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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...
Velocity and Acceleration of a Wave00:51

Velocity and Acceleration of a Wave

A wave propagates through a medium with a constant speed, known as a wave velocity. It is different from the speed of the particles of the medium, which is not constant. In addition, the velocity of the medium is perpendicular to the velocity of the wave. The variable speed of the particles of the medium implies that there must be acceleration associated with it. 
The velocity of the particles can be obtained by taking the partial derivative of the position equation with respect to time. We can...
Graphing the Wave Function01:13

Graphing the Wave Function

Consider the wave equation for a sinusoidal wave moving in the positive x-direction. The wave equation is a function of both position and time. From the wave equation, two different graphs can be plotted.
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.
However, although electric and magnetic fields were first introduced as mathematical constructs to simplify the description of mutual forces between charges, a natural question emerges from Maxwell's equations: What...
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.
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...

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Related Experiment Video

Updated: Jun 14, 2026

Measurements of Waves in a Wind-wave Tank Under Steady and Time-varying Wind Forcing
08:54

Measurements of Waves in a Wind-wave Tank Under Steady and Time-varying Wind Forcing

Published on: February 13, 2018

Vector wave propagation method.

M Fertig1, K-H Brenner

  • 1ZITI, University of Heidelberg, B6, 23-29, 68131 Mannheim, Germany. matthias.fertig@ziti.uni-heidelberg.de

Journal of the Optical Society of America. A, Optics, Image Science, and Vision
|April 3, 2010
PubMed
Summary
This summary is machine-generated.

This study extends the scalar wave propagation method (WPM) to vector fields (VWPMs), enabling accurate optical simulations for elements like prisms and gratings. The new method offers significant runtime advantages for complex 3D optical problems.

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Continuous-Wave Propagation Channel-Sounding Measurement System - Testing, Verification, and Measurements
09:36

Continuous-Wave Propagation Channel-Sounding Measurement System - Testing, Verification, and Measurements

Published on: June 25, 2021

Related Experiment Videos

Last Updated: Jun 14, 2026

Measurements of Waves in a Wind-wave Tank Under Steady and Time-varying Wind Forcing
08:54

Measurements of Waves in a Wind-wave Tank Under Steady and Time-varying Wind Forcing

Published on: February 13, 2018

Continuous-Wave Propagation Channel-Sounding Measurement System - Testing, Verification, and Measurements
09:36

Continuous-Wave Propagation Channel-Sounding Measurement System - Testing, Verification, and Measurements

Published on: June 25, 2021

Area of Science:

  • Optics and Photonics
  • Computational Electromagnetics

Background:

  • The scalar wave propagation method (WPM) overcomes limitations of the beam propagation method (BPM) for optical simulations.
  • WPM is effective for waveguides, lenses, prisms, and gratings, handling large angles and index variations.

Purpose of the Study:

  • Extend the scalar WPM to handle three-dimensional (3D) vectorial fields (VWPMs).
  • Incorporate polarization-dependent Fresnel coefficients for accurate field transmission.
  • Maintain electric field continuity in all three dimensions.

Main Methods:

  • Developed a vectorial wave propagation method (VWPM).
  • Utilized polarization-dependent Fresnel coefficients for transmission.
  • Employed an enhanced propagation vector and transfer matrix for field continuity.

Main Results:

  • Validated the VWPM by simulating transmission through a prism and comparing with vectorial Debye theory.
  • Verified the method by simulating a 2D grating against 3D rigorous coupled-wave analysis (RCWA).
  • Demonstrated significant runtime advantages of VWPM over RCWA for 3D problems.

Conclusions:

  • The developed VWPM accurately simulates vectorial optical fields.
  • VWPM provides a computationally efficient alternative to RCWA for 3D optical simulations.
  • This method enhances the simulation capabilities for complex optical elements and systems.