Abstract

Fresnel-type diffractive optical elements (DOEs) for general beam shaping of monochromatic, spatially incoherent light are demonstrated. Direct and indirect methods, i.e., adding a lens' phase to the designed Fraunhofer-type DOEs, are used for the design. The indirect method can reduce the calculation time by approximately half without loss of design accuracy. Two different design examples are shown. For one design the direct method gives a maximum sidelobe intensity of 5.0% of the maximum intensity in the signal window. For the second design the indirect method gives 23.0% of this value. The generated patterns can maintain their basic shapes over a long distance. The elements have been fabricated by directly using gray-scale commercial slides as masks. Experimental results are in close agreement with numerical predictions.

© 2006 Optical Society of America

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References

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2005 (4)

J. Saarinen, M. Rossi, and M. T. Gale, "Micro-optics technology fulfills its promise," Laser Focus World 41(10), 76-80 (2005).

B. Staager, M. T. Gale, and M. Rossi, "Replicated micro-optics for automotive applications," in Photonics in the Automobile, D. Kessel, ed., Proc. SPIE 5663, 238-245 (2005).

C. W. Jeon, E. Gu, and M. D. Dawson, "Mask-free photolightographic exposure using a matrix-addressable micropixellated AlInGaN ultraviolet light-emitting diode," Appl. Phys. Lett. 86, 221105 (2005).
[CrossRef]

C. Griffin, E. Gu, H. W. Choi, C. W. Jeon, J. M. Girkin, M. D. Dawson, and G. McConnell, "Beam divergence measurement of InGaN/GaN micro-array light-emitting diodes using confocal microscopy," Appl. Phy. Lett. 86, 041111 (2005).
[CrossRef]

2004 (1)

O. Ripoll, V. Kettunen, and H. P. Herzig, "Review of iterative Fourier-transform algorithms for beam shaping applications," Opt. Eng. 43, 2549-2556 (2004).
[CrossRef]

2003 (1)

M. J. Thomson and M. R. Taghizadeh, "Diffractive elements for high-power fiber coupling applications," J. Mod. Opt. 50, 1691-1699 (2003).
[CrossRef]

2002 (1)

2001 (2)

1998 (1)

1997 (1)

1995 (3)

1994 (1)

H. Aagedal, S. Teiwes, and F. Wyrowski, "Consequence of illumination wave on optical function of nonperiodic diffractive elements," Opt. Commun. 109, 22-28 (1994).
[CrossRef]

1993 (1)

J. Cordingley, "Application of a binary diffractive optic for beam shaping in semiconductor processing by lasers," Appl. Opt. 13, 2534-2537 (1993).

1992 (1)

1987 (1)

1983 (1)

S. Kirkpatrick, C. D. Gelatt, Jr., and M. P. Vecchi, "Opimization by simulated annealing," Science 220, 671-680 (1983).
[CrossRef] [PubMed]

1973 (1)

Aagedal, H.

H. Aagedal, S. Teiwes, and F. Wyrowski, "Consequence of illumination wave on optical function of nonperiodic diffractive elements," Opt. Commun. 109, 22-28 (1994).
[CrossRef]

Allebach, J. P.

Blough, G.

Choi, H. W.

C. Griffin, E. Gu, H. W. Choi, C. W. Jeon, J. M. Girkin, M. D. Dawson, and G. McConnell, "Beam divergence measurement of InGaN/GaN micro-array light-emitting diodes using confocal microscopy," Appl. Phy. Lett. 86, 041111 (2005).
[CrossRef]

Cordingley, J.

J. Cordingley, "Application of a binary diffractive optic for beam shaping in semiconductor processing by lasers," Appl. Opt. 13, 2534-2537 (1993).

Dawson, M. D.

C. Griffin, E. Gu, H. W. Choi, C. W. Jeon, J. M. Girkin, M. D. Dawson, and G. McConnell, "Beam divergence measurement of InGaN/GaN micro-array light-emitting diodes using confocal microscopy," Appl. Phy. Lett. 86, 041111 (2005).
[CrossRef]

C. W. Jeon, E. Gu, and M. D. Dawson, "Mask-free photolightographic exposure using a matrix-addressable micropixellated AlInGaN ultraviolet light-emitting diode," Appl. Phys. Lett. 86, 221105 (2005).
[CrossRef]

Ehbets, P.

