physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which r ...

, X-waves are localized solutions of the

wave equation The (two-way) wave equation is a second-order linear partial differential equation for the description of waves or standing wave fields — as they occur in classical physics — such as mechanical waves (e.g. water waves, sound waves and s ...

that travel at a constant

velocity Velocity is the directional speed of an object in motion as an indication of its rate of change in position as observed from a particular frame of reference and as measured by a particular standard of time (e.g. northbound). Velocity is a ...

in a given direction. X-waves can be

sound In physics, sound is a vibration that propagates as an acoustic wave, through a transmission medium such as a gas, liquid or solid. In human physiology and psychology, sound is the ''reception'' of such waves and their ''perception'' by the ...

electromagnetic In physics, electromagnetism is an interaction that occurs between particles with electric charge. It is the second-strongest of the four fundamental interactions, after the strong force, and it is the dominant force in the interactions of a ...

, or

gravitational wave Gravitational waves are waves of the intensity of gravity generated by the accelerated masses of an orbital binary system that propagate as waves outward from their source at the speed of light. They were first proposed by Oliver Heaviside in 1 ...

s. They are built as a non-

monochromatic A monochrome or monochromatic image, object or color scheme, palette is composed of one color (or lightness, values of one color). Images using only Tint, shade and tone, shades of grey are called grayscale (typically digital) or Black and wh ...

superposition of

Bessel beam A Bessel beam is a wave whose amplitude is described by a Bessel function of the first kind. Electromagnetic, acoustic, gravitational, and matter waves can all be in the form of Bessel beams. A true Bessel beam is non-diffractive. This means ...

s. Ideal X-waves carry

infinite Infinite may refer to: Mathematics *Infinite set, a set that is not a finite set *Infinity, an abstract concept describing something without any limit Music * Infinite (group), a South Korean boy band *''Infinite'' (EP), debut EP of American m ...

energy In physics, energy (from Ancient Greek: ἐνέργεια, ''enérgeia'', “activity”) is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of heat a ...

, but finite-energy realizations have been observed in various frameworks. Electromagnetic X-waves travel

faster than the speed of light Faster-than-light (also FTL, superluminal or supercausal) Superluminal motion, travel and Faster-than-light communication, communication are the conjectural propagation of matter or information faster than the speed of light (). The special theor ...

, and X-wave pulses can have superluminal

phase Phase or phases may refer to: Science *State of matter, or phase, one of the distinct forms in which matter can exist *Phase (matter), a region of space throughout which all physical properties are essentially uniform * Phase space, a mathematic ...

and

group velocity The group velocity of a wave is the velocity with which the overall envelope shape of the wave's amplitudes—known as the ''modulation'' or ''envelope'' of the wave—propagates through space. For example, if a stone is thrown into the middl ...

. In optics, X-waves solution have been reported within a quantum mechanical formulation.A. Ciattoni and C. Conti
Quantum electromagnetic X-waves
''arxiv.org'' 0704.0442v1.

References

* J. Lu and J. F. Greenleaf, "Nondiffracting X waves: exact solutions to free-space

scalar wave In mathematics and physics, a scalar field is a function associating a single number to every point in a space – possibly physical space. The scalar may either be a pure mathematical number (dimensionless) or a scalar physical quantity (wi ...

equation and their infinite realizations",

IEEE The Institute of Electrical and Electronics Engineers (IEEE) is a 501(c)(3) professional association for electronic engineering and electrical engineering (and associated disciplines) with its corporate office in New York City and its operation ...

Trans. Ultrasonic Ferroelectric Frequency. ''

Control Control may refer to: Basic meanings Economics and business * Control (management), an element of management * Control, an element of management accounting * Comptroller (or controller), a senior financial officer in an organization * Controlling ...

'' 39, 19–31 (1992). * Erasmo Recami and Michel Zamboni-Rached and Hugo E. Hernandez-Figueroa,
Localized waves: A scientific and historical introduction
''arxiv.org'' 0708.1655v2. * Various authors in the boo
Localized Waves
edited by Erasmo Recami, Michel Zamboni-Rached and Hugo E. Hernandez-Figueroa

External links

The Virtual Institute for Nonlinear Optics (VINO)
a research collaboration devoted to the investigation of X-waves and conical waves in general

page at th
nlo.phys.uniroma1.it
website. Wave mechanics {{classicalmechanics-stub

See also

References

External links