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SUMMARY:Wave diagnostics of inhomogeneous inclusions in low-dimensional qu
 asi-periodic structures
DTSTART;VALUE=DATE-TIME:20211221T093000Z
DTEND;VALUE=DATE-TIME:20211221T095000Z
DTSTAMP;VALUE=DATE-TIME:20260316T192628Z
UID:indico-contribution-235@indico.bitp.kiev.ua
DESCRIPTION:Speakers: Liudmyla Sidletska (Odessa State Environmental Unive
 rsity)\nIn the classical work Rayleigh showed that a plane wave propagatin
 g in a one-dimensional periodic unbounded structure\, for some wavelengths
 \, undergoes total reflection at the boundaries of a fragment\, called in 
 the modern terminology accepted in the theory of such structures\, called 
 photonic crystals\, a forbidden band. In this case (by the Bloch – Floqu
 et theorem) the wave amplitude inside the periodic system decays exponenti
 ally [1].\nIn this paper\, we consider a quasi-one-dimensional\, semi-boun
 ded layered periodic structure\, in which the first (in order) layer has c
 haracteristics (refractive index\, dielectric constant) that differ from o
 ther elements. We postulate that such a construction can serve as a model\
 , for example\, of a granular chain starting from an isotopic defect (or f
 rom an impurity particle).\nIn this work\, a criterion is established for 
 the condensation of the spectrum near one of the boundaries of the forbidd
 en zone corresponding to the non-propagating wave mode. In a real prototyp
 e\, a granular chain\, such a mode (for example\, in an electromagnetic wa
 ve) is\, as it were\, "arrested" in a certain vicinity of the impurity.\nA
 s a result\, it was demonstrated how\, when the symmetry of the initial st
 ate of the system is violated\, say\, due to the formation of defects (or 
 deterministic incorporation of impurities)\, it is possible to form expone
 ntially growing and decaying modes with the formation of a separate one lo
 calized in the vicinity of the defect. The established regularities can be
  used as the basis for wave diagnostics of impurity inclusions\, as well a
 s defects in quasi-one-dimensional quasi-periodic physical systems\, for e
 xample\, inhomogeneous low-dimensional crystal structures operating on the
  principle of a wave diode [2].\n\n[1] P.G. Kevrekidis. Non-linear waves i
 n lattices: Past\, present\, future. IMA J. Appl. Math. 2011.  V. 76 (3). 
 P. 389-423\; https://doi.org/10.1093/imamat/hxr015	\n[2] S. Kasap\, H. Rud
 a\, Y. Boucher. Cambridge Illustrated Handbook of Optoelectronics and Phot
 onics. - Cambridge\, 2009 . P. 352\n\nhttps://indico.bitp.kiev.ua/event/8/
 contributions/235/
LOCATION:Online meeting
URL:https://indico.bitp.kiev.ua/event/8/contributions/235/
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