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Related Concept Videos

Propagation of Waves01:07

Propagation of Waves

When a wave propagates from one medium to another, part of it may get reflected in the first medium, and part of it may get transmitted to the second medium. In such a case, the interface of the two mediums can be considered as a boundary that is neither fixed nor free.
Consider a scenario where a wave propagates from a string of low linear mass density to a string of high linear mass density. In such a case, the reflected wave is out of phase with respect to the incident wave, however the...
Interference and Diffraction02:18

Interference and Diffraction

Interference is a characteristic phenomenon exhibited by waves. When two electromagnetic waves interact with their peaks and troughs coinciding, a resulting wave with enhanced amplitude is produced. This is known as constructive interference. In this case, the two waves interacting are in phase with each other.
Reflection of Waves01:07

Reflection of Waves

When a wave travels from one medium to another, it gets reflected at the boundary of the second medium. A common example of this is when a person yells at a distance from a cliff and hears the echo of their voice. The sound waves (longitudinal waves) traveling in the air are reflected from the bounding cliff. Similarly, flipping one end of a string whose other end is tied to a wall causes a pulse (transverse wave) to travel through the string, which gets reflected upon reaching the wall. In...
Plane Electromagnetic Waves I01:30

Plane Electromagnetic Waves I

The existence of combined electric and magnetic fields that propagate through space as electromagnetic (EM) waves is the most significant prediction of Maxwell's equations. As Maxwell's equations hold in free space, the predicted electromagnetic waves do not require a medium for their propagation. An EM wave comprises an electric field, defined as the force per charge on a stationary charge, and a magnetic field, which is the force per charge on a moving charge.
The EM field is assumed to be a...
Equations of Wave Motion01:02

Equations of Wave Motion

Mathematically, the motion of a wave can be studied using a wavefunction. Consider a string oscillating up and down in simple harmonic motion, having a period T. The wave on the string is sinusoidal and is translated in the positive x-direction as time progresses. Sine is a function of the angle θ, oscillating between +A and −A and repeating every 2π radians. To construct a wave model, the ratio of the angle θ and the position x is considered.
Electromagnetic Wave Equation01:24

Electromagnetic Wave Equation

Maxwell's equations for electromagnetic fields are related to source charges, either static or moving. These fields act on a test charge, whose trajectory can thus be determined using suitable boundary conditions. The objective of electromagnetism is thus theoretically complete.
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Updated: Jun 22, 2026

Evanescent Field Based Photoacoustics: Optical Property Evaluation at Surfaces
10:21

Evanescent Field Based Photoacoustics: Optical Property Evaluation at Surfaces

Published on: July 26, 2016

Generalized optical theorem for surface waves and layered media.

David Halliday1, Andrew Curtis

  • 1School of GeoSciences, Grant Institute, University of Edinburgh, Kings Buildings, West Mains Road, Edinburgh EH93JW, United Kingdom.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|June 13, 2009
PubMed
Summary
This summary is machine-generated.

A generalized optical theorem for surface waves is introduced, applicable to body waves as well. This extends the theorem

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Interfacial Molecular-level Structures of Polymers and Biomacromolecules Revealed via Sum Frequency Generation Vibrational Spectroscopy
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Interfacial Molecular-level Structures of Polymers and Biomacromolecules Revealed via Sum Frequency Generation Vibrational Spectroscopy

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Last Updated: Jun 22, 2026

Evanescent Field Based Photoacoustics: Optical Property Evaluation at Surfaces
10:21

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Published on: July 26, 2016

Interfacial Molecular-level Structures of Polymers and Biomacromolecules Revealed via Sum Frequency Generation Vibrational Spectroscopy
09:43

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Area of Science:

  • Seismology
  • Wave Propagation

Background:

  • The optical theorem is a fundamental principle in wave physics, typically applied to scattering phenomena in homogeneous media.
  • Existing formulations of the optical theorem are limited in their applicability to complex wave propagation scenarios.

Purpose of the Study:

  • To generalize the optical theorem to accommodate surface wave propagation.
  • To extend the applicability of the optical theorem to layered elastic media, including both body and surface waves.

Main Methods:

  • Development of a generalized mathematical framework for the optical theorem.
  • Demonstration of its application to surface-wave modal summations.
  • Extension to encompass body wave phenomena under specific conditions.

Main Results:

  • A novel generalized optical theorem for surface waves has been derived.
  • The theorem's applicability is shown to extend to body waves when represented by surface-wave modal summations.
  • The generalized theorem is validated for layered elastic media.

Conclusions:

  • The generalized optical theorem significantly broadens the scope of wave propagation analysis in complex media.
  • This provides a more unified approach to understanding wave interactions in layered elastic environments.