Multiple vortex with different topological charge generated by means of SLM Victor Kotlyar and Alexey Kovalev Image Processing Systems Institute, Russian Academy of Sciences, Samara State Aerospace University, 151 Molodogvardejskaya, Samara 443001, Russia Valeria Garbin, Enrico Ferrari and Dan Cojoc CNR- Istituto Nazionale per la Fisica della Materia, Laboratorio Nazionale TASC, Area Science Park – Basovizza, S.S. 14 Km. 163,5, 34012 Basovizza (TS), Italy ABSTRACT We present techniques to generate multiple vortex with different topological charge by means of diffractive optical elements. Analytical formulae to describe the Fresnel and Fraunhofer diffraction of the Gaussian beam by a helical axicon (HA) are introduced. The relations are presented as a series of the hypergeometric functions. By setting the axicon parameter equal to zero, the solution for the HA changes to that for the spiral phase plate (SPP). The performance of the aforesaid optical elements is tested both through computer simulation and by experiments using a spatial light modulator, in view of optical miroparticle manipulation. Keywords: diffractive optical elements, optical vortex, axicon, diffraction 1. INTRODUCTION The photolithographic fabrication and experimental studies of the helical axicon (HA) [1] and the spiral phase plate (SPP) [2] were presented for the first time in 1992. The HA is used to generate diffraction-free laser Bessel beams, and the SPP is able to generate optical vortices and perform the radial Hilbert transform [2-4]. Interest in the potential uses of the HA and SPP [5-19] has markedly quickened in the recent years. This is because the improved quality of fabrication of spatial light modulators (SLM) has made them suitable for generating diffractive optical elements, including the HA and SPP. For example, in Ref. [5] the higher-order SPPs (n>30) were generated using the SLM and the higher-order optical vortices were studied. Using the SLM enables producing a composite SPP to generate a laser beam composed of several coaxial optical vortices [6]. Also, the diffraction-free Bessel beams [7, 8], elliptic Bessel beams [9], Ince- Gaussian beams [10], and hollow beams [11] were generated using the SLM. On the other hand, studies of the HA and SPP fabricated through the traditional e-beam lithography have been in progress [12-15]. Diffraction of a plane wave by a second- and third-order SPP was experimentally studied in Refs. [12, 13]. In Ref. [14] a fifth-order HA was studied, and a double axicon to generate two conical light beams that mutually interfere to produce the zero axial intensity was presented in Ref. [15]. The theoretical analysis of the paraxial Fresnel and Fraunhofer diffraction by the SPP was conducted for the incident Gaussian beam [16], unbounded plane wave [2, 12], bounded plane wave [5, 13], and elliptical beam [17]. Diffraction by the HA was theoretically studied for the unbounded plane wave [14] and the Gaussian beam [18]. Interest in the studies of the HA and SPP is also due to the potential for optical micromanipulation they show [5, 14, 19]. Nanoengineering: Fabrication, Properties, Optics, and Devices III edited by Elizabeth A. Dobisz, Louay A. Eldada, Proc. of SPIE Vol. 6327 632710, (2006) · 0277-786X/06/$15 · doi: 10.1117/12.680759 Proc. of SPIE Vol. 6327 632710-1 Downloaded from SPIE Digital Library on 30 Dec 2009 to 89.186.234.25. Terms of Use: http://spiedl.org/terms