Post-graduate theses
Current Record: 5043 of 6549
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| Identifier |
000410106 |
| Title |
Periodic lattices with flat bands |
| Alternative Title |
Περιοδικά πλέγματα με επίπεδες ζώνες |
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Author
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Χαβιάρας, Μιχάλης
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Thesis advisor
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Εφραιμίδης, Νικόλαος
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| Abstract |
In this work our aim is to describe analytically and show numerically what is the flat band of a photonic
laice consisted of waveguides. e differential equations that we shall see later are derived from the
Coupled Mode Equations which describe the variation of the amplitude of the electromagnetic field between
fiber cores or ”waveguides” as are called. e propagation of the electromagnetic fields are affected of the
neighbouring fields of the waveguides so we consider various laices of the waveguides and therefore
various differential equations which describes them.
Initially we provide basic concepts of travelling waves such as phase velocity, group velocity and dispersion
relation. Band and therefore the flat band, which is a specific type of band, is an extension of the
dispersion relation for periodic systems. Aer that we consider some laices 1d or 2d which have no flat
bands and we observe various excitations of the fields for each of them.
Later we examine the Kagome and the Lieb laice which possess flat bands and we see some excitations
of them. We examine the excitations of these laices considering interaction between only nearest
neighbours at the first time and at the next stage we consider interaction between nearest and next nearest
neighbours. At both of the laices the flat bands vanishing with the consideration of the next nearest
neighbours .
Finally we present an idea of how to construct flat band laices based on the corresponding paper which
is referred. We start from an initial (fundamental) system and we find the supported solution of this system.
Next we are extend the fundamental system in a specific way and we look for relations in order to remain
as solution to the extended system, the solution of the fundamental system in isolation. Aer that we
construct the full periodic laice which is constructed by extend infinitely many times the fundamental
system as previous.
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| Language |
English |
| Subject |
Coupled mode theory |
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Θεωρία συζευγμένων ρυθμών |
| Issue date |
2017-07-21 |
| Collection
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School/Department--School of Sciences and Engineering--Department of Mathematics and Applied Mathematics--Post-graduate theses
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Type of Work--Post-graduate theses
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| Permanent Link |
https://elocus.lib.uoc.gr//dlib/f/4/e/metadata-dlib-1500634368-303716-9903.tkl
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| Views |
518 |
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