Cylindrical Metamaterial Lens for Single-feed Adaptive Beamforming Jeremiah P. Turpin, Douglas H. Werner Department of Electrical Engineering The Pennsylvania State University University Park, PA 16802 USA
[email protected] Abstract – A design is presented for a beam-scanning Transformation Electromagnetics (TE) lens that allows an arbitrary number of beams at controlled magnitudes to be dynamically synthesized from a single omnidirectional source. A cylindrical slab of zero-index magnetic metamaterial controls the radiation pattern by altering the effective shape of the lens through switching regions of it ‘off’ to emulate free-space conditions. This lens offers the potential for fast solid-state multi- beam control with application to advanced terrestrial communication systems or adaptive radars. I. INTRODUCTION Metamaterials are collections of subwavelength structures engineered to create interesting electromagnetic interactions, often enabling properties without parallels in natural materials. Although the science of metamaterials is still developing, many applications have been proposed or demonstrated where their use facilitates some type of novel behavior. In particular, the design techniques that have been introduced by Transformation Electromagnetics (TE) [1] rely on the use of metamaterials for the construction of novel devices within which EM waves may be controlled with a high degree of design flexibility. Application of TE and metamaterial-based devices to antennas for the augmentation of radiation performance or reduction of antenna dimensions is a productive field of current research. Metamaterial lenses designed with TE techniques have been presented for use in compact, high-gain [2], [3] and multibeam [4–9] antennas based on single feeds. Prototypes of these lenses have confirmed the predicted performance thereby validating the TE/metamaterial design method [3], [4] and the use of metamaterial lenses for antenna pattern control. With traffic congestion increasing on popular terrestrial microwave communication bands, multibeam or steerable- beam antennas are particularly compelling due to the possibility of placing pattern nulls or peaks at desired locations in real time so as to reduce interference. Anisotropic near-zero- index metamaterials (ZIM) have been used in several TE lenses that allow the number, direction, and relative strength of the beams to be chosen arbitrarily during lens design [4], [6–8]. However, the beam locations are fixed when the lens is constructed, without the possibility of dynamic beam steering during operation. Conventional phased array antenna systems are electrically steerable and capable of producing nearly arbitrary beam patterns with high gains given a sufficient number of elements. However, cost and feed structure complexity increase rapidly with the size of the array. In comparison, the single feed required for a multibeam metamaterial lens is attractive, but the static radiation pattern greatly limits their application. The potential of arbitrarily configurable TE lenses has been suggested in [6], [8], but the proposed implementation was impractical and limited. In this paper, we describe the design considerations necessary for a dynamically tunable beam- steering metamaterial lens. II. TUNABLE LENS DESIGN PRINCIPLES The lens design begins with the near-zero-index uniaxial TE lens introduced in [6]. This lens used an electric near-ZIM implemented by a wire-mesh metamaterial with a single dipole feed. For this lens, the extraordinary axis of the metamaterial is oriented in the z-direction, parallel to the E-field. For single- polarization operation, waves in the material behave as though the structure is isotropic. The number and relative magnitude of the beams are determined by the shape of the lens; a beam radiates from each planar face of the lens. Instead of changing the physical shape of the lens to control the beams, which would freeze the beam configuration at design stage, a cylindrical slab of tunable ZIM can be used to change the effective shape of the lens. ZIMs are narrowband, resonant metamaterials, allowing a small change, perhaps caused by a state change in a MEMS switch or varactor diode, to shift the resonance frequency away from the lens operational band so as to operate in a quasi-free-space mode. Selectively switching exterior regions of the lens ‘on’ and ‘off’ between ZIM and near-free-space conditions changes the effective shape of the lens and, thus, the number and magnitude of the beams, as illustrated in Fig. 1. With a dynamically-switchable z-oriented anisotropic ZIM metamaterial controlled in real time, only on/off control for each pixel of the lens is required to allow completely dynamic control of the effective lens shape. A tunable metamaterial implemented using printed circuit board (PCB) technology