Theory of Frozen Waves
arXiv:physics/0502105 · doi:10.1364/JOSAA.22.002465
Abstract
In this work, starting by suitable superpositions of equal-frequency Bessel beams, we develop a theoretical and experimental methodology to obtain localized stationary wave fields, with high transverse localization, whose longitudinal intensity pattern can approximately assume any desired shape within a chosen interval 0 < z < L of the propagation axis z. Their intensity envelope remains static, i.e. with velocity v=0; so that we have named ``Frozen Waves" (FW) these new solutions to the wave equations (and, in particular, to the Maxwell equations). Inside the envelope of a FW only the carrier wave does propagate: And the longitudinal shape, within the interval 0 < z < L, can be chosen in such a way that no nonnegligible field exists outside the pre-determined region (consisting, e.g., in one or more high intensity peaks). Our solutions are noticeable also for the different and interesting applications they can have, especially in electromagnetism and acoustics, such as optical tweezers, atom guides, optical or acoustic bistouries, various important medical apparata, etc.
29 pages, 9 figures
References in corpus (11)
- Frozen Waves: Stationary optical wavefields with arbitrary longitudinal shape, by superposing equal-frequency Bessel beams
- On Localized "X-shaped" Superluminal Solutions to Maxwell Equations
- New localized Superluminal solutions to the wave equations with finite total energies and arbitrary frequencies
- On the Localized superluminal Solutions to the Maxwell Equations
- Localized Superluminal solutions to Maxwell equations propagating along a normal-sized waveguide
- Superluminal Localized Solutions to the wave equation, in (vacuum or) dispersive media, for arbitrary frequencies and with adjustable bandwidth
- Superluminal X-shaped beams propagating without distortion along a coaxial guide
- Superluminal Localized Solutions to Maxwell Equations propagating along a waveguide: The finite-energy case
- Focused X-shaped (Superluminal) pulses
- Chirped optical X-shaped pulses in material media
- Classical solutions of Maxwell equations and the tunneling photon effect
Cited by in corpus (18)
- Experimental optical trapping of micro-particles with Frozen Waves
- Longitudinal patterning of twisted light
- Modelling the spatial shape of nondiffracting beams: Experimental generation of Frozen Waves via computer generated holograms
- Sub-luminal wave bullets: Exact Localized subluminal Solutions to the Wave Equations
- Diffraction-Attenuation Resistant Beams: their Higher Order Versions and Finite-Aperture Generations
- Unidirectional decomposition method for obtaining exact localized waves solutions totally free of backward components
- Localized Waves: A not-so-short Review
- Arbitrary control of the polarization and intensity profiles of diffraction-attenuation-resistant beams along their propagation direction
- Production of Dynamic Frozen Waves: Controlling shape, location (and speed) of diffraction-resistant beams
- Analytical expressions for the longitudinal evolution of nondiffracting pulses truncated by finite apertures
- Modelling the longitudinal intensity pattern of diffraction resistant beams in stratified media
- Soliton-like solutions to the ordinary Schroedinger equation
- Structured Light by linking together diffraction-resistant spatially shaped beams: "LEGO-BEAMS"
- Mathematical description of a Frozen Wave beam after passing through a pair of convex lenses with different focal distance
- Frozen spatial coherence
- Shaping the longitudinal intensity pattern of Cartesian beams in lossless and lossy media
- Carving light beams
- Fusion Between Frozen-Wave-Type Beams and Airy-Type Pulses: Diffraction-Dispersion-Attenuation Resistant Vortex Pulses in Absorbing Media