A taste of photonics: band structure, null gaps, non-Bragg gaps, and symmetry properties of one-dimensional superlattices

2007 ◽  
Author(s):  
L. E. Oliveira ◽  
S. B. Cavalcanti ◽  
E. Reyes-Gómez
Keyword(s):  
Band Structure ◽  
One Dimensional ◽  
Symmetry Properties

Bloch wave degeneracies in systematic high energy electron diffraction

1976 ◽  
Vol 282 (1308) ◽  
pp. 485-525 ◽  
Keyword(s):  
Band Structure ◽  
Incident Beam ◽  
High Energy ◽  
Real Space ◽  
Bloch Wave ◽  
Critical Voltage ◽  
Bloch Waves ◽  
One Dimensional ◽  
Symmetry Properties ◽  
Reflexion Coefficient

For the systematic diffraction of high energy electrons by a thin crystalline slab, we study the accidental degeneracies of the Bloch waves excited in the specimen by the incident beam. It is shown that these Bloch waves are the eigenstates of a one dimensional band structure problem, and this is solved by wave matching methods. For a symmetric potential, the symmetry properties of the Bloch waves are discussed, and it is shown how accidental degeneracies of these waves can occur when the reflexion coefficient for waves incident on one unit cell of the one dimensional periodic potential vanishes. The form of the band structure and the Bloch waves in the neighbourhood of a degeneracy are derived by expanding the Kramers function in a Taylor series. It is then shown analytically how the degeneracy affects the diffracted waves emerging from the crystalline specimen (in particular, the Kikuchi pattern). To understand these effects fully, W. K. B. approximations for the Bloch waves are used to derive the Bloch wave excitations and the absorption coefficients. However, to predict the degeneracies themselves, it is shown that a different formula for the reflexion coefficient, due to Landauer, must be used. This formula shows how the critical voltage at which the Bloch waves degenerate depends on the form of the potential, and allows quick, accurate, computations of the critical voltages to be made. Also, a new higher order degeneracy is predicted for some of the systematic potentials of cadmium, lead and gold. Finally, to infer the potential in real space from measurements of critical voltages and several other quantities, we suggest an inversion scheme based on the Landauer formula for the reflexion coefficient. To a close approximation this potential is proportional to V 2 of the crystal charge density.

Quantum Boxes, Stringed Instruments

2017 ◽  
Author(s):  
Frank S. Levin
Keyword(s):  
Energy Level ◽  
Schrödinger Equation ◽  
Quantum System ◽  
Schrodinger Equation ◽  
Probability Distributions ◽  
Wave Functions ◽  
Energy Level Diagram ◽  
One Dimensional ◽  
Stringed Instruments ◽  
Symmetry Properties

Chapter 7 illustrates the results obtained by applying the Schrödinger equation to a simple pedagogical quantum system, the particle in a one-dimensional box. The wave functions are seen to be sine waves; their wavelengths are evaluated and used to calculate the quantized energies via the de Broglie relation. An energy-level diagram of some of the energies is constructed; on it are illustrations of the corresponding wave functions and probability distributions. The wave functions are seen to be either symmetric or antisymmetric about the midpoint of the line representing the box, thereby providing a lead-in to the later exploration of certain symmetry properties of multi-electron atoms. It is next pointed out that the Schrödinger equation for this system is identical to Newton’s equation describing the vibrations of a stretched musical string. The different meaning of the two solutions is discussed, as is the concept and structure of linear superpositions of them.

scholarly journals Band structure, phase transitions, and semiconductor analogs in one-dimensional solid light systems

2009 ◽  
Vol 80 (6) ◽  
Author(s):  
James Quach ◽  
Melissa I. Makin ◽  
Chun-Hsu Su ◽  
Andrew D. Greentree ◽  
Lloyd C. L. Hollenberg
Keyword(s):  
Phase Transitions ◽  
Band Structure ◽  
One Dimensional ◽  
Structure Phase

Robust One-Dimensional Metallic Band Structure of Silicide Nanowires

2005 ◽  
Vol 95 (20) ◽  
Author(s):  
H. W. Yeom ◽  
Y. K. Kim ◽  
E. Y. Lee ◽  
K.-D. Ryang ◽  
P. G. Kang
Keyword(s):  
Band Structure ◽  
One Dimensional

Peculiarities of band structure of one-dimensional photonic crystals

Optik ◽  
2019 ◽  
Vol 180 ◽  
pp. 745-753 ◽  
Author(s):  
A.H. Gevorgyan ◽  
H. Gharagulyan ◽  
S.A. Mkhitaryan
Keyword(s):  
Photonic Crystals ◽  
Band Structure ◽  
One Dimensional

One-dimensional photonic crystals of inhomogeneous thin films: band structure of rugate filters

2005 ◽  
Vol 244 (1-6) ◽  
pp. 259-267 ◽  
Author(s):  
F. Aguayo-Ríos ◽  
F. Villa-Villa ◽  
J.A. Gaspar-Armenta
Keyword(s):  
Thin Films ◽  
Photonic Crystals ◽  
Band Structure ◽  
One Dimensional

The band structure of the quasi-one-dimensional layered semiconductor TiS3(001)

2018 ◽  
Vol 112 (5) ◽  
pp. 052102 ◽  
Author(s):  
Hemian Yi ◽  
Takashi Komesu ◽  
Simeon Gilbert ◽  
Guanhua Hao ◽  
Andrew J. Yost ◽  
...  
Keyword(s):  
Band Structure ◽  
Layered Semiconductor ◽  
One Dimensional

Bifurcations, symmetries and the notion of fixed subspace

2021 ◽  
pp. 2130006
Author(s):  
Giampaolo Cicogna
Keyword(s):  
Topological Index ◽  
Ad Hoc ◽  
Index Theory ◽  
Typical Case ◽  
One Dimensional ◽  
Dimension Formula ◽  
Symmetry Properties ◽  
Equivariant Bifurcation ◽  
Stationary Bifurcation ◽  
Bifurcation Problems

In the context of stationary bifurcation problems admitting a symmetry, this paper is focused on the key notion of Fixed Subspace (FS), and provides a review of some applications aimed at detecting bifurcating solutions in various situations. We start recalling, in its commonly used simplified version, the old Equivariant Bifurcation Lemma (EBL), where the FS is one-dimensional; then we provide a first generalization in a typical case of non-semisimple critical eigenvalues, where the presence of the symmetry produces a non-trivial situation. Next, we consider the case of FSs of dimension [Formula: see text] in very different contexts. First, relying on the topological index theory and in particular on the Krasnosel’skii theorem, we provide a largely applicable statement of an extension of the EBL. Second, we propose a completely different and new application which combines symmetry properties with the notion of stability of bifurcating solutions. We also provide some simple examples, constructed ad hoc to illustrate the various situations.

Band structure of a one-dimensional bilayer magnonic crystal

2019 ◽  
Vol 100 (14) ◽  
Author(s):  
P. Alvarado-Seguel ◽  
R. A. Gallardo
Keyword(s):  
Band Structure ◽  
One Dimensional ◽  
Magnonic Crystal
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