1. Generation of nondiffracting caustic beam

In this letter, we explore the possibilities of generating diffraction-free caustics over a predetermined range. For the first time we demonstrate the possibility to generate diffraction-free caustic beams. Caustic beams are a topic of increased interest over the past few years. Diffraction-free caustics may find applications in situations where large depth of field and uniform axial energy distributions are important. Introduction One of the most important effects present in wave phenomenon is diffraction. It becomes evident whenever a beam propagates beyond Rayleigh’s range. A tightly focused Gaussian beam rapidly diverges away from the focus. A number of researchers have discussed the possibility of generating beams which can propagate without the usual degree of transverse spreading. Generation of beams that can propagate without diffraction have gained tremendous importance for theoretical and applied research. Typical examples of such beams are Bessel beams, Laguerre-Gaussian beam, Mathieu beams, Airy beams, etc. Perhaps the best known is the so-called Correspondence/Reprint request: Dr. Marcelino Anguiano-Morales, Instituto Tecnológico de Chihuahua Av.Tecnológico # 2909 C.P. 31310 Chihuahua, Chih., México. E-mail: [email protected] Marcelino Anguiano-Morales 2 Bessel beam first suggested and observed by Durnin et al. [1]. Bessel beams are completely invariant upon propagation; the central core can maintain a small beam waist over a much larger propagation range than a Gaussian beam. However, do not be discussed, the existence of caustic that preserving the shape during their propagation. In the last few decades, interest in caustics it has been increased, stimulated by the significant focusing of a field which occurs on caustics. In general, caustic fields have a spatially complex structure. In this work, the generation of other interesting nondiffracting beam, has been demonstrated. Such non-spreading beam is named diffraction-free caustic beam. The caustic beam displays properties similar not only to Bessel beams but also Airy beams. These properties include a self-healing effect. The profiles of Airy beams, similar to Bessel beams, do not change at all on propagation, Laguerre-Gaussian beams also display self-healing, but at much longer distances, comparable to the Rayleigh distance. 1. Generating Bessel beams The Bessel beam is a solution to the scalar wave equation in a homogeneous medium and was first reported in 1987 by Durnin [1]. Durnin et al. published experimental evidence of the resistant to the diffractive spreading of these waves, which exceeded the Rayleigh range before significant beam spreading was observed. The amplitude of an ideal Bessel beam can be conveniently expressed using the circular cylindrical coordinates as: