Optics & Laser Technology 33 (2001) 97–102 www.elsevier.com/locate/optlastec Refractive system for generation of high-power diraction-free laser beams A.A.S. Awwal ∗ , J.U. Ahmed 1 Department of Computer Science and Engineering, Wright State University, 3640 Colonel Glenn Highway, Dayton, OH 45435-0001, USA Received 15 June 2000; received in revised form 29 August 2000; accepted 14 September 2000 Abstract A refractive system is designed to convert a high-power annular beam into a circular Bessel beam. The input and output surface of the proposed system is derived. We provide cubic polynomial approximation of the surface proles. A ray tracing through the complete system is provided to verify the design. The design parameters can be selected to choose the desired beam power in the central lobe and length of the refractive system. c 2001 Elsevier Science Ltd. All rights reserved. Keywords: Lens design; Bessel beam; Annular laser; Diraction-free beams 1. Introduction All laser beams suer from the eect of diraction which results in spreading of a beam when it propagates through free space or creates boundary eects which makes shadows blurred near the edges. Diraction is a fundamental prop- erty of light and limits the size requirement of optical data processing system. Durnin [1, 2] recently made a fundamen- tal discovery that it is possible for a diraction-free beam to exist. He showed that when a beam has Bessel intensity characteristics across its cross-section, it will be diraction free in nature. Such diraction-free beams [3] will be ex- tremely useful in optical signal processing, welding, printing and other laser-based air-defense application. Recently, we have proposed the design of such refractive system for generating diraction-free beam [4 – 6] from a Gaussian laser beam. It may be noted that many high-power laser beams are generated in unstable resonator [7]. The cou- pling of such beams from the resonator to outside is imple- mented using a ring-type reective mirror, which results in an annular beam prole. No one has proposed a way to con- vert such a beam to Bessel beam so that the extreme high power contained in the beam may be transported to appro- * Corresponding author. Tel.: +1-937-775-5131; fax: +1-937-775-5133. E-mail address: aawwal@cs.wright.edu (A.A.S. Awwal). 1 Current address: Hewlett Packard, Fort Collins, CO, USA. priate target. We have already designed refractive systems for converting annular beam to a uniform intensity circular laser beam [8] and Gaussian circular and Gaussian annular laser beam to uniform and Bessel intensity [9 –11] beams. In this paper, we further extend the previous works to design a system to generate such beams specially for generating high-power diraction-free beams. Previously, we designed refractive system for annular laser system with Gaussian intensity [6,11]. In coupling high-power resonator, use of variable reectivity mirror [7] may lead to an almost uni- form laser beam output for the annular laser. The objective of the present work, is to design a system which can con- vert this uniform intensity annular laser beam to a Bessel beam. The design also shows that it is possible to control the output power contained in the main lobe with some design constraint. Verication of the design results are performed using ray tracing of the complete system. 2. Design consideration In order to develop an appropriate refracting system, the input and output surfaces must be found as a function of ra- dial distances. The important physical parameters are given as shown in Fig. 1. The two horizontal reference planes are separated by a distance D. It is desirable to nd the vertical displacement (s) from reference plane (s), y i (y 0 ) as a func- tion of radial distance, r i (r 0 ) respectively. The conditions that must be met to realize the transformation from annular 0030-3992/01/$ - see front matter c 2001 Elsevier Science Ltd. All rights reserved. PII:S0030-3992(00)00125-0