View source for X-wave

{{Short description|Stable type of wave in physics}}
{{distinguish|X-ray|X-band}}
{{Technical|date=May 2020}}
In [[physics]], '''X-waves''' are a type of wave [[Superposition principle|superposition]] (or wavepacket) exhibiting a distinctive double-cone structure with its axis aligned along the propagation direction.  The energy of the wave is concentrated along the vertex of this double cone, creating an "X" shape when intersected by a plane containing the propagation axis. These structures are also known as [[conical waves]]. X-waves possess several remarkable properties: 
# Weak Localization: They are weakly [[localized solution]]s of the wave equation, meaning they are extended both spatially and temporally.
# Propagation Invariance: Under specific conditions, they maintain their shape during propagation, resisting the effects of [[diffraction]] and [[dispersion relation|dispersion]]. This occurs when dispersion precisely balances diffraction, preventing the wavepacket from spreading.
X-waves can manifest as [[sound wave|sound]], [[electromagnetic wave|electromagnetic]], or [[gravitational wave]]s. 

X-waves generalize the concept of diffraction-free solutions, exemplified by [[monochromatic]] Bessel beams, to include wavepackets composed of multiple frequency components. To achieve propagation invariance, each frequency component must have the same velocity along the propagation axis. Therefore, an X-wave can be constructed as a non-monochromatic [[Superposition principle|superposition]] of [[Bessel beam]]s.

Like ideal Bessel beams, ideal X-waves are mathematical constructs possessing [[Infinity#Physics|infinite]] [[energy]]. However, finite-energy approximations have been experimentally observed in various physical contexts. X-wave pulses can exhibit superluminal [[phase velocity|phase]] and [[group velocity]].<ref>{{cite journal |title=Measurement of the spatiotemporal electric field of ultrashort superluminal Bessel-X pulses |first1=Pamela |last1=Bowlan |first2=Heli |last2=Valtna-Lukner |display-authors=etal |journal=Optics and Photonics News |page=42 |volume=20 |issue=12 |date=December 2009|doi=10.1364/OPN.20.12.000042 }}</ref> Furthermore, X-wave solutions have been reported within a quantum mechanical framework in optics.<ref>A. Ciattoni and C. Conti, [https://arxiv.org/abs/0704.0442v1 Quantum electromagnetic X-waves] ''arxiv.org'' 0704.0442v1.</ref> 

== See also ==
* [[Nonlinear X-wave]]
* [[Droplet-shaped wave]]

== References==
<references/>
* J. Lu and J. F. Greenleaf, "Nondiffracting X waves: exact solutions to free-space [[scalar wave]] equation and their infinite realizations", [[IEEE]] Trans. Ultrasonic Ferroelectric Frequency. ''[[Control (journal)|Control]]'' 39, 19–31 (1992).
* Erasmo Recami and Michel Zamboni-Rached and Hugo E. Hernandez-Figueroa, "[https://arxiv.org/abs/0708.1655 Localized waves: A scientific and historical introduction]" ''arxiv.org'' 0708.1655v2.
* Various authors in the book [https://www.amazon.com/dp/0470108851 Localized Waves] edited by Erasmo Recami, Michel Zamboni-Rached and Hugo E. Hernandez-Figueroa

==External links ==
* [http://mother.dipscfm.uninsubria.it/vinoteam/ The Virtual Institute for Nonlinear Optics (VINO)], a research collaboration devoted to the investigation of X-waves and conical waves in general
* [https://web.archive.org/web/20080415011632/http://nlo.phys.uniroma1.it/nonlinear_and_quantum_x.htm Nolinear X-waves] page at the [https://web.archive.org/web/20080414093751/http://nlo.phys.uniroma1.it/ nlo.phys.uniroma1.it] website.

[[Category:Wave mechanics]]


{{classicalmechanics-stub}}