P. Ehbets, M. Rossi, and H. P. Herzig, "Continuous-relief fan-out elements with optimized fabrication tolerance," Opt. Eng. 34, 3456-3464 (1995).
[CrossRef]

Friberg, A. T.

Gale, M.

M. Rossi and M. Gale, "Micro-optics promote use of LEDs in consumer goods," LEDs Mag. (July 2005), pp. 27-29.

Gale, M. T.

J. Saarinen, M. Rossi, and M. T. Gale, "Micro-optics technology fulfills its promise," Laser Focus World 41(10), 76-80 (2005).

B. Staager, M. T. Gale, and M. Rossi, "Replicated micro-optics for automotive applications," in Photonics in the Automobile, D. Kessel, ed., Proc. SPIE 5663, 238-245 (2005).

Gallagher, N. C.

Gelatt, C. D.

S. Kirkpatrick, C. D. Gelatt, Jr., and M. P. Vecchi, "Opimization by simulated annealing," Science 220, 671-680 (1983).
[CrossRef] [PubMed]

Girkin, J. M.

C. Griffin, E. Gu, H. W. Choi, C. W. Jeon, J. M. Girkin, M. D. Dawson, and G. McConnell, "Beam divergence measurement of InGaN/GaN micro-array light-emitting diodes using confocal microscopy," Appl. Phy. Lett. 86, 041111 (2005).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996), pp. 40-53.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996), p. 57.

Griffin, C.

C. Griffin, E. Gu, H. W. Choi, C. W. Jeon, J. M. Girkin, M. D. Dawson, and G. McConnell, "Beam divergence measurement of InGaN/GaN micro-array light-emitting diodes using confocal microscopy," Appl. Phy. Lett. 86, 041111 (2005).
[CrossRef]

Gu, E.

C. Griffin, E. Gu, H. W. Choi, C. W. Jeon, J. M. Girkin, M. D. Dawson, and G. McConnell, "Beam divergence measurement of InGaN/GaN micro-array light-emitting diodes using confocal microscopy," Appl. Phy. Lett. 86, 041111 (2005).
[CrossRef]

C. W. Jeon, E. Gu, and M. D. Dawson, "Mask-free photolightographic exposure using a matrix-addressable micropixellated AlInGaN ultraviolet light-emitting diode," Appl. Phys. Lett. 86, 221105 (2005).
[CrossRef]

Hecht, E.

E. Hecht, Optics, 3rd ed. (Addison-Wesley, 1998), p. 164.

Herzig, H. P.

O. Ripoll, V. Kettunen, and H. P. Herzig, "Review of iterative Fourier-transform algorithms for beam shaping applications," Opt. Eng. 43, 2549-2556 (2004).
[CrossRef]

P. Ehbets, M. Rossi, and H. P. Herzig, "Continuous-relief fan-out elements with optimized fabrication tolerance," Opt. Eng. 34, 3456-3464 (1995).
[CrossRef]

H. P. Herzig, Micro-Optics, Elements, Systems and Applications (Taylor & Francis, 1997), p. 11.

Jaroszewicz, Z.

Jeon, C. W.

C. W. Jeon, E. Gu, and M. D. Dawson, "Mask-free photolightographic exposure using a matrix-addressable micropixellated AlInGaN ultraviolet light-emitting diode," Appl. Phys. Lett. 86, 221105 (2005).
[CrossRef]

C. Griffin, E. Gu, H. W. Choi, C. W. Jeon, J. M. Girkin, M. D. Dawson, and G. McConnell, "Beam divergence measurement of InGaN/GaN micro-array light-emitting diodes using confocal microscopy," Appl. Phy. Lett. 86, 041111 (2005).
[CrossRef]

Jiang, H. X.

