Abstract

A novel design method is presented for a simple laser beam shaper. Unlike earlier reports and designs based on the 2-element model, we prove it is possible to convert a laser beam from a non-uniform profile to a uniform flat-top distribution with one single aspherical lens.

© 2003 Optical Society of America

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References

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  1. F. M. Dickey, S. C. Holswade, Laser Beam Shaping-Theory and Techniques (Marcel Dekker, Inc. 2000).
    [CrossRef]
  2. J.A. Hoffnagle and C.M. Johnson, �??Design and performance of a refractive optical system that converts a Gaussian to a flattop beam,�?? Appl. Opt. 39, 5488-5499 (2000).
    [CrossRef]
  3. W. Jiang, D. L. Shealy, �??Development and testing of a laser beam shaping system,�?? in Laser BeamShaping, F. M. Dickey and S. C. Holswade, eds., Proc. SPIE 4095, 165-175 (2000).
    [CrossRef]
  4. B. R. Frieden, �??Lossless conversion of a plane laser wave to a plane wave of uniform irradiance,�?? Appl. Opt. 4, 1400-1403 (1965).
    [CrossRef]
  5. G. Erdei, G. Szarvas, E. Lorincz, P. Richer, �??Optimization method for the design of beam shaping systems,�?? Opt. Eng. 41, 575-591 (2002).
    [CrossRef]
  6. S. R. Jahan and M. A. Karim, �??Refracting systems for Gaussian-to-uniform beam transformations,�?? Opt. Laser Technol. 21, 27-30 (1987).
    [CrossRef]

Appl. Opt. (2)

Opt. Eng. (1)

G. Erdei, G. Szarvas, E. Lorincz, P. Richer, �??Optimization method for the design of beam shaping systems,�?? Opt. Eng. 41, 575-591 (2002).
[CrossRef]

Opt. Laser Technol. (1)

S. R. Jahan and M. A. Karim, �??Refracting systems for Gaussian-to-uniform beam transformations,�?? Opt. Laser Technol. 21, 27-30 (1987).
[CrossRef]

Proc. SPIE (1)

W. Jiang, D. L. Shealy, �??Development and testing of a laser beam shaping system,�?? in Laser BeamShaping, F. M. Dickey and S. C. Holswade, eds., Proc. SPIE 4095, 165-175 (2000).
[CrossRef]

Other (1)

F. M. Dickey, S. C. Holswade, Laser Beam Shaping-Theory and Techniques (Marcel Dekker, Inc. 2000).
[CrossRef]

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Figures (7)

Fig. 1.
Fig. 1.

A conventional 2-element beam shaping system.

Fig. 2.
Fig. 2.

Geometric configuration of a beam reshaping system. Dotted lines refer to the case where minus signs are taken from equations.

Fig. 3.
Fig. 3.

Optical schematic of single-element beam reshaping system.

Fig. 4.
Fig. 4.

Calculated lens surfaces of a single-element beam shaper. The lens material is fused silica. Red color solid lines denote the ray paths. Input and output beam radiuses are 4mm and 10mm, respectively.

Fig. 5.
Fig. 5.

Beam irradiance profiles before and after the transformation by a single-element beam shaper. Lens material is fused silica.

Fig. 6.
Fig. 6.

Beam profile variation caused by input beam profiles for single-lens shaping system designed for input GNS2. GSN stands for Gaussian and Sech2 for sec h 2(asr/rs ).

Fig. 7.
Fig. 7.

A design for a thin single-element beam shaper with 1:1 magnification. The center thickness is about 2mm. Red color solid lines represent ray paths.

Equations (12)

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R = [ ( 2 E o ) 0 r 0 E i ( r ) r dr ] 1 2
( z ' ) 4 [ γ 1 2 ( R r ) 2 + ( γ 1 2 1 ) ( Z z ) 2 ] ( z ' ) 3 [ 2 ( R r ) ( Z z ) ]
( z ' ) 2 ( 1 γ 1 2 ) [ ( R r ) 2 + ( Z z ) 2 ]
z ' [ 2 ( R r ) ( Z z ) ] ( R r ) 2 = 0
C ( cons tan t ) = n 1 t 1 + ( Z 0 t 1 ) n 0 + n 2 t 2
= n 1 z + n 0 [ ( R r ) 2 + ( Z z ) 2 ] 1 2 + n 2 ( Z 0 + t 2 Z )
Z = ( n 2 2 n 0 2 ) 1 { [ ( n 1 n 2 n 0 2 ) z + n 2 C ] ± n 0 [ ( C + n 1 γ 1 n 2 z ) 2
+ ( n 2 2 n 0 2 ) ( R r ) 2 ] 1 2 }
Z ' = z ' γ 2 { γ 1 [ 1 + ( z ' ) 2 ( 1 γ 1 2 ) ] 1 2 } { 1 + ( z ' ) 2 γ 1 γ 2 ( z ' ) 2
γ 2 [ 1 + ( z ' ) 2 ( 1 γ 1 2 ) ] 1 2 }
z ' = { ( R r ) ( Z z ) ± γ 1 ( R r ) [ ( Z z ) 2 + ( R r ) 2 ] 1 2 }
/ [ ( γ 1 2 1 ) ( Z z ) 2 + γ 1 2 ( R r ) 2 ]

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