will require interconnections and control signals passing between unit cells as electrically long traces, complicating the design of the metamaterial. Any extraneous metal within the lens will tend to distort the local fields and possibly degrade the quality of the focusing effect. To minimize the effects of the control traces, this lens uses a magnetic metamaterial and magnetic dipole feed, the dual 978-1-4673-0462-7/12/$31.00 ©2012 IEEE design to [6]. The effects of the magnetic metamaterial will be less affected by the long, electrically-connected traces, which would primarily affect the electric field. Simulations of the lens use an electrically-small loop as an approximation to a magnetic dipole source, but the final lens will employ an efficient TE10 source, such as the electrically-small magnetic dipole antennas introduced in [9], [10]. III. HOMOGENEOUS LENS SIMULATIONS A TE lens design was chosen and simulated according to the principles and design considerations presented above. Planar 2D simulations, as demonstrated in Fig. 1, are not very sensitive to the lens size. However, the thickness of a finite cylindrical ZIM slab must be chosen to produce good performance. In addition, the top and bottom surfaces must be covered in PEC to prevent energy leakage from creating strong axial beams. The magnetic dipole, which cannot be placed near the ground plane, is centered within the lens as illustrated in Fig. 2. Some choices of dimensions (r,h) will produce a non- radiating dielectric resonator instead of an antenna, requiring lens proportions to be selected for good radiation performance at the desired frequency. This constraint, along with the narrow bandwidth of a metamaterial implementation, will limit the overall operating bandwidth of the lens. IV. CONCLUSIONS A design for a tunable beam-steering transformation electromagnetics-based metamaterial lens has been presented along with simulations of homogeneous materials to demonstrate feasibility. This lens, when combined with an appropriate tunable magnetic metamaterial, will allow for solid-state real-time beam scanning from a single feed antenna, without the complex phasing and amplitude adjustment networks required for array systems with equivalent performance. When compared to static TE or metamaterial lenses, the beam-scanning capability of the new lens more than compensates for the increased complexity of designing and constructing a tunable metamaterial. A metamaterial implementation of this lens will be presented at the conference. REFERENCES [1] D.-H. Kwon and D. H. Werner, “Transformation electromagnetics: An overview of the theory and applications,” IEEE Antennas and Propagation Magazine, vol. 52, no. 1, pp. 24-46, Feb. 2010. [2] S. Enoch, G. Tayeb, P. Sabouroux, N. Guérin, and P. Vincent, “A metamaterial for directive emission,” Physical Review Letters, vol. 89, no. 21, pp. 213902/1-4, Nov. 2002. [3] Q. Wu, J. P. Turpin, D. H. Werner, and E. Lier, “Thin metamaterial lens for directive radiation,” IEEE International Symposium on Antennas and Propagation, Spokane, WA, 2011, pp. 2890-2893. [4] Z. H. Jiang, M. Gregory, and D. Werner, “Experimental demonstration of a broadband transformation optics lens for highly directive multibeam emission,” Physical Review B, vol. 84, pp. 165111/1-6, Oct. 2011. [5] W. X. Jiang, T. J. Cui, H. F. Ma, X. Y. Zhou, and Q. Cheng, “Cylindrical-to-plane-wave conversion via embedded optical transformation,” Applied Physics Letters, vol. 92, no. 26, pp. 261903/1- 3, 2008. [6] J. P. Turpin, A. T. Massoud, Z. H. Jiang, P. L. Werner, and D. H. Werner, “Conformal mappings to achieve simple material parameters for transformation optics devices,” Opt. Express, vol. 18, pp. 244-252, 2010. [7] J. P. Turpin, Z. H. Jiang, P. L. Werner, D. H. Werner, and D.-H. Kwon, “Embedded transformation optics lenses for antenna performance enhancement,” ACES 2011, Williamsburg, VA, 2011. [8] J. P. Turpin, Z. H. Jiang, P. L. Werner, and D. H. Werner, “Tunable metamaterials for conformally mapped transformation optics lenses,” IEEE International Symposium on Antennas and Propagation, Toronto, Ontario, Canada, 2010. [9] S. R. Best, “A low Q electrically small magnetic (TE mode) dipole,” IEEE Antennas and Wireless Propagation Letters, vol. 8, pp. 572-575, 2009. [10] O. S. Kim, “Low-Q electrically small spherical magnetic dipole antennas,” IEEE Transactions on Antennas and Propagation, vol. 58, no. 7, pp. 2210-2217, Jul. 2010. Figure 1. Beam steering from a cylindrical slab of tunable ZIM metamaterial by selectively de-tuning the metamaterial to return to near-free-space conditions. (a) Lens diagram for two beams. (b) Planar simulation results. Figure 2. (a) Model illustrating lens construction using tunable ZIM slab with PEC plates at top and bottom. 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