Innovations in beam shaping & illumination applications David L. Shealy Department of Physics University of Alabama at Birmingham E-mail: dls@uab.edu
Innovation Novelty The introduction of something new A new idea, method, or device => patent trends? The making of a change in something established So, what innovations are being made in laser beam shaping and illumination applications?
Growth in US patents involving beam shaping 1600 1400 1200 1000 800 600 400 200 0 1976-80 1981-85 1986-90 1991-95 1996-02 US Patents Involving Beam Shaping
What is Laser Beam Shaping? Process of redistributing the irradiance and phase Optical design methods based on geometrical or physical optics are available in literature.
Examples of Laser Beam Shapers Uniform illumination of a surface can be achieved with a 1-element beam shaper, such as, mirror, plano-aspheric lens, or DOE. Transforming beam irradiance profile (Gaussian to more uniform) while retaining the wavefront shape requires 2 beam shaping elements, such as: 2 mirrors or 2 plano-aspheric lenses 1 bi-aspheric lens 2 or 3-element spherical GRIN system 2 DOEs 1 DOE and 1 plano-aspheric lens
Physical or Geometrical Optics-based Design* β = 2 2π ry f λ 0 0 λ = wavelength, r 0 = waist or radius of input beam, Y 0 = 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 *Laser Beam Shaping: Theory and Techniques, F.M. Dickey & S.C.Holswade,eds., Mercel Dekker, 2000.
What innovations have been made in laser beam shaping? Consider 2 element laser beam shapers
Selected Literature on 2-element Laser Beam Shapers 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 equiphase surface. Rhodes & Shealy, Appl. Opt. 19, 3545-3553, 1980: Refractive optical systems for irradiance redistribution of collimated radiation their design and analysis. Jiang, Shealy, & Martin, Proc. SPIE 2000, 64-75, 1993: Design and testing of a refractive reshaping system. Hoffnagle & Jefferson, Appl. Opt. 39.30, 5488-5499, 2000: Design and performance of a refractive optical system that converts a Gaussian to a flattop beam and US Patent 6,295,168, September 25, 2001: Refractive optical system that converts a laser beam to a collimated flat-top beam.
Frieden, Appl. Opt. 4.11, 1400-1403, 1965: Lossless conversion of a plane wave to a plane wave of uniform irradiance. Conservation of Energy: 2π I in (r)r dr = 2π I out (R)R dr 2 2 1 exp( r 2α ) ( ) =± R max 2 2 1 exp( r 2α ) max R r Intensity shaping leads to OPL variation of 20λ Need to shape of output wavefront when phase is important Frieden requires rays to be parallel Z-axis Leads to OPL variation of λ/20 1 2
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.
Kreuzer, US Patent 3,476,463, 1969. Conservation of Energy & Ray Trace Equations: 2 2 ( r r0 ) 1 e r + R ( s, S )sinθ Rmax 2 = 0 2 ( rmax r0 ) 1 e Constant OPL: ( ) ( ) d n 1 + R 1 n cosθ = 0 1 2 zr Mirror Surface Equations: ( ) = r dr ZR ( ) 2 0 ( ) 2 n 1 d ( n 1) + Rr ( ) = R dr 2 0 ( ) 2 1 + ( n 1) n d Rr ( )
Laser Beam Shaping Equations Conservation of energy within a bundle of rays geometrical optics intensity law. Ray trace equations. Constant optical path length condition.
Optical Design of Laser Beam Shapers Geometrical optics (Frieden, Kreuzer, Rhodes, & Shealy) leads to equations of two optical surfaces: Hoffnagle and Jefferson note the importance of output beam uniformity; efficient utilization of input beam power; propagation of beam over useful region; and using surfaces which can be fabricated Gaussian Super-Gaussian or Fermi-Dirac distribution
Jiang, Ph.D. Dissertation, UAB, 1993 First work to build and test a 2-element beam shaper for operation with HeCd laser at 441.57nm. Optics fabricated in 1992 by Janos Optics by diamond turning of CaF 2.
Input and Output Beam Profile
Illustrates the relationship λ and d.
Input and output intensity profiles of an HeNe laser use with HeCd beam shaping optics. Increased the lens spacing from 150.0 mm to 152.2mm
J.A. Hoffnagle & C. M. Jefferson, Design and performance of a refractive optical system that converts a Gaussian to a flattop beam, Appl. Opt. 39.30, 5488-5499, 2000.
Gaussian to Flat Top High Efficiency Accepts 99.7% of the input beam while minimizing diffraction by using a Fermi-Dirac output beam profile High Uniformity - 78% incident power is within region with 5% rms power variation Good Propagation features Large Bandwidth from 257 to 1550nm
Collimated Output Beam
Cover Graphics for Nov 2003 issue of Optical Engineering Irradiance of Gaussian beam propagating through beam shaper developed by Hoffnagle & Jefferson, who contributed this graphics for the special section on laser beam shaping.
Newport - Refractive Beam Shaper* *Based on New Product Concept literature distributed at SPIE 2002, Seattle.
GRIN Beam Shapers Can a spherical-surface GRIN beam shaping system be designed using catalog GRIN materials? System would have practical applications. Literature: Wang & Shealy, Appl. Opt. 32.25, 4763-4769, 1993 design of 2 spherical surface GRIN lenses where GRIN materials are determined from beam shaping equations, but are not from glass catalogs. N. C. Evans, D. L. Shealy, Proc. SPIE 4095, pp. 27-39, 2000 design of 3 spherical surface GRIN beam shaper using catalog glasses. This problem is well suited for Genetic Algorithms (GAs) using both discrete parameters (small # of GRIN glasses, # elements) and continuous parameters (radii, thickness).
Optical Design of Laser Beam Shapers We know that geometrical optics leads to equations of two aspherical optical surfaces. Global Optimization works well with discrete & continuous variables: Beam shaping merit function
Beam Shaping Merit Function M M M Diameter Collimation = = M Uniformity exp exp 1 cos ( ) N 2 2 Q s( RTarget RN ) γ i i= 1 N N 1 1 Iout ( Ri) Iout R N i= 1 N k= 1 ( ) k R target = Output Beam Radius R N = Marginal Ray Height on Output Plane γ i = Angle i th Ray Make with the Optical Axis Q and s = Convergence Constants
3-Element GRIN Shaping System Element 1 Element 2 Element 3
3-Element GRIN Shaping System Average evaluation time for a generation: 7.80s Total execution time: 26.8 hrs Integrating Output Profile over Output Surface yields 21.9 units; integrating Input Profile over Input Surface yields 21.7 units
Innovations in laser beam shaping using geometrical optics Theory laser beam shaping equations; trade-off between efficiency, uniformity & propagation losses; and merit function for use with GA optimization Analysis better software for graphics, ray tracing aspherics and computing irradiance Fabrication of aspherics has improved Testing of beam shaping (afocal) optics Some applications are revolutionary