H. X. Jiang, S. X. Jin, J. Li, J. Shakya, and J. Y. Lin, "III-nitride blue microdisplays," Appl. Phy. Lett. 78, 1303-1305 (2001).
[CrossRef]

Jin, S. X.

H. X. Jiang, S. X. Jin, J. Li, J. Shakya, and J. Y. Lin, "III-nitride blue microdisplays," Appl. Phy. Lett. 78, 1303-1305 (2001).
[CrossRef]

Kettunen, V.

O. Ripoll, V. Kettunen, and H. P. Herzig, "Review of iterative Fourier-transform algorithms for beam shaping applications," Opt. Eng. 43, 2549-2556 (2004).
[CrossRef]

Khajurivala, K.

Kirkpatrick, S.

S. Kirkpatrick, C. D. Gelatt, Jr., and M. P. Vecchi, "Opimization by simulated annealing," Science 220, 671-680 (1983).
[CrossRef] [PubMed]

Knapp, W.

Li, J.

H. X. Jiang, S. X. Jin, J. Li, J. Shakya, and J. Y. Lin, "III-nitride blue microdisplays," Appl. Phy. Lett. 78, 1303-1305 (2001).
[CrossRef]

Lin, J. Y.

H. X. Jiang, S. X. Jin, J. Li, J. Shakya, and J. Y. Lin, "III-nitride blue microdisplays," Appl. Phy. Lett. 78, 1303-1305 (2001).
[CrossRef]

Liu, B.

Liu, J. S.

Mait, J. N.

McConnell, G.

C. Griffin, E. Gu, H. W. Choi, C. W. Jeon, J. M. Girkin, M. D. Dawson, and G. McConnell, "Beam divergence measurement of InGaN/GaN micro-array light-emitting diodes using confocal microscopy," Appl. Phy. Lett. 86, 041111 (2005).
[CrossRef]

Michael, R.

O'Shea, D. C.

Popov, S. Y.

Ripoll, O.

O. Ripoll, V. Kettunen, and H. P. Herzig, "Review of iterative Fourier-transform algorithms for beam shaping applications," Opt. Eng. 43, 2549-2556 (2004).
[CrossRef]

Rossi, M.

J. Saarinen, M. Rossi, and M. T. Gale, "Micro-optics technology fulfills its promise," Laser Focus World 41(10), 76-80 (2005).

B. Staager, M. T. Gale, and M. Rossi, "Replicated micro-optics for automotive applications," in Photonics in the Automobile, D. Kessel, ed., Proc. SPIE 5663, 238-245 (2005).

P. Ehbets, M. Rossi, and H. P. Herzig, "Continuous-relief fan-out elements with optimized fabrication tolerance," Opt. Eng. 34, 3456-3464 (1995).
[CrossRef]

M. Rossi and M. Gale, "Micro-optics promote use of LEDs in consumer goods," LEDs Mag. (July 2005), pp. 27-29.

Saarinen, J.

J. Saarinen, M. Rossi, and M. T. Gale, "Micro-optics technology fulfills its promise," Laser Focus World 41(10), 76-80 (2005).

Schubert, E. F.

E. F. Schubert, Light-Emitting Diodes (Cambridge University Press, 2003), pp. 94-95.

Seldowitz, M. A.

Shakya, J.

H. X. Jiang, S. X. Jin, J. Li, J. Shakya, and J. Y. Lin, "III-nitride blue microdisplays," Appl. Phy. Lett. 78, 1303-1305 (2001).
[CrossRef]

Staager, B.

B. Staager, M. T. Gale, and M. Rossi, "Replicated micro-optics for automotive applications," in Photonics in the Automobile, D. Kessel, ed., Proc. SPIE 5663, 238-245 (2005).

Suleski, T. J.

Sweeney, D. W.

Taghizadeh, M. R.

