Enhancement of Localization in One-Dimensional Random Potentials with Long-Range Correlations Page: 4
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PRL 100, 126402 (2008)
PHYSICAL REVIEW LETTERS
28 MARCH 2008
a) 0.4 -..
0 20 40 60 80 100
FIG. 6 (color online). Profiles of two enhanced-localized states
at kd/7rr 0.63 (a) and 0.69 (b) for the correlated sequence
(marked by vertical dotted lines in Figs. 4 and 5. Graph (b) is the
state responsible for a sharp decrease of IS22 I shown at the top of
Fig. 5. Crosses show an exponential decay with a localization
length of 10 scatterer spacings.
Two enhanced-localized states are shown in Fig. 6. The
quantity 1 - IS22I, which is proportional to the intensity
I /2 of the wave function , is plotted versus the coor-
dinate of the moving antenna. Exponentially localized
states are clearly seen inside the waveguide. The localiza-
tion length is about 10 spacings d between the scatterers.
Thus, the emergence of enhanced-localized states due to
long-range correlations is found experimentally. It is
highly nontrivial that such strong enhancement of local-
ization occurs for relatively weak fluctuations of the
We would like to stress the good agreement between
theory and experiment, in spite of the fact that (i) the
analytical results are based on the analysis of the
Lyapunov exponent for an infinite sample, (ii) the effect
of long-range correlations is based on the binary correlator
that is correct in the first Born approximation, (iii) the
number of scatterers is quite small, and (iv) there is ab-
sorption of about 0.04 dB per unit cell d for the empty
waveguide. Also, the potential was scaled linearly to the
micrometer screw depth, which is an approximation.
However, a strong enhancement of localization due to
long-range correlations is clearly seen, indicating that the
observed effect is robust. The method may find various
applications in the design of 1D structures especially as
such localized states are controlled in the frequency space,
a fact that may be important, for example, in random lasing
In conclusion, we performed experimental study of the
effect of an enhancement of localization, that is due to
specific long-range correlations in random potentials.
Enhanced-localized states emerge inside the single-mode
microwave waveguide, within two narrow frequency inter-
vals. The enhancement factor (of about 16 in the experi-
ment) for the localization length is inversely proportional
to the width of frequency intervals. The positions of these
intervals are in a good agreement with our theoretical
predictions. These localized states appear for a quite small
number of scatterers, N = 100, thus the theory works well
far beyond the region of its applicability.
This work was supported by the DFG via the
Forschergruppe 760 "Scattering Systems with Complex
Dynamics," and by the DOE Grant No. DE-FG02-
 P.W. Anderson, Phys. Rev. 109, 1492 (1958).
 A. Z. Genack, Phys. Rev. Lett. 58, 2043 (1987).
 A. A. Chabanov, M. Stoytchev, and A. Z. Genack, Nature
(London) 404, 850 (2000).
 T. Schwartz, G. Bartal, S. Fishman, and M. Segev, Nature
(London) 446, 52 (2007).
 A. Z. Genack and A. A. Chabanov, J. Phys. A 38, 10465
 I. M. Lifshitz, S. Gredeskul, and L. Pastur, Introduction to
the Theory of Disordered Systems (Wiley, New York,
 N. M. Makarov, "Spectral and Transport Properties of
One-Dimensional Disordered Conductors," http://www.
 D. H. Dunlap, H.-L. Wu, and P. W. Phillips, Phys. Rev.
Lett. 65, 88 (1990).
 P. Phillips and H.-L. Wu, Science 252, 1805 (1991).
 V. Bellani, E. Diez, R. Hey, L. Toni, L. Tarricone, G. B.
Parravicini, F. Dominguez-Adame, and R. Gomez-Alcala,
Phys. Rev. Lett. 82, 2159 (1999).
 F. A. B. F. de Moura and M. L. Lyra, Phys. Rev. Lett. 81,
 F. M. Izrailev and A. A. Krokhin, Phys. Rev. Lett. 82, 4062
 U. Kuhl, F. M. Izrailev, A. A. Krokhin, and H.-J.
Stockmann, Appl. Phys. Lett. 77, 633 (2000).
 M. Titov and H. Schomerus, Phys. Rev. Lett. 95, 126602
 H. Cao, Y. G. Zhao, S. T. Ho, E. W. Seelig, Q. H. Wang,
and R. P. H. Chang, Phys. Rev. Lett. 82, 2278 (1999).
 M. Patra, Phys. Rev. E 67, 065603(R) (2003).
 U. Kuhl and H.-J. Stockmann, Phys. Rev. Lett. 80, 3232
 In fact, Eq. (6) is a conservation of the integrated
Lyapunov exponent. This becomes clear if the function
W(2bt) is replaced [using Eq. (3)] by 1-'(E)/o1 '(E),
where lo(E) corresponds to white noise with W(2bt) = 1.
 G.A. Luna-Acosta, H. Schanze, U. Kuhl, and H.-J.
Stickmann, "Transport Properties of One-Dimensional
Photonic Crystals with Defects: Experiment and
Theory" (to be published); arXiv:0711.1760.
 U. Kuhl, Eur. J. Phys. Special Topics 145, 103 (2007).
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Kuhl, Ulrich; Izrailev, Felix M. & Krokhin, Arkadii A. Enhancement of Localization in One-Dimensional Random Potentials with Long-Range Correlations, article, March 28, 2008; [College Park, Maryland]. (digital.library.unt.edu/ark:/67531/metadc103275/m1/4/: accessed September 20, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT College of Arts and Sciences.