IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 59, NO. 6, JUNE 2011 2241 Microwave Bessel Beams Generation Using Guided Modes Mohamed A. Salem, Aladin H. Kamel, and Edip Niver, Member, IEEE Abstract—A novel method is devised for Bessel beams genera- tion in the microwave regime. The beam is decomposed in terms of a number of guided transverse electric modes of a metallic wave- guide. Modal expansion coefficients are computed from the modal power orthogonality relation. Excitation is achieved by means of a number of inserted coaxial loop antennas, whose currents are cal- culated from the excitation coefficients of the guided modes. The efficiency of the method is evaluated and its feasibility is discussed. Obtained results can be utilized to practically realize microwave Bessel beam launchers. Index Terms—Array signal processing, beams, mode matching method, waveguide excitation. I. INTRODUCTION B ESSEL beams are solutions to Helmholtz equation. They appear to propagate without diffraction and thus have a potential to replace Gaussian beams in a number of applications. The ideal Bessel beam was first noted by Durnin in 1987 [1]. In his work, Durnin showed that particular solutions of the Bessel type have a transverse localization that is independent of the propagation distance. Moreover, he showed that such a beam could have near diffraction limited features [1]. The name of such beams stems from the Bessel function, which describes the beam shape in the transverse plane. While the ideal Bessel beam extends indefinitely in the transverse plane, thus deeming any practical realization of such a beam impossible, it was shown that a practical approximation is possible. The experimentally verified approximation to the Bessel beam exhibited the same qualities of the ideal beam over a finite distance [2]. One of the earliest developed and simplest techniques for Bessel beams generation requires an annular slit placed in the back focal plane of a positive lens [2]. Other methods to generate Bessel beams utilize axicons, computer generated holograms and lasing devices [3]–[7]. Nevertheless, the focus of these methods is generating Bessel beams in the optical regime. In the microwave regime, the generation of monochromatic Bessel beams is much less explored, though microwave Bessel Manuscript received May 23, 2010; revised October 12, 2010; accepted De- cember 10, 2010. Date of publication May 05, 2011; date of current version June 02, 2011. M. A. Salem is with King Abdullah University of Science and Technology, Division of Physical Sciences and Engineering, Thuwal, Saudi Arabia. A. H. Kamel is with the ECE Department, Faculty of Engineering, Ain Shams University, Cairo 11566, Egypt. E. Niver is with New Jersey Institute of Technology, Electrical and Computer Engineering, University Heights, Newark, NJ 07102 USA. Digital Object Identifier 10.1109/TAP.2011.2143683 beams could be used in remote power transmission, electro- magnetic propulsion and secure, long-distance communication, among other applications. Alternatively, the generation of other types of microwave fields based on superpositions of Bessel beams were reported, such as localized waves in the microwave regime [8] and super-resolving pupils [9]. In this study, we show a new method to generate Bessel beams in the microwave regime. For simplicity, only the trans- verse electric (TE) case is considered. This does not limit the applicability of the method, but rather simplifies the analysis and elucidates the steps of the scheme. A truncated Bessel beam is set to be the aperture field at the open-end of a flanged metallic circular waveguide section. Fig. 1 depicts the Bessel beam launching system. As this aperture field would propagate outside the waveguide, it is taken as the transmitted field. Re- flection from the aperture is ignored due to the presence of the metallic flange and the incident TE modes coefficients inside the waveguide are computed from the decomposition of the aperture field in terms of the waveguide’s TE modes. The de- composition is possible, because the waveguide’s modes form a complete and orthogonal (through their power orthogonality relation) set over the waveguide’s cross section. This allows the matching of the tangential fields to be carried out for each mode separately. In order to excite the modes inside the waveguide with the calculated coefficients, a set of loop antennas are placed coaxially inside the waveguide. For power efficiency, we consider a finite waveguide section in the -direction termi- nated by a perfect electric conductor. The antennas are placed well away from each other to avoid cross-talk. From the axial symmetry of this configuration, the currents on the antennas could only excite TE modes. We establish a relation between the current on an antenna and the excitation coefficient of each TE mode. For the same number of TE modes and antennas, we construct a system of linear equations in the unknown currents. After solving the linear system and determining the antenna currents, the forward problem is solved to reconstruct the Bessel beam at the aperture. Finally, the generated beam is propagated away from the aperture and compared against the ideal truncated beam. This approach to Bessel beams generation offers a lot of flex- ibility. As the generated beam is controlled directly by the an- tenna currents, it could be relatively easy to manipulate the beam intensity, spot size and modulation, by controlling the excitation currents. In Section II, the vector electromagnetic TE Bessel beam so- lution is introduced. Beam expansion in terms of the circular waveguide’s propagating TE modes is presented in Section III. In Section IV, the method to determine the excitation currents 0018-926X/$26.00 © 2011 IEEE