M. J. Thomson and M. R. Taghizadeh, "Diffractive elements for high-power fiber coupling applications," J. Mod. Opt. 50, 1691-1699 (2003).
[CrossRef]

J. S. Liu and M. R. Taghizadeh, "Iterative algorithm for the design of diffractive phase elements for laser beam shaping," Opt. Lett. 27, 1463-1465 (2002).
[CrossRef]

J. S. Liu and M. R. Taghizadeh, Diffractive Optics 2003 (Oxford University, 2003), available on CD.

Tatian, B.

Teiwes, S.

H. Aagedal, S. Teiwes, and F. Wyrowski, "Consequence of illumination wave on optical function of nonperiodic diffractive elements," Opt. Commun. 109, 22-28 (1994).
[CrossRef]

Thaning, A.

Thomson, M. J.

M. J. Thomson and M. R. Taghizadeh, "Diffractive elements for high-power fiber coupling applications," J. Mod. Opt. 50, 1691-1699 (2003).
[CrossRef]

van der Gracht, J.

Vecchi, M. P.

S. Kirkpatrick, C. D. Gelatt, Jr., and M. P. Vecchi, "Opimization by simulated annealing," Science 220, 671-680 (1983).
[CrossRef] [PubMed]

Volk, B.

Wyrowski, F.

H. Aagedal, S. Teiwes, and F. Wyrowski, "Consequence of illumination wave on optical function of nonperiodic diffractive elements," Opt. Commun. 109, 22-28 (1994).
[CrossRef]

Appl. Opt. (5)

Appl. Phy. Lett. (2)

H. X. Jiang, S. X. Jin, J. Li, J. Shakya, and J. Y. Lin, "III-nitride blue microdisplays," Appl. Phy. Lett. 78, 1303-1305 (2001).
[CrossRef]

C. Griffin, E. Gu, H. W. Choi, C. W. Jeon, J. M. Girkin, M. D. Dawson, and G. McConnell, "Beam divergence measurement of InGaN/GaN micro-array light-emitting diodes using confocal microscopy," Appl. Phy. Lett. 86, 041111 (2005).
[CrossRef]

Appl. Phys. Lett. (1)

C. W. Jeon, E. Gu, and M. D. Dawson, "Mask-free photolightographic exposure using a matrix-addressable micropixellated AlInGaN ultraviolet light-emitting diode," Appl. Phys. Lett. 86, 221105 (2005).
[CrossRef]

J. Mod. Opt. (1)

M. J. Thomson and M. R. Taghizadeh, "Diffractive elements for high-power fiber coupling applications," J. Mod. Opt. 50, 1691-1699 (2003).
[CrossRef]

J. Opt. Soc. Am. A (1)

Laser Focus World (1)

J. Saarinen, M. Rossi, and M. T. Gale, "Micro-optics technology fulfills its promise," Laser Focus World 41(10), 76-80 (2005).

LEDs Mag. (1)

M. Rossi and M. Gale, "Micro-optics promote use of LEDs in consumer goods," LEDs Mag. (July 2005), pp. 27-29.

Opt. Commun. (1)

H. Aagedal, S. Teiwes, and F. Wyrowski, "Consequence of illumination wave on optical function of nonperiodic diffractive elements," Opt. Commun. 109, 22-28 (1994).
[CrossRef]

Opt. Eng. (2)

P. Ehbets, M. Rossi, and H. P. Herzig, "Continuous-relief fan-out elements with optimized fabrication tolerance," Opt. Eng. 34, 3456-3464 (1995).
[CrossRef]

O. Ripoll, V. Kettunen, and H. P. Herzig, "Review of iterative Fourier-transform algorithms for beam shaping applications," Opt. Eng. 43, 2549-2556 (2004).
[CrossRef]

Opt. Lett. (4)

Science (1)

S. Kirkpatrick, C. D. Gelatt, Jr., and M. P. Vecchi, "Opimization by simulated annealing," Science 220, 671-680 (1983).
[CrossRef] [PubMed]

Other (7)

H. P. Herzig, Micro-Optics, Elements, Systems and Applications (Taylor & Francis, 1997), p. 11.

J. S. Liu and M. R. Taghizadeh, Diffractive Optics 2003 (Oxford University, 2003), available on CD.

B. Staager, M. T. Gale, and M. Rossi, "Replicated micro-optics for automotive applications," in Photonics in the Automobile, D. Kessel, ed., Proc. SPIE 5663, 238-245 (2005).

