Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Hyperbolas01:30

Hyperbolas

172
A hyperbola is a conic section produced when a double-napped cone is intersected by a plane at an angle steeper than the slope of the cone, such that it cuts through both nappes. This intersection yields two separate, mirror-image curves known as branches, which open away from each other along the transverse axis. The nearest points on each branch to the hyperbola’s center are termed vertices, and the distance from the center to a vertex is denoted by a. Perpendicular to the transverse...
172
Geometry of Hyperbolas01:30

Geometry of Hyperbolas

177
A hyperbola consists of all points where the absolute difference of distances to two fixed points, called foci, remains constant. The standard equation isEach branch extends infinitely and approaches two asymptotes, which guide the curve’s behavior. The parameters a and b define key features: a measures the distance from the center to each vertex along the transverse axis, while b influences the slopes of the asymptotes. The asymptotes have equationsA rectangle centered at the origin with...
177
Bewley Lattice Diagram01:12

Bewley Lattice Diagram

1.3K
The Bewley lattice diagram, developed by L. V. Bewley, effectively organizes the reflections occurring during transmission-line transients. It visually represents how voltage waves propagate and reflect within a transmission line, making it easier to understand the complex interactions that occur.
1.3K
Lattice Centering and Coordination Number02:33

Lattice Centering and Coordination Number

11.0K
The structure of a crystalline solid, whether a metal or not, is best described by considering its simplest repeating unit, which is referred to as its unit cell. The unit cell consists of lattice points that represent the locations of atoms or ions. The entire structure then consists of this unit cell repeating in three dimensions. The three different types of unit cells present in the cubic lattice are illustrated in Figure 1.
Types of Unit Cells
Imagine taking a large number of identical...
11.0K
Graphs of Polar Equations01:17

Graphs of Polar Equations

130
The polar coordinate system represents points using a distance from a central point (the pole) and an angle from a reference direction (the polar axis). Unlike rectangular coordinates, polar coordinates are ideal for graphing curves with radial symmetry or periodic behavior.Some general forms of graphs in polar coordinates include the following:Equation of a Circle (Centered at the Pole):A graph where the radius remains constant for all angles traces a circle centered at the pole:Equation of a...
130
Gauss's Law: Planar Symmetry01:27

Gauss's Law: Planar Symmetry

9.1K
A planar symmetry of charge density is obtained when charges are uniformly spread over a large flat surface. In planar symmetry, all points in a plane parallel to the plane of charge are identical with respect to the charges. Suppose the plane of the charge distribution is the xy-plane, and the electric field at a space point P with coordinates (x, y, z) is to be determined. Since the charge density is the same at all (x, y) - coordinates in the z = 0 plane, by symmetry, the electric field at P...
9.1K

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Fully Programmable Slow Light Based on a Spinor Representation of Generalized Coupled-Resonator-Induced Transparency.

Advanced science (Weinheim, Baden-Wurttemberg, Germany)·2026
Same author

Programmable Lattices for Non-Abelian Topological Photonics and Braiding.

Physical review letters·2026
Same author

Scalable unitary computing using time-parallelized photonic lattices.

Nanophotonics (Berlin, Germany)·2025
Same author

Multicolor nanoring arrays with uniform and decoupled scattering for augmented reality displays.

Nanophotonics (Berlin, Germany)·2025
Same author

CD8<sup>+</sup> T Cells Negatively Modulate Ischemia-Induced Angiogenesis in Mice.

FASEB journal : official publication of the Federation of American Societies for Experimental Biology·2025
Same author

Spontaneous Emission Decay and Excitation in Photonic Time Crystals.

Physical review letters·2025

Related Experiment Video

Updated: Dec 12, 2025

Using Microwave and Macroscopic Samples of Dielectric Solids to Study the Photonic Properties of Disordered Photonic Bandgap Materials
10:35

Using Microwave and Macroscopic Samples of Dielectric Solids to Study the Photonic Properties of Disordered Photonic Bandgap Materials

Published on: September 26, 2014

12.6K

Topological Hyperbolic Lattices.

Sunkyu Yu1, Xianji Piao1, Namkyoo Park1

  • 1Photonic Systems Laboratory, Department of Electrical and Computer Engineering, Seoul National University, Seoul 08826, Korea.

Physical Review Letters
|August 16, 2020
PubMed
Summary
This summary is machine-generated.

Researchers developed a Euclidean photonic platform mimicking hyperbolic lattices to explore topological states of matter. This work extends quantum spin Hall effect analogs to non-Euclidean geometry, revealing unique spectral-magnetic properties for topological immunity.

More Related Videos

Optimized Fabrication Procedure for High-Quality Graphene-based Moir&#233; Superlattice Devices
11:24

Optimized Fabrication Procedure for High-Quality Graphene-based Moiré Superlattice Devices

Published on: July 11, 2025

13.2K
Indirect Fabrication of Lattice Metals with Thin Sections Using Centrifugal Casting
08:32

Indirect Fabrication of Lattice Metals with Thin Sections Using Centrifugal Casting

Published on: May 14, 2016

12.8K

Related Experiment Videos

Last Updated: Dec 12, 2025

Using Microwave and Macroscopic Samples of Dielectric Solids to Study the Photonic Properties of Disordered Photonic Bandgap Materials
10:35

Using Microwave and Macroscopic Samples of Dielectric Solids to Study the Photonic Properties of Disordered Photonic Bandgap Materials

Published on: September 26, 2014

12.6K
Optimized Fabrication Procedure for High-Quality Graphene-based Moir&#233; Superlattice Devices
11:24

Optimized Fabrication Procedure for High-Quality Graphene-based Moiré Superlattice Devices

Published on: July 11, 2025

13.2K
Indirect Fabrication of Lattice Metals with Thin Sections Using Centrifugal Casting
08:32

Indirect Fabrication of Lattice Metals with Thin Sections Using Centrifugal Casting

Published on: May 14, 2016

12.8K

Area of Science:

  • Physics
  • Mathematics
  • Materials Science

Background:

  • Non-Euclidean geometry, particularly hyperbolic geometry, is crucial for describing diverse phenomena from relativity to network infrastructures.
  • Hyperbolic lattices are theoretical extensions of Euclidean Bravais lattices, promising new wave phenomena.
  • Topological states of matter in hyperbolic lattices remain largely unexplored.

Purpose of the Study:

  • Investigate topological phenomena in hyperbolic geometry.
  • Explore the influence of quantized curvature and edge effects on topological phases.
  • Develop a platform to realize non-Euclidean topological states.

Main Methods:

  • Constructed a Euclidean photonic platform simulating hyperbolic lattice properties.
  • Applied a uniform, pseudospin-dependent magnetic field.
  • Analyzed topological band properties and helical edge states.

Main Results:

  • Achieved a non-Euclidean analog of the quantum spin Hall effect.
  • Demonstrated topological protection of edge states in hyperbolic lattices with varying curvatures.
  • Generalized Hofstadter's butterfly using parameters for edge confinement and defect immunity.
  • Observed unique spectral-magnetic sensitivity in topological immunity.

Conclusions:

  • The proposed Euclidean platform effectively inherits topological band properties from hyperbolic lattices.
  • This approach enables the study of topological phenomena in non-Euclidean geometries.
  • The findings open avenues for exploiting infinite lattice degrees of freedom in band theory and designing novel topological materials.