Abstract

We report the first experimental demonstration of Gaussian beam-shaping based on the Generalized Phase Contrast (GPC) approach. We show that, when using a dynamic spatial light modulator (SLM), this approach can rapidly generate arbitrarily shaped beams. Moreover, we demonstrate that low-cost binary-phase optics fabricated using photolithography and chemical etching techniques can replace the SLM in static and high power beam shaping applications. The design parameters for the binary-phase elements of the module are chosen according to the results of our previously conducted analysis and numerical demonstrations [Opt. Express 15, 11971 (2007)]. Beams with a variety of cross-sections such as circular, rectangular and square, with near flat-top intensity distributions are demonstrated. GPC-based beam shaping is inherently speckle-free and the shaped beams maintain a flat output phase. The non-absorbing components used in this beam-shaping approach have a high-damage-threshold and are thus ideally suited for high power applications.

©2011 Optical Society of America

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References

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  1. F. M. Dickey, and S. C. Holswade, Laser Beam Shaping: Theory and Techniques (Marcel Dekker, New York, 2000).
  2. H. Herzig, Micro-Optics: Elements, Systems & Applications (Taylor and Francis Ltd, London (1997).
  3. W. B. Veldkamp, “Laser beam profile shaping with binary diffraction grating,” Opt. Commun. 38(5-6), 381–386 (1981).
    [Crossref]
  4. A. J. Caley, M. J. Thomson, J. Liu, A. J. Waddie, and M. R. Taghizadeh, “Diffractive optical elements for high gain lasers with arbitrary output beam profiles,” Opt. Express 15(17), 10699–10704 (2007).
    [Crossref] [PubMed]
  5. J. Cordingley, “Application of a binary diffractive optic for beam shaping in semiconductor processing by lasers,” Appl. Opt. 32(14), 2538–2542 (1993).
    [Crossref] [PubMed]
  6. C. Dorrer, “High-damage-threshold beam shaping using binary phase plates,” Opt. Lett. 34(15), 2330–2332 (2009).
    [Crossref] [PubMed]
  7. M. A. Karim, A. M. Hanafi, F. Hussain, S. Mustafa, Z. Samberid, and N. M. Zain, “Realization of a uniform circular source using a two-dimensional binary filter,” Opt. Lett. 10(10), 470–471 (1985).
    [Crossref] [PubMed]
  8. R. Brandstetter and K. Leib, “Fabrication of a binary phase only filter (BPOF) on transparency film,” Opt. Laser Technol. 23(4), 247–250 (1991).
    [Crossref]
  9. J. Yang and M. Wang, “Analysis and optimization on single-zone binary flat-top beam shaper,” Opt. Eng. 42(11), 3106–3113 (2003).
    [Crossref]
  10. J. S. Liu and M. R. Taghizadeh, “Iterative algorithm for the design of diffractive phase elements for laser beam shaping,” Opt. Lett. 27(16), 1463–1465 (2002).
    [Crossref]
  11. Y. Lin, T. J. Kessler, and G. N. Lawrence, “Distributed phase plates for super-Gaussian focal-plane irradiance profiles,” Opt. Lett. 20(7), 764–766 (1995).
    [Crossref] [PubMed]
  12. X. Deng, Y. Li, D. Fan, and Y. Qiu, “Pure-phase plates for super-Gaussian focal-plane irradiance profile generations of extremely high order,” Opt. Lett. 21(24), 1963–1965 (1995).
    [Crossref]
  13. X. Tan, B. Y. Gu, G. Z. Yang, and B. Z. Dong, “Diffractive phase elements for beam shaping: a new design method,” Appl. Opt. 34(8), 1314–1320 (1995).
    [Crossref] [PubMed]
  14. J. Glückstad, and D. Palima, “Generalized Phase Contrast: Applications in Optics and Photonics,” Springer Series in Optical Sciences146, (2009) 310.
  15. F. Zernike, “How I discovered phase contrast,” Science 121(3141), 345–349 (1955).
    [Crossref] [PubMed]
  16. P. J. Rodrigo, V. R. Daria, and J. Glückstad, “Real-time interactive optical micromanipulation of a mixture of high-and low-index particles,” Opt. Express 12(7), 1417–1425 (2004).
    [Crossref] [PubMed]
  17. V. R. Daria, P. J. Rodrigo, and J. Glückstad, “Dynamic array of dark optical traps,” Appl. Phys. Lett. 84(3), 323–325 (2004).
    [Crossref]
  18. P. J. Rodrigo, L. Gammelgaard, P. Bøggild, I. Perch-Nielsen, and J. Glückstad, “Actuation of microfabricated tools using multiple GPC-based counterpropagating-beam traps,” Opt. Express 13(18), 6899–6904 (2005).
    [Crossref] [PubMed]
  19. E. Papagiakoumou, F. Anselmi, A. Begue, V. de Sars, J. Glückstad, E. Y. Isacoff, and V. Emiliani, “Scanless two-photon excitation of channelrhodopsin-2,” Nat. Methods 7(10), 848–854 (2010).
    [Crossref] [PubMed]
  20. P. C. Mogensen, R. L. Eriksen, and J. Glückstad, “High capacity optical encryption system using ferro-electric spatial light modulators,” J. Opt. A, Pure Appl. Opt. 3(1), 10–15 (2001).
    [Crossref]
  21. P. C. Mogensen and J. Glückstad, “Phase-only optical decryption of a fixed mask,” Appl. Opt. 40(8), 1226–1235 (2001).
    [Crossref]
  22. P. J. Rodrigo, D. Palima, and J. Glückstad, “Accurate quantitative phase imaging using generalized phase contrast,” Opt. Express 16(4), 2740–2751 (2008).
    [Crossref] [PubMed]
  23. D. Palima, C. A. Alonzo, P. J. Rodrigo, and J. Glückstad, “Generalized phase contrast matched to Gaussian illumination,” Opt. Express 15(19), 11971–11977 (2007).
    [Crossref] [PubMed]
  24. D. Palima and J. Glückstad, “Gaussian to uniform intensity shaper based on generalized phase contrast,” Opt. Express 16(3), 1507–1516 (2008).
    [Crossref] [PubMed]
  25. C. Maurer, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “What Spatial Light modulators can do for optical microscopy,” Laser Photon. Rev. 5(1), 81–101 (2011).
    [Crossref]
  26. J. Glückstad and P. C. Mogensen, “Reconfigurable ternary-phase array illuminator based on the generalised phase contrast method,” Opt. Commun. 173(1-6), 169–175 (2000).
    [Crossref]
  27. D. Palima and J. Glückstad, “Multi-wavelength spatial light shaping using generalized phase contrast,” Opt. Express 16(2), 1331–1342 (2008).
    [Crossref] [PubMed]
  28. Z. Kuang, W. Perrie, J. Leach, M. Sharp, S. P. Edwardson, M. Padgett, G. Dearden, and K. G. Watkins, “High throughput diffractive multi-beam femtosecond laser processing using a spatial light modulator,” Appl. Surf. Sci. 255(5), 2284–2289 (2008).
    [Crossref]

