Study of the Bessel beams with opaque obstructions along the propagation direction M. AnguianoMora1esa, s. E. Ba1derasMatab, M. M. Méndez Oteroa, S. ChávezCerdab and M. D. IturbeCasti11ob apostgrado en Optoelectrónica, FCFM, BUAP, C. P.72570/ Apdo. Postal 1 152. Puebla; Pue. Mexico blnstituto Nacional de AstrofIsica, Optica y Electrónica, C. P.7200 Apdo. Postal 51 y 216. Puebla, Pue. Mexico ABSTRACT We study the property of propagation beams disturbed by a opaque obstacle. The fronts of the Hankel waves are disturbed and beyond the obstacle they are reconstructed. We report the observation of two shadow produced by the obstacle, and the fact that the Bessel beam is formed of ingoing and outgoing conical waves. We numerically solve the Helmholtz equation to show the evolution and the reconstruction of the Bessel beam and we demonstrate the correspondence of these results with the experimental part. Keywords: Self-reconstruction ofbeams, Bessel beams, invariant in propagation. 1. INTRODUCTION Many phenomena observable in our everyday life indicate that light propagates rectilinearly. Rectilinear propagation is one of the most apparent properties of light. It serves as an argument that light is a stream of particles. However, some optical phenomena and experiments indicate that the law of rectilinear propagation oflight does not hold. They can be satisfactorily explained only on the assumption that light is a wave. In optics, the diffraction effects are less apparent1. Diffraction of light was first reported by Leonardo da Vinci, but the first steps to its understanding were only made in the 17th (Grimaldi, Huygens, Hook, Newton) and 18th centuries (Fresnel, Young). Historically, diffraction is what we call the phenomenon when light is not traveling in straight lines although it should be according to the laws of ray optics. The discovery of diffraction served as an important argument for overcoming corpuscular Newtonian optics2. Stratton first derived expressions for invariant beams3. Durnin, was the first to point out that one could obtain a set of solutions for the free-space scalar wave equation that were propagation invariant. The zero-order Bessel beam is one such solution and results in a beam with a narrow central region surrounded by a series of concentric rings4. Bessel beams have distinct advantages in metrology, in particle confinement and acceleration5, and in nonlinear optics6, where they also show a self-reconstruction property7. 2. PROPERTIES OF PROPAGATION INVARIANT BEAMS Beams with a large depth of field were first developed by Brittingham in 1983. He discovered electromagnetic waves that are localized solutions to the free-space Maxwell's equations and would propagate to an infinite distance with only local deformations8. Independent ofBrittingham and Ziolkowski's work, in 1987 Durnin discovered the invariant beam, in optics and called them invariant beams4. The invariant beams exhibit interesting properties by which they differ from the common beams9, for example Gaussian beams. Recently, an increasing attention has been devoted to those properties because offer many potential applications and their explanation can be important for better understanding of the origin of the diffraction phenomena and of the nature of the electromagnetic field. An important property of the invariant beam is its resistance against amplitude and phase distortions. Other important property is observed when a Bessel beam is obstructed by an obstacle, after some distance beyond the obstacle. One of the most important tasks in design of Micro Electro Mechanical Systems is to find ways how to power machines that measure only microns across. The promising solution is to rotate them by the blowing of "the light wind". It can be produced by the optical vortices carrying the orbital angular momentum'°. 5th Iberoamerican Meeting on Optics and 8th Latin American Meeting on Optics, Lasers, and Their Applications, edited by A. Marcano O., J. L.Paz, Proc. of SPIE Vol. 5622 (SPIE, Bellingham, WA, 2004) · 0277-786X/04/$15 · doi: 10.1117/12.591722 1440