Related Experiment Video
Updated: Aug 6, 2026
08:54
Measurements of Waves in a Wind-wave Tank Under Steady and Time-varying Wind Forcing
Published on: February 13, 2018
Wake-tail effects in two-dimensional wave refocusing
1National Technical University of Athens, School of Electrical and Computer Engineering, Athens GR-15780, Greece.
Physical Review. E
|July 24, 2026
Summary
Wave propagation in two dimensions violates Huygens' principle, creating a wake tail that hinders perfect refocusing. Both spatial and temporal mirrors fail to achieve ideal wave concentration due to this intrinsic tail structure.
Area of Science:
- Physics
- Wave phenomena
- Acoustics and optics
Background:
- Wave propagation in even spatial dimensions deviates from Huygens' principle.
- This deviation results in a persistent wake tail, complicating wave focusing.
- The wake tail poses challenges for achieving sharply localized propagating fronts.
Purpose of the Study:
- To investigate the impact of the wake-tail structure on wave refocusing in two dimensions.
- To analyze the effectiveness of spatial and temporal mirrors in concentrating waves.
- To understand the fundamental limitations on perfect wave refocusing in 2D.
Main Methods:
- Analysis of the two-dimensional wave equation with a localized source.
- Modeling of wave propagation and reflection using a spatial mirror.
- Modeling of wave propagation and reflection using a time mirror with phase velocity modulation.
Main Results:
- Spatial mirroring broadens the reflected signal, with the wake tail maintaining causal order.
- Temporal mirroring introduces an anticausal wake tail response but still results in pulse distortion.
- Both methods show persistent wake-tail contributions and secondary radiation at the refocus point.
Conclusions:
- The wake-tail structure inherent in 2D wave propagation fundamentally limits perfect refocusing.
- Huygens' principle is intrinsically linked to wave concentration capabilities.
- Idealized concentration strategies are insufficient to overcome the limitations imposed by the 2D wave equation's wake tail.
Related Concept Videos
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...
01:05Doppler Effect - II
The Doppler effect has several practical, real-world applications. For instance, meteorologists use Doppler radars to interpret weather events based on the Doppler effect. Typically, a transmitter emits radio waves at a specific frequency toward the sky from a weather station. The radio waves bounce off the clouds and precipitation and travel back to the weather station. The radio frequency of the waves reflected back to the station appears to decrease if the clouds or precipitation are moving...
00:53Sound Waves: Interference
Sound waves can be modeled either as longitudinal waves, wherein the molecules of the medium oscillate around an equilibrium position, or as pressure waves. When two identical waves from the same source superimpose on each other, the combination of two crests or two troughs results in amplitude reinforcement known as constructive interference. If two identical waves, that are initially in phase, become out of phase because of different path lengths, the combination of crests with troughs...
01:17Standing Waves
Sometimes waves do not seem to move; rather, they just vibrate in place. Unmoving waves can be seen on the surface of a glass of milk kept in a refrigerator, which is one example of standing waves. Vibrations from the refrigerator motor create waves on the milk that oscillate up and down but do not seem to move across the surface. These waves are formed or created by the superposition of two or more identical moving waves in opposite directions. The waves move through each other, with their...
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.
01:07Effective Value of a Periodic Waveform
The concept of effective value, the root mean square (RMS) value, is crucial in understanding electrical circuits and power delivery. This idea emerges from the necessity to measure the effectiveness of a voltage or current source in supplying power to a resistive load.
The effective value of a periodic current represents the direct current (DC) that conveys the same average power to a resistor as the periodic current itself. This concept is crucial when assessing AC circuits. To determine the...
The effective value of a periodic current represents the direct current (DC) that conveys the same average power to a resistor as the periodic current itself. This concept is crucial when assessing AC circuits. To determine the...