E. Hecht, Optics, 3rd ed. (Addison-Wesley, 1998), p. 164.

E. F. Schubert, Light-Emitting Diodes (Cambridge University Press, 2003), pp. 94-95.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996), pp. 40-53.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996), p. 57.

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Figures (6)

Fig. 1
Fig. 1

Fraunhofer-type configuration used for beam shaping of spatially incoherent light. For Fresnel-type configuration the Fourier lens should be removed from the setup.

Fig. 2
Fig. 2

Cross-sectional structures of the design DOEs:(a) Fresnel-type DOE for design (a) in Table 1; (b) Fraunhofer-type DOE for design (b) in Table 1; (c) Fresnel-type DOE for design (b) in Table 1; (d) magnified structure of (c).

Fig. 3
Fig. 3

(Color online) Left column [(a) to (d)] is the desired [(a)] and simulated [(b), (c), and (d)] performance of Fresnel-type DOEs at different image distances z out = 400 , 500, and 600   mm for design (a) in Table 1; while the right column [(e) to (h)] is the desired and simulated performance at z out = 60 , 70, and 80   mm for design (b) in Table 1. 512 and 12288 sample points are used, respectively. We can see that the generated patterns can maintain their basic shape over a long distance.

Fig. 4
Fig. 4

Optimization of the sidelobe intensity during the DBS process for design (b). The maximum sidelobe intensity S decreases to 21.7 % after 70 DBS iterations, and the decreasing trend continues but at a markedly slower pace.

Fig. 5
Fig. 5

(Color online) Simulated performance of Fraunhofer- and Fresnel-type DOEs for design (b) in Table 1. The effective sample point numbers used in the simulation are shown in Table 2. By comparing the curve “Fraunhofer-type” in (a) and the curve “Fresnel-type 6” in (b), we can see the design results are reasonably accurate. From the curve “Fresnel-type 6” in the lower figure, we can see that the maximum sidelobe intensity is 23.0 % of the average intensity in the signal window.

Fig. 6
Fig. 6

(Color online) Simulated (solid and dashed curves) and experimental (dotted curve) intensity profiles of design (b) in Table 1 at z out = 70   mm . “Simulated 1” shows the intensity profiles when the feature size is 2.0 μ m and no vertical profile scaling errors exist; “Simulated 2” is the situation when the feature size is 11.7 μ m and the etching depth error is 20 % . The feature size for the measured curve is 4.5 μ m .

Tables (2)

Tables Icon

Table 1 Double-Line Pattern Shaping and Performance Indicated by the Maximum Sidelobe Intensity a

Tables Icon

Table 2 Effective Sample Point Numbers Used in Fig. 5 a

Equations (9)

Equations on this page are rendered with MathJax. Learn more.

size image = size object × z out / z in ,
U 2 _ ind ( y ) = D cos ( ψ ) exp ( j k R ) cos ( ψ ) R ,
cos ( ψ ) = z in R ,
R = z in 1 + ( y β z in ) 2 ,
U 2 _ ind ( y , z in ) = D [ cos ( ψ ) ] 3 / 2 exp ( j k R ) R = D 1 [ 1 + ( y β z in ) ] 3 / 4 × exp [ j k z in 1 + ( y β z in ) 2 ] z in 1 + ( y β z in ) 2 = D exp [ j k z in 1 + ( y β z in ) 2 ] z in [ 1 + ( y β z in ) ] 5 / 4 .
I out ( y ) = [ U out ( y ) ] 2 = β = w / 2 β = w / 2 | P z out { U 2 _ ind ( y , z in ) × exp [ j ( ϕ DOE + ϕ lens ) ] } | 2 ,
z in { 1 + ( y β z in ) 2 } 5 / 4
z in [ 1 + ( y β z in ) 2 ] .
S = max [ I out ( y y signal ) ] max [ I out ( y y signal ) ] ,

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