Beyond Anderson localization in 1D: Anomalous localizacion of microwaves in random waveguides

Experimental evidence demonstrating that anomalous localization of waves can be induced in a controllable manner is reported. A microwave waveguide with dielectric slabs randomly placed is used to confirm the presence of anomalous localization. If the random spacing between slabs follows a distribution with a power-law tail (Lévy-type distribution), unconventional properties in the microwave-transmission fluctuations take place revealing the presence of anomalous localization. We study both theoretically and experimentally the complete distribution of the transmission through random waveguides characterized by α ¼ 1=2 (“Lévy waveguides”) and α ¼ 3=4, α being the exponent of the power-law tail of the Lévy-type distribution. As we show, the transmission distributions are determined by only two parameters, both of them experimentally accessible. Effects of anomalous localization on the transmission are compared with those from the standard Anderson localization.J.C., F.C., J.S.-D., and V.A.G. acknowledge financial support from MINECO (Spain) under the Projects No. FIS2012-35719-C02-02, No. TEC2010-19751, and No. CSD2008-00066 (CONSOLIDER Program). A.A.F.-M. and J.A.M.-B. thank Fondo Institucional PIFCA through Grant No. BUAP-CA-169 for partial support.Fernandez Marin, AA.; Mendez Bermudez, J.; Carbonell Olivares, J.; Cervera Moreno, FS.; Sánchez-Dehesa Moreno-Cid, J.; Gopar, VA. (2014). Beyond Anderson localization in 1D: Anomalous localizacion of microwaves in random waveguides. PHYSICAL REVIEW LETTERS. 113(23):233901-1-233901-5. doi:10.1103/PhysRevLett.113.233901233901-1233901-511323Anderson, P. W. (1958). Absence of Diffusion in Certain Random Lattices. Physical Review, 109(5), 1492-1505. doi:10.1103/physrev.109.1492Lagendijk, A., Tiggelen, B. van, & Wiersma, D. S. (2009). Fifty years of Anderson localization. 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