There is an increasing demand for laser beams with uniform intensity distribution for such applications as material processing, lithography, medical applications, laser printing, optical data storage, micromachining, isotope separation optical processing and a variety of laboratory applications. In particular, in the field of particle accelerators, laser beam shapers can be used in photon-injectors to provide a quasi-flat drive laser which then produces quasi-flat electron bunches whose emittance can be preserved along the beam line.
The basic principle of laser beam reshaping by a pair of aspheric lenses was proposed by Frieden (B. R. Frieden, “Lossless conversion of a plane laser wave to a plane wave of uniform irradiance,” Appl. Opt. 4, 1400-1403 (1965)) and Kreuzer (J. L. Kreuzer, “Coherent light optical system yielding an output beam of desired intensity distribution at a desired equiphase surface,” U.S. Pat. No. 3,476,463 (4 Nov. 1969), and later by Shealy and co-workers (P. Rhodes and D. Shealy, “Refractive optical systems for irradiance redistribution of collimated radiation: their design and analysis”, Appl. Opt. 19, 3545-3553 (1980); C. Wang and D. L. Shealy, “Design of gradient-index lens systems for laser beam reshaping,” Appl. Opt. 32, 4763-4769 (1993).
Since then, much has been done to optimize designs and experimental results (W. Jiang, D. L. Shealy, and J. C. Martin, “Design and testing of a refractive reshaping system,” in Current Developments in Optical Design and Optical Engineering III, R. E. Fischer and W. J. Smith, eds., Proc. SPIE 2000, 64-75 (1993). W. Jiang and D. L. Shealy, “Development and testing of a laser beam shaping system,” in Laser Beam Shaping, F. M. Dickey and S. C. Holswade, eds., Proc. SPIE 4095, 165-175 (2000). S. Zhang, “A simple bi-convex refractive laser beam shaper”, J. Opt. A: Pure Appl. Opt. 9 945-950; J. A. Hoffnagle and C. M. Jefferson, “Beam shaping with a plano-aspheric lens pair,” Opt. Eng. 42, 3090-3099 (2003).
According to the literature in this field, all refractive shaping systems can be divided into four types (C. Liu and S. Zhang, “Study of singular radius and surface boundary constraints in refractive beam shaper design,” Opt. Express 16, 6675-6682 (2008); J. A. Hoffnagle and C. M. Jefferson, “Refractive optical system that converts a laser beam to a collimated flat-top beam,” U.S. Pat. No. 6,295,168 (25 Sep. 2001); J. A. Hoffnagle and C. M. Jefferson, “Design and performance of a refractive optical system that converts a Gaussian to a flattop beam,” Appl. Opt. 39, 5488-5499 (2000); S. Zhang, G. Neil, and M. Shinn, “Single-element laser beam shaper for uniform flat-top profiles,” Opt. Express 14, 1942-1948 (2003); D. L. Shealy and J. A. Hoffnagle, “Laser beam shaping profiles and propagation,” Appl. Opt. 45, 5118-5131 (2006); A. E. Siegman, Lasers, University Science. Type-1 is the conventional Galilean design, which can be considered as a Galilean telescope with radially varying magnification. The type-2 design of Keplerian, was proposed and patented by Hoffnagle and Jefferson J. A. (Hoffnagle and C. M. Jefferson, “Refractive optical system that converts a laser beam to a collimated flat-top beam,” U.S. Pat. No. 6,295,168 (25 Sep. 2001); J. A. Hoffnagle and C. M. Jefferson, “Design and performance of a refractive optical system that converts a Gaussian to a flattop beam,” Appl. Opt. 39, 5488-5499 (2000)).
Two convex surfaces are adopted in this system so the beam converges first and then diverges between two lenses. This configuration is most commonly used because it is easier to fabricate a convex surface than a concave surface. Shapers of type-3 and type-4 are concave-convex and convex-convex single lens shaping systems respectively. The analysis in S. Zhang, G. Neil, and M. Shinn, “Single-element laser beam shaper for uniform flat-top profiles,” Opt. Express 14, 1942-1948 (2003) shows that a single lens shaper can be obtained by taking the alternative solution of his well-established differential equation. In a type-4 design, the first aspheric surface refracts and converges the input light beams inside the lens. The light rays toward the edge of the beam are bent at a bigger angle than those toward the center of the beam. All rays diverge from each other after the focal plane. The rays refract on the second surface again and get collimated. Referring to the work by Kreuzer, analysis of the design procedure for type-4 shaper produces a similar lucid sag expression which also applies to other types. It has now been determined that a shaper of any type can be designed by solving the sag expression numerically together with the Energy Conservation Law which is another essential condition for shaping systems. Usually, a round flat-top output profile with sharp edges is assumed when solving the differential equation. The sharp edges result in severe diffraction effects which lead to degradation of beam uniformity. With the new method to be presented in this paper, any flat-top or other output profile can be easily chosen. For example, diffraction effects can be effectively suppressed by selecting a continuous roll-off beam profile, like super-Gaussian. Here, the design of a new single lens shaper with two convex aspheric surfaces will be presented. Using convex surfaces reduces fabrication difficulty and allows for large apertures to suppress diffraction while the single element choice simplifies overall configuration and eases optical alignment. Most importantly, this new design converts a Gaussian laser beam to a super-Gaussian beam which alleviates severe diffraction effects and increases the working distance of the shaped output laser beam.