Innovations in beam shaping & illumination applications

David L. ShealyDepartment of Physics

University of Alabama at BirminghamE-mail: dls@uab.edu

Innovation

NoveltyThe introduction of something newA 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

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200

400

600

800

1000

1200

1400

1600

1976-80 1981-85 1986-90 1991-95 1996-02

US PatentsInvolvingBeam Shaping

What is Laser Beam Shaping?

Process of redistributing the irradiance and phaseOptical 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 lens2 or 3-element spherical GRIN system 2 DOEs1 DOE and 1 plano-aspheric lens

Physical or Geometrical Optics-based Design*

0 02 2f

r Yπβλ

=λ = wavelength, r0 = waist or radius of input beam, Y0= half-width of the desired output dimensionf = focal length of the focusing optic, or the working distance from the optical system to the target plane

ββββ < 4, Beam shaping will not produce acceptable results4 < β < 32, 4 < β < 32, 4 < β < 32, 4 < β < 32, Diffraction effects are significantβ > 32,β > 32,β > 32,β > 32, Geometrical optics methods should be adequate

Beam Shaping Guidelines:

*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 equi-phase 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.”

( )( )

( )

122 2

max 2 2max

1 exp 2

1 exp 2

rR r R

r

α

α

− − = ± − −

Conservation of Energy:

Frieden, Appl. Opt. 4.11, 1400-1403, 1965:“Lossless conversion of a plane wave to a plane wave of

uniform irradiance.”

• Intensity shaping leads to OPL variation of 20λλλλ• Need to shape of output wavefront when phase is important• Frieden requires rays to be parallel Z-axis• Leads to OPL variation of λ/20λ/20λ/20λ/20

2π∫ Iin(r)r dr = 2π∫ Iout(R)R dR

•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.

( )

( )

20

2m a x 0

122

m ax 2

1( , ) s in 01

θ−

−

−+ − = −

r r

r r

er s S Re

R

( ) ( )1 1 cos 0d n n θ− + − =R

( )

( ) ( )( )

20 2 11

r drz rn dnR r

= −− + −

∫ ( )( ) ( )

( )

= −− + −

∫ 20 2 11

R dRZRn dnR r

•Conservation of Energy & Ray Trace Equations:

•Constant OPL:

Mirror Surface Equations:

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 HeCdlaser at 441.57nm.

Optics fabricated in 1992 by Janos Optics by diamond turning of CaF2.

Input and Output Beam Profile

Illustrates the relationship λ and d.

Input and output intensity profiles of an HeNelaser 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 EngineeringIrradiance 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

( )

( )

22

Target N1Diameter Collimation

Uniformityout out

1 1

exp exp 1 cos ( )

1 1( )

NQ

ii

N N

i ki k

s R RM MM

MI R I R

N N

γ=

= =

− − − − = = −

∏

∑ ∑

Beam Shaping Merit Function

Rtarget = Output Beam RadiusRN = Marginal Ray Height on Output Planeγi = Angle ith Ray Make with the Optical AxisQ and s = Convergence Constants

3-Element GRIN Shaping System

Element 1

Element 2Element 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 optimizationAnalysis – better software for graphics, ray tracing aspherics and computing irradianceFabrication of aspherics has improvedTesting of beam shaping (afocal) opticsSome applications are revolutionary