Related Experiment Video
Updated: Jul 18, 2026

08:41
Ultrasound Velocity Measurement in a Liquid Metal Electrode
Published on: August 5, 2015
X-wave bullets with negative group velocity in vacuum.
Carlos J Zapata-Rodríguez1, Miguel A Porras
1Departamento de Optica, Universidad de Valencia, Burjassot, Spain. carlos.zapata@uv.es
Optics Letters
|November 14, 2006
Summary
Researchers report on X-waves, a type of optical signal that travels without spreading and moves backward in time. Beam aperturing was used to study signal causality and forerunner formation.
Area of Science:
- Optics and Photonics
- Wave Phenomena
Background:
- Optical signals typically spread out during propagation.
- Understanding wave propagation is crucial for optical communication and imaging.
Purpose of the Study:
- To report on the generation and analysis of X-waves with negative group velocity.
- To investigate the causality and forerunner formation in these unique optical signals.
Main Methods:
- Generation of propagation-invariant X-waves.
- Utilizing beam aperturing for detailed analysis.
- Investigating optical signal causality.
Main Results:
- Successfully generated X-waves exhibiting negative group velocity.
- Demonstrated that beam aperturing enables comprehensive analysis of signal causality.
- Observed and analyzed forerunner formation in relation to X-wave propagation.
Conclusions:
- X-waves with negative group velocity can be generated and analyzed.
- Beam aperturing is an effective technique for studying causality and forerunners in optical signals.
- The findings contribute to the understanding of non-spreading wave propagation and causality in optics.
Related Concept Videos
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...
The EM field is assumed to be a...
Conservation of Momentum: Problem Solving
Solving problems using the conservation of momentum requires four basic steps:
Electromagnetic Waves in Matter
Electromagnetic waves can travel in the vacuum as well as in matter. For example light, which is an electromagnetic wave, can travel through air, water, or glass.
Consider the electromagnetic wave passing through a dielectric medium. In such a case, Maxwell's equations get modified. In Ampere's law, ε0 , the dielectric permittivity of free space is replaced with ε, the permittivity of dielectric. Also, the vacuum permeability μ0 is replaced by the permeability of the medium, μ.
Furthermore, the...
Consider the electromagnetic wave passing through a dielectric medium. In such a case, Maxwell's equations get modified. In Ampere's law, ε0 , the dielectric permittivity of free space is replaced with ε, the permittivity of dielectric. Also, the vacuum permeability μ0 is replaced by the permeability of the medium, μ.
Furthermore, the...
The de Broglie Wavelength
In the macroscopic world, objects that are large enough to be seen by the naked eye follow the rules of classical physics. A billiard ball moving on a table will behave like a particle; it will continue traveling in a straight line unless it collides with another ball, or it is acted on by some other force, such as friction. The ball has a well-defined position and velocity or well-defined momentum, p = mv, which is defined by mass m and velocity v at any given moment. This is the typical...
The Uncertainty Principle
Werner Heisenberg considered the limits of how accurately one can measure properties of an electron or other microscopic particles. He determined that there is a fundamental limit to how accurately one can measure both a particle’s position and its momentum simultaneously. The more accurate the measurement of the momentum of a particle is known, the less accurate the position at that time is known and vice versa. This is what is now called the Heisenberg uncertainty principle. He mathematically...
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...
The velocity of the particles can be obtained by taking the partial derivative of the position equation with respect to time. We can...

