In this study, a novel periodic leaky-wave antenna (LWA) with wide beam-scanning angle and low crosspolarisation is proposed by using miniaturised composite right/left-handed transmission line (CRLH TL). By introducing the metallic holes loaded in the interdigital lines of the miniaturised CRLH TL, not only the parasitic resonant modes can be eliminated, but also the miniaturisation is realised. Considering the continuous phase constants from negative to positive values of the balanced CRLH TL, a continuous beam-scanning property from backward to forward of the resultant LWA can be obtained. For verification, a periodic LWA, which consists of 20 unit cells of the balanced CRLH TL, is fabricated and measured; the measured and simulated results are in good agreements with each other, indicating that the fabricated LWA operates from 3.90 to 4.90 GHz (a bandwidth of 22.7%), and has a wide continuous beam-scanning capability from backward −61°to forward 67°(including the broadside) within the operating band. Moreover, it also has very low cross-polarisation, which remains at a level of at least 25 dB below the co-polarisation across the entire radiation region. As a result, the presented LWA should find promising applications in modern wireless communication systems and the high-resolution radar system due to these wonderful electromagnetic performances.

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A class of semilinear fractional difference equations is introduced in this paper. The fixed point theorem is adopted to find stability conditions for fractional difference equations. The complete solution space is constructed and the contraction mapping is established by use of new equivalent sum equations in form of a discrete Mittag-Leffler function of two parameters. As one of the application, finite-time stability is discussed and compared. Attractivity of fractional difference equations is proved, and Mittag-Leffler stability conditions are provided. Finally, the stability results are applied to fractional discrete-time neural networks with and without delay, which show the fixed point technique’s efficiency and convenience.

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