IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 56, NO. 1, JANUARY 2008 245 Talbot Effect Applied to Antennas M. G. Keller, J. Shaker, and Y. M. M. Antar Abstract—An experimental investigation is reported on how the Talbot effect may be exploited to produce a low volume antenna configuration that is suitable for high effective isotropic radiated power applications. In this architecture a periodic phase grating is combined with a sparse antenna array to form a structure that is simpler to fabricate than an equivalent active antenna array. This configuration is shown to have improved gain and lower grating lobe levels as compared to the sparse array. Finally, a simple technique is described to predict the far-field radiation pattern of this Talbot antenna array. Index Terms—Antennas, diffraction, interference, Talbot effect. I. INTRODUCTION The Talbot effect is an optical phenomenon that was discovered in 1836 by H. F. Talbot [1]. It is a near-field diffraction and interference phenomenon which occurs when a periodic amplitude or phase grating is illuminated by a plane wave of electromagnetic energy. Constructive and destructive interference of the diffracting waves emerging from be- hind a periodic grating form “bright spot” field pattern zones at frac- tions of the periodic “Talbot distance” that resemble the grating in form or in contrast, while in other regions shifted or multiple “bright spot” image zones appear. Following the pioneering work performed by Lohmann [2] on op- tical applications of the Talbot effect, a millimeter-wave Talbot array illuminator (TAIL) was investigated [3]. The Talbot effect has also been employed as a means to perform power combining within a planar waveguide at 8 GHz [4]. In addition, there have been several experi- mental and theoretical investigations of the free-space Talbot phenom- enon in the millimeter-wave band which introduced several applica- tions such as high power transmitting antennas, spatial power com- bining architectures, oscillators, and frequency doublers [5]–[7]. These interesting applications involved a quasi-optic approach, whereby the active array elements are spatially fed, thereby avoiding transmission line losses. However, this approach leads to structures that are electri- cally large in the longitudinal direction. This problem can be mitigated by employing a circuit feeding scheme for the active array elements. Antennae serve to radiate energy into a region of space in a manner that is quantified by their radiation patterns. Further, some system ap- plications may additionally require a certain effective isotropic radiated power (EIRP). One low-volume approach to achieve the required EIRP specification has been to employ active antenna arrays. This solution typically merges densely packed microstrip patch antennas with active devices such that a high-gain antenna is combined with a large power output to produce a suitable EIRP. One limitation of this approach is the requirement for a large number of active radiating elements. This lends itself to complex design and fabrication issues, as well as heat dissipa- tion problems that may potentially restrict its EIRP. To overcome some Manuscript received November 29, 2006; revised May 3, 2007. This work was carried out at the Communications Research Centre Canada. M. G. Keller and Y. M. M. Antar are with the Department of Electrical and Computer Engineering, Royal Military College of Canada, Station Forces Kingston, ON K7K 7B4, Canada (e-mail: michael.keller@crc.ca; antar-y@ rmc.ca). J. Shaker is with the Communications Research Centre Canada, Ottawa, ON K2H 8S2, Canada (e-mail: jafar.shaker@crc.ca). Digital Object Identifier 10.1109/TAP.2007.913167 Fig. 1. Normalized power distribution (dB) over an surface at beyond a 2-D phase grating. of these issues, it would be desirable if a sparse antenna array architec- ture could be adapted so as to allow for less dense packing of the active elements, and hence easier thermal considerations. This paper reports on an experimental and theoretical investigation on how the Talbot ef- fect may be exploited to produce a low volume antenna configuration that is suitable for high EIRP applications. II. TALBOT EFFECT APPLIED TO ANTENNAS It is worthwhile to briefly review some of the previously obtained results for when a 2-D phase grating is illuminated by a Gaussian nor- mally incident wave. For instance, in [3], a nine period by nine period phase grating, with a phase duty cycle (PDC) equal to 1/3, was formed by 81 identical unit cells, each of which had three phase shifts elements of 0 , 120 , and 240 . The grating period was 20 mm. As shown in the contour plot of Fig. 1, when illuminated by a Gaussian beam, 81 “bright spots” were generated at the fractional Talbot distance of beyond the structure, This figure displays the normalized power mea- sured by a planar near-field measurement system. A Talbot effect antenna may be formed from the amalgamation of a periodic phase grating and a periodic antenna array. As shown in Fig. 2, these two structures are combined to form an antenna based on the circuit-fed/spatially combined power combiner architecture [8]. In this configuration, the antenna elements are circuit-fed, and their indi- vidual outputs are combined in free-space. The underlying foundation of this concept is the fact that a periodic Talbot phase grating under plane wave illumination yields a periodic array of “bright spots” at a fractional Talbot distance [3]. In this particular application, a circuit-fed array of antenna elements is placed coincident with selected “bright spot” locations. By reciprocity the phase grating will act to transform the “bright spots” (now formed by the radiating elements) into a plane wave. The following sections will describe the design and analysis of Talbot antenna elements and arrays. A configuration suitable for high EIRP applications is now intro- duced. As a corporate-fed microstrip patch antenna array was used to illuminate the phase grating, its design will be described first. In this example, passive antenna elements are utilized; however, it would be a straight forward step to integrate active devices into the antenna array structure [9]. 0018-926X/$25.00 © 2008 IEEE