• Document: Optical Design of Laser Beam Shaping Systems
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Optical Design of Laser Beam Shaping Systems David L. Shealy University of Alabama at Birmingham Department of Physics, 1530 3rd Avenue South, CH310 Birmingham, AL 35294-1170 USA Tucson, 5 June 2002 IODC-IWA2 1 Outline of Presentation • Overview of history and current practices • Geometrical methods for design • Applications: • Two-plano-aspheric lens system • Two-mirror system with no central obscuration • Three-element GRIN system Tucson, 5 June 2002 IODC-IWA2 2 Historical Background • Frieden, Appl. Opt. 4.11, 1400-1403, 1965: “Lossless conversion of a plane wave to a plane wave of uniform irradiance.” • Kreuzer, US patent 3,476,463, 1969: “Coherent light optical system yielding an output beam of desired intensity distribution at a desired equi-phase surface.” • Rhodes & Shealy, Appl. Opt. 19, 3545-3553, 1980: “Refractive optical systems for irradiance redistribution of collimated radiation – their design and analysis.” Tucson, 5 June 2002 IODC-IWA2 3 Contemporary Beam Shaping* •Process of redistributing the irradiance and phase •Two functional categories: •Field Mapping •Beam Integrators *Laser Beam Shaping: Theory and Techniques, F.M. Dickey & S.C. Holswade,eds., Mercel Dekker, 2000; Laser Beam Shaping, F.M. Dickey & S.C. Holswade,eds., Proc. SPIE 4095, 2000; Laser Beam Shaping, F.M. Dickey, S.C. Holswade, D.L. Shealy, eds., Proc. SPIE 4443, 2001. Tucson, 5 June 2002 IODC-IWA2 4 Field Mapping Beam Shaper Tucson, 5 June 2002 IODC-IWA2 5 Beam Integrators d D S f F Tucson, 5 June 2002 IODC-IWA2 6 Physical versus Geometrical Optics 2 2π r0Y0 β= fλ λ = wavelength, r0 = waist or radius of input beam, Y0= half-width of the desired output dimension f = focal length of the focusing optic, or the working distance from the optical system to the target plane Beam Shaping Guidelines: β < 4, Beam shaping will not produce acceptable results 4 < β < 32, Diffraction effects are significant β > 32, Geometrical optics methods should be adequate Tucson, 5 June 2002 IODC-IWA2 7 Selected Chapter Titles: •“Mathematical and Physical Theory of Lossless Beam Shaping,” L.A. Romero, F.M Dickey. •“Gaussian Beam Shaping: Diffraction Theory and Design,” F.M. Dickey, S.C. Holswade. •“Geometrical Methods,” D.L. Shealy •“Optimization-based Techniques for Laser Shaping Optics,” N.C. Evans, D.L. Shealy. •“Beam Shaping with Diffractive Diffusers,” D.R. Brown. •“Multi-aperture Beam Integration Systems,” D.M. Brown, F.M. Dickey, L.S. Weichman. •“Current Technology of Beam Profile Measurements,” C.B. Roundy. Tucson, 5 June 2002 IODC-IWA2 8 Overview of Geometrical Methods • Geometrical optics intensity law: ∇ i( I a ) = 0 I 2dA2 I1dA1 I 1 dA1 = I 2 dA2 Source • Constant optical path length condition: (OPL)0 = (OPL)r Tucson, 5 June 2002 IODC-IWA2 9 Optical Design of Laser Beam Shaping Systems: Differential Equations vs. Global Optimization • Geometrical methods leads to equations of the optical surfaces: • Global Optimization with discrete & continuous variables: – Beam shaping merit function Tucson, 5 June 2002 IODC-IWA2 10 Applications of Geometrical Methods • Two plano-aspheric lens system for shaping rotationally symmetric Gaussian beam. • Two mirror system with no central obscuration for shaping elliptical Gaussian beam. • Three-element GRIN system for shaping rotationally symmetric Gaussian beam. Tucson, 5 June 2002 IODC-IWA2 11 Two Lens Bea

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