadside angular power density (W/steradian) at broadside easily be seen from (1) that, for both electric and magnetic (u ¼ 0) is found to be sources, the broadside power density is maximised when h ¼ (2n 2 1)l1/4(n ¼ 1, 2, ...). For an electric source, k2h h2 sin2ðk h Þ by letting n ¼ 1, the optimum source location is h ¼ h, P ð0Þ¼ 0 0 r 1 s ð1aÞ s J 2 2 2 2 for which (1a) gives the broadside power density as 8p cos ðk1hÞþhr sin ðk1hÞ 2 2 k0 1 k0 h0 P ð0Þ¼ ð1bÞ PJð0Þ¼ ð5Þ M 2 2 2 2 8p2 8p h0 cos ðk1hÞþhr sin ðk1hÞ which is independent of hr. In contrast, for a magnetic for a unit-amplitude electric dipole moment and for a source, (1b) gives the broadside power density as unit-amplitudep magnetic dipolep moment, respectively,p where k ¼ v (m 1 ), h ¼ (m /1 ), k ¼ k (m 1 ) and 2 p 0 0 0 0 0 0 1 0 r r k0 h ¼ (m /1 ). The power density at broadside is investi- P ð0Þ¼ ð6Þ r r r M 8p2h h2 gated below assuming two cases: high- and low-impedance 0 r materials, since a large broadside power density requires which can be made very large by decreasing the normalised one of these two cases. slab impedance hr either by using a MNZ and/or a EVL material. The relevant power enhancement factor is Case 1: Materials with high intrinsic impedance. 4 Considering metamaterial slabs with very high values of ¼ ð Þ EP;M 2 7 normalised intrinsic impedance, that is, with hr 1, it hr can easily be seen from (1) that, for both electric and mag- netic sources, the broadside power density is maximised It can be concluded that, for low-impedance slabs, magnetic p sources must be employed in order to enhance broadside when h ¼ nl1/2 (where l1 ¼ l0 (mr1r) and n ¼ 1, 2, ...).