Stationary optical wave fields with arbitrary longitudinal shape by superposing equal frequency Bessel beams: Frozen Waves

Abstract

-In this paper it is shown how one can use Bessel beams to obtain a stationary localized wavefield with high transverse localization, and whose longitudinal intensity pattern can assume any desired shape within a chosen interval 0 ≤ z ≤ L of the propagation axis. This intensity envelope remains static, i.e., with velocity v = 0; and because of this we call "Frozen Waves" such news solutions to the wave equations (and, in particular, to the Maxwell equations). These solutions can be used in many different and interesting applications, as optical tweezers, atom guides, optical or acoustic bistouries, various important medical purposes, etc.

Diffraction-Attenuation resistant beams in absorbing media

“…The problem was already solved by us and the method developed for the particular case of lossless media [12,13], i.e., when n I = 0 → β Im = 0. For those cases, it was shown that the choice…”

“…The method is a generalization of a previous one [12,13] and consists in the superposition of Bessel beams in (7), the real and imaginary parts of their longitudinal wave numbers being given by Eqs. (5)and (8) happily enough, this condition is satisfied in a great number of situations.…”

“…The method that will be developed here is a generalization of a previous one (also developed by us) [12,13], which was conceived for lossless media, where suitable superpositions of Bessel beams are used to construct stationary wave fields with arbitrary longitudinal intensity shape. Those new solutions were called Frozen Waves.…”

“…In the next Section we shall extend the previous method [12,13] to absorbing media. Section 3 is devoted to obtaining examples of these new beams in some interesting situations.…”

Theory of “frozen waves”: modeling the shape of stationary wave fields

“…This intensity envelope remains static, i.e., has velocity v = 0; and because of this in a previous paper [6] we have called "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 high-intensity region.…”