design and analysis of an elliptical gaussian laser beam shaping...
TRANSCRIPT
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2 August 2001 SPIE’s 46th Annual Meeting,Laser Beam Shaping II Conf.
Paper 4443-3: slide 1
Design and Analysis of an Elliptical Gaussian Laser Beam Shaping System
David L. Shealya and Shao-Hua ChaobaUniversity of Alabama at Birmingham, Department of
Physics, Birmingham, AL 35294-1170 USAbHualien Teacher College, Hua Lien, Taiwan
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2 August 2001 SPIE’s 46th Annual Meeting,Laser Beam Shaping II Conf.
Paper 4443-3: slide 2
Laser Beam Shaping System for Cymer ELS-5000A KrF Excimer Laser
See http://www.cymer.com
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2 August 2001 SPIE’s 46th Annual Meeting,Laser Beam Shaping II Conf.
Paper 4443-3: slide 3
Historical Background• 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.”
• DL Shealy, “Geometrical Methods,” in Laser Beam Shaping –Theory and Techniques, FM Dickey and SC Holswade, eds, Marcel Dekker, New York, 2000.
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2 August 2001 SPIE’s 46th Annual Meeting,Laser Beam Shaping II Conf.
Paper 4443-3: slide 4
Overview of Geometrical Methods
• Conservation of energy within a bundle of rays – geometrical optics intensity law.
• Ray trace equations.
• Constant optical path length condition.
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2 August 2001 SPIE’s 46th Annual Meeting,Laser Beam Shaping II Conf.
Paper 4443-3: slide 5
Geometrical Optics Intensity Law
• Conservation of energy within geometrical optics:
1 1 2 2I dA I dA=
Source
1 1I dA
2 2I dA
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2 August 2001 SPIE’s 46th Annual Meeting,Laser Beam Shaping II Conf.
Paper 4443-3: slide 6
Ray Trace Equations
• Ray Trace Equations:
• Law Reflection & Refraction:
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2 August 2001 SPIE’s 46th Annual Meeting,Laser Beam Shaping II Conf.
Paper 4443-3: slide 7
Constant Optical Path Length Condition
• Impose the constant optical path length condition for all rays:
OPL( ) ( , , )C
C n x y z ds= ∫( ) ( )OPL OPL r0 =
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2 August 2001 SPIE’s 46th Annual Meeting,Laser Beam Shaping II Conf.
Paper 4443-3: slide 8
Optical Design of Laser Beam Shaping Systems:
• Global Optimization with discrete & continuous variables using the beam shaping merit function:
• Geometrical methods leads differential equations:
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2 August 2001 SPIE’s 46th Annual Meeting,Laser Beam Shaping II Conf.
Paper 4443-3: slide 9
Input and Output Beam Profiles
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2 August 2001 SPIE’s 46th Annual Meeting,Laser Beam Shaping II Conf.
Paper 4443-3: slide 10
Lens 1
Lens 2
GA Solution to the Two-lens Shaper Problem
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2 August 2001 SPIE’s 46th Annual Meeting,Laser Beam Shaping II Conf.
Paper 4443-3: slide 11
Two-Mirror SystemInput Intensity with 1-to-3 beam waist in x-to-y directions:
Parameters:0
0 0 max 0
00 max 0
max 0 max
1; ;2
3 ; 32
2
rr x x r
ry y r
X r Y
= = =
= =
= =
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2 August 2001 SPIE’s 46th Annual Meeting,Laser Beam Shaping II Conf.
Paper 4443-3: slide 12
Input and Output Beam Coordinates for Elliptical Gaussian-to-circular Top-hat System
Y vs. yX vs. x
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2 August 2001 SPIE’s 46th Annual Meeting,Laser Beam Shaping II Conf.
Paper 4443-3: slide 13
Sag of First Mirror
00 0 max 0
00 max 0
max 0 max
1; ;2
3 ; 32
2
rr x x r
ry y r
X r Y
= = =
= =
= =
2 20
10; 5L h
l L h
= =
= +
Parameters:
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2 August 2001 SPIE’s 46th Annual Meeting,Laser Beam Shaping II Conf.
Paper 4443-3: slide 14
Optical Performance Analysis
• ZEMAX was used.
• Elliptical Gaussian input beam profile was modeled as user-defined surface.
• Two mirror surfaces were also modeled as user-defined surfaces.
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2 August 2001 SPIE’s 46th Annual Meeting,Laser Beam Shaping II Conf.
Paper 4443-3: slide 15
Relative IlluminationInput Beam
Output Beam
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2 August 2001 SPIE’s 46th Annual Meeting,Laser Beam Shaping II Conf.
Paper 4443-3: slide 16
First Mirror Surface Analysis
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2 August 2001 SPIE’s 46th Annual Meeting,Laser Beam Shaping II Conf.
Paper 4443-3: slide 17
Second Mirror Surface Analysis
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2 August 2001 SPIE’s 46th Annual Meeting,Laser Beam Shaping II Conf.
Paper 4443-3: slide 18
Tolerance Analysis• In A, the first mirror was decentered 10% of its diameter about x-axis.• In B, both mirrors were decentered by 2.5% of their diameter about x- and y-axes and tilted about the three axes by 0.25 degrees.
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2 August 2001 SPIE’s 46th Annual Meeting,Laser Beam Shaping II Conf.
Paper 4443-3: slide 19
Summary and Conclusions
• Geometrical methods used to design a two-mirror system with rectangular symmetry and no central obscuration which can transform a 3:1 elliptical Gaussian beam into a uniform output beam.
• ZEMAX used to do optical modeling and tolerance analysis.
• First mirror has strong aspherical component along direction of smaller waist.
• Output beam profile is stable for decentering of less than 2.5% of mirror diameter and 0.25degrees about coordinate axis.
Design and Analysis of an Elliptical Gaussian Laser Beam Shaping SystemLaser Beam Shaping System for Cymer ELS-5000A KrF Excimer LaserHistorical BackgroundOverview of Geometrical MethodsGeometrical Optics Intensity LawRay Trace EquationsConstant Optical Path Length ConditionOptical Design of Laser Beam Shaping Systems:Input and Output Beam ProfilesGA Solution to the Two-lens Shaper ProblemTwo-Mirror SystemInput and Output Beam Coordinates for Elliptical Gaussian-to-circular Top-hat SystemSag of First MirrorOptical Performance AnalysisRelative IlluminationFirst Mirror Surface AnalysisSecond Mirror Surface AnalysisTolerance AnalysisSummary and Conclusions