2011 (1)

C. Maurer, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “What Spatial Light modulators can do for optical microscopy,” Laser Photon. Rev. 5(1), 81–101 (2011).
[Crossref]

2010 (1)

E. Papagiakoumou, F. Anselmi, A. Begue, V. de Sars, J. Glückstad, E. Y. Isacoff, and V. Emiliani, “Scanless two-photon excitation of channelrhodopsin-2,” Nat. Methods 7(10), 848–854 (2010).
[Crossref] [PubMed]

2009 (1)

2008 (4)

2007 (2)

2005 (1)

2004 (2)

2003 (1)

J. Yang and M. Wang, “Analysis and optimization on single-zone binary flat-top beam shaper,” Opt. Eng. 42(11), 3106–3113 (2003).
[Crossref]

2002 (1)

2001 (2)

P. C. Mogensen, R. L. Eriksen, and J. Glückstad, “High capacity optical encryption system using ferro-electric spatial light modulators,” J. Opt. A, Pure Appl. Opt. 3(1), 10–15 (2001).
[Crossref]

P. C. Mogensen and J. Glückstad, “Phase-only optical decryption of a fixed mask,” Appl. Opt. 40(8), 1226–1235 (2001).
[Crossref]

2000 (1)

J. Glückstad and P. C. Mogensen, “Reconfigurable ternary-phase array illuminator based on the generalised phase contrast method,” Opt. Commun. 173(1-6), 169–175 (2000).
[Crossref]

1995 (3)

1993 (1)

1991 (1)

R. Brandstetter and K. Leib, “Fabrication of a binary phase only filter (BPOF) on transparency film,” Opt. Laser Technol. 23(4), 247–250 (1991).
[Crossref]

1985 (1)

1981 (1)

W. B. Veldkamp, “Laser beam profile shaping with binary diffraction grating,” Opt. Commun. 38(5-6), 381–386 (1981).
[Crossref]

1955 (1)

F. Zernike, “How I discovered phase contrast,” Science 121(3141), 345–349 (1955).
[Crossref] [PubMed]

Alonzo, C. A.

Anselmi, F.

E. Papagiakoumou, F. Anselmi, A. Begue, V. de Sars, J. Glückstad, E. Y. Isacoff, and V. Emiliani, “Scanless two-photon excitation of channelrhodopsin-2,” Nat. Methods 7(10), 848–854 (2010).
[Crossref] [PubMed]

Begue, A.

E. Papagiakoumou, