Related Experiment Video
Updated: May 24, 2026
11:08
Fabrication And Characterization Of Photonic Crystal Slow Light Waveguides And Cavities
Published on: November 30, 2012
Propagation of guided waves through weak penetrable scatterers
Agnès Maurel1, Jean-François Mercier
1Institut Langevin/LOA, UMR 7587, CNRS-ESPCI, 10 rue Vauquelin, 75231 Paris Cedex 05, France. agnes.maurel@espci.fr
The Journal of the Acoustical Society of America
|March 20, 2012
Summary
This study analyzes wave scattering in waveguides with penetrable scatterers using the Born approximation. Analytical results for transmission and reflection coefficients are derived and validated against numerical simulations.
Area of Science:
- Acoustics and Wave Propagation
- Electromagnetism
- Fluid Dynamics
Background:
- Wave propagation in confined geometries is crucial for various physical phenomena.
- Understanding scattering from inclusions is key to characterizing complex media.
- Penetrable scatterers with varying density and wavespeed present a complex wave interaction scenario.
Purpose of the Study:
- To investigate scalar wave scattering in a waveguide with weak penetrable scatterers.
- To derive analytical expressions for transmission and reflection coefficients.
- To compare analytical findings with numerical simulations and existing low-frequency results.
Main Methods:
- Application of the Born approximation for weak scatterers.
- Derivation of analytical expressions for transmission and reflection coefficients.
- Numerical simulations for validation and comparison.
Main Results:
- Analytical expressions for transmission and reflection coefficients were successfully derived for small inclusions.
- Results showed good agreement between analytical predictions and numerical simulations.
- The study analyzed periodic and random scatterer distributions, comparing them to unbounded propagation.
Conclusions:
- The Born approximation provides accurate predictions for wave scattering in waveguides with weak penetrable scatterers.
- Analytical methods are effective for characterizing wave behavior in such complex systems.
- This work offers a foundation for understanding wave phenomena in various physical contexts, including acoustics and electromagnetism.
Related Concept Videos
01:07Propagation 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...
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...
01:30Propagation Speed of Electromagnetic Waves
Electromagnetic waves are consistent with Ampere's law. Assuming there is no conduction current Ampere's law is given as:
02:18Interference 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.
01:28Standing Waves in a Cavity
A household microwave and lasers are examples of standing electromagnetic waves in a cavity. When two conducting metal plates are placed parallel at the nodal planes, it creates a cavity where standing waves are formed. The cavity between the two planes is analogous to a stretched string held at the points x = 0 and x = L. Here, the distance 'L' between the two planes must be an integer multiple of half of the wavelength. The wavelengths that satisfy this condition are given by:
01:07Reflection 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...
01:04Travelling Waves
A wave is a disturbance that propagates from its source, repeating itself periodically, and is typically associated with simple harmonic motion. Mechanical waves are governed by Newton's laws and require a medium to travel. A medium is a substance in which a mechanical wave propagates, and the medium produces an elastic restoring force when it is deformed.
Water waves, sound waves, and seismic waves are some examples of mechanical waves. For water waves, the wave propagation medium is water;...
Water waves, sound waves, and seismic waves are some examples of mechanical waves. For water waves, the wave propagation medium is water;...