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Related Concept Videos

Hyperbolic and Inverse Hyperbolic Functions: Problem Solving01:30

Hyperbolic and Inverse Hyperbolic Functions: Problem Solving

An arched gate can be effectively modeled using a hyperbolic cosine profile because this type of function is smooth and symmetric about the vertical axis. When the arch is centered at the origin, its maximum height occurs at the center point. This symmetry ensures that any height below the crown of the arch is reached at two horizontal positions that are equal in distance from the centerline but lie on opposite sides.To determine where the gate reaches a height of five meters, the height of the...
Geometry of Hyperbolas01:30

Geometry of Hyperbolas

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...
Hyperbolas01:30

Hyperbolas

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 axis is...
Hyperbolic Functions01:26

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A flexible cable suspended between two points at the same height naturally forms a curve known as a catenary. This shape results from the balance between the cable’s weight and the tension acting along its length, representing a state of mechanical equilibrium. Unlike simpler approximations, the true shape of a hanging cable is described using hyperbolic functions.Hyperbolic functions are closely related to exponential functions and are named for their connection to the geometry of the...
Prismatic Beams: Problem Solving01:15

Prismatic Beams: Problem Solving

In the design of a supported timber beam subjected to a distributed load, both the beam's physical dimensions and the timber's characteristics, such as its grade and species, are critical. These factors determine the allowable stress values, which are crucial for calculating the necessary beam depth to ensure structural integrity and safety.
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A parabola is a basic type of conic section that results from the intersection of a plane with a double-napped cone in a direction parallel to one of the cone's sides. This U-shaped curve has a distinctive reflective property: all incoming rays parallel to its axis of symmetry are directed toward a single point, known as the focus. This property is widely utilized in optical and communication technologies that require precise signal concentration.In analytic geometry, a parabola is defined as...

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Simulation, Fabrication and Characterization of THz Metamaterial Absorbers
13:44

Simulation, Fabrication and Characterization of THz Metamaterial Absorbers

Published on: December 27, 2012

Focus issue: hyperbolic metamaterials.

Mikhail Noginov1, Mikhail Lapine, Viktor Podolskiy

  • 1Department of Physics, Norfolk State University, Norfolk, VA, USA.

Optics Express
|June 22, 2013
PubMed
Summary
This summary is machine-generated.

This special issue covers recent advancements in the optics of hyperbolic metamaterials. These engineered materials offer unique light-manipulating properties for future optical technologies.

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Area of Science:

  • Optics
  • Materials Science
  • Nanotechnology

Background:

  • Hyperbolic metamaterials exhibit unique optical properties due to their anisotropic permittivity.
  • Recent research focuses on novel designs and fabrication techniques for these advanced materials.

Discussion:

  • The special issue highlights key developments in the theoretical and experimental understanding of hyperbolic metamaterials.
  • Applications span subwavelength imaging, enhanced light emission, and novel optical devices.

Key Insights:

  • Progress in controlling light-matter interactions at the nanoscale.
  • Demonstration of unprecedented optical phenomena enabled by hyperbolic dispersion.

Outlook:

  • Future research directions include exploring new material compositions and expanding device functionalities.
  • Potential for transformative impact on integrated photonics and optical sensing.