The discovery of ``quasi-crystals,'' whose X-ray diﬀraction patterns reveal certain unusual features which do not conform with spatial periodicity, has motivated studies of the wave-dynamical implications of ``aperiodic order.'' This paper discusses various aperiodic configurations generated by Rudin-Shapiro (RS) sequences. These RS sequences constitute ones of the simplest conceivable examples of deterministic aperiodic geometries featuring random-like (dis)order. The scattering properties of aperiodically-ordered thinned 2-D patch arrays based on RS sequences are analyzed by using physical optics approximation. Compared to a periodic case, RS-based antenna array is found to have a substantial reduction in the magnitude of the backscattering component of the scattered signal with half of the elements and the same magnitude of specular reflection. This property is verified by illustrative numerical parametric studies.
1. Senechal, M., Quasicrystals and Geometry, Cambridge Univ. Press, Cambridge, U.K., 1995.
2. Baake, M., J.-B. Suck, M. Schreiber, and P. Häussler (eds.), "A guide to mathematical quasicrystals," Quasicrystals: An Introduction to Structure, Physical Properties, and Applications, 17-48, Springer, Berlin, Germany, 2002.
3. Levine, D. and P. J. Steinhardt, "Quasicrystals: A new class of ordered structures," Phys. Rev. Lett., Vol. 53, No. 26, 2477-2480, Dec. 1984. doi:10.1103/PhysRevLett.53.2477
5. Steinberg, B. D., "Comparison between the peak sidelobe of the random array and algorithmically designed aperiodic arrays," IEEE Trans. Antennas Propagat., Vol. 21, 366-370, May 1973. doi:10.1109/TAP.1973.1140493
6. Kim, Y. and D. L. Jaggard, "The fractal random array," Proc. of the IEEE, Vol. 74, No. 9, 1278-1280, Sep. 1986. doi:10.1109/PROC.1986.13617
7. Sallam, T. and A. Attiya, "Sidelobe reduction and resolution enhancement by random perturbations in periodic antenna arrays," The 34th National Radio Science Conference (NRSC’17), 49-55, Alexandria, Egypt, Mar. 2017.
8. Prakash, V. V. S. and R. Mittra, "An efficient technique for analyzing multiple frequency-selective-surface screens with dissimilar periods," Microwave Opt. Technol. Letts., Vol. 35, No. 1, 23-27, Oct. 2002. doi:10.1002/mop.10506
9. Chiau, C. C., X. Chen, and C. Parini, "Multiperiod EBG structure for wide stopband circuits," IEE Proc. Microwaves, Antennas and Propagat., Vol. 150, No. 6, 489-492, Dec. 2003. doi:10.1049/ip-map:20031087
13. Galdi, V., V. Pierro, G. Castaldi, I. M. Pinto, and L. B. Felsen, "Radiation properties of one-dimensional random-like antenna arrays based on Rudin-Shapiro sequences," IEEE Trans. Antennas Propagat., Vol. 53, No. 11, 3568-3575, Nov. 2005. doi:10.1109/TAP.2005.858863
14. Stephen, D. S., T. Mathew, K. A. Jose, C. K. Aanandan, P. Mohanan, and K. G. Nair, "New simulated corrugated scattering surface giving wideband characteristics," Electron. Lett., Vol. 29, No. 4, 329-331, Feb. 1993. doi:10.1049/el:19930223
15. Swandic, J. R., "Bandwidth limits and other considerations for monostatic RCS reduction by virtual shaping,", Tech. Rep. A927 224, Naval Surface Warfare Center, Carderock Div., Bethesda, MD, Jan. 2004.
16. Jayasinghe, J. W., J. Anguera, and D. N. Uduwawala, "A high-directivity microstrip patch antenna design by using genetic algorithm optimization," Progress In Electromagnetics Research C, Vol. 37, 131-144, 2013. doi:10.2528/PIERC13010805
17. Balanis, C. A., Advanced Engineering Electromagnetics, 2nd Ed., John Wiley & Sons, Inc., New York, 2012.
18. Kolár, M., "New class of one-dimensional quasicrystals," Phys. Rev. B, Vol. 47, No. 9, 5489-5492, Mar. 1993. doi:10.1103/PhysRevB.47.5489
19. Kolár, M., B. Iochum, and L. Raymond, "Structure factor of 1D systems (superlattices) based on two-letter substitution rules: I. δ (Bragg) peaks," J. Phys. A: Math. Gen., Vol. 26, No. 24, 7343-7366, Dec. 1993. doi:10.1088/0305-4470/26/24/011
20. Brillhart, J. and P. Morton, "A case study in mathematical research: The Golay-Rudin-Shapiro sequence," Amer. Math. Mon., Vol. 103, No. 10, 854-869, Dec. 1996. doi:10.1080/00029890.1996.12004830
21. Queffélec, M., "Substitution dynamical systems - Spectral analysis," Lecture Notes in Mathematics, Vol. 1294, Springer, Berlin, 1987.
22. Fogg, N. P., V. Berthé, S. Ferenczi, C. Mauduit, and A. Siegel (eds.), "Substitutions in dynamics, arithmetics, and combinatorics," Lecture Notes in Mathematics, Vol. 1794, Springer, Berlin, 2002.
23. Berthé, V., "Conditional entropy of some automatic sequences," J. Phys. A, Math. Gen., Vol. 27, No. 24, 7993-8006, Dec. 1994. doi:10.1088/0305-4470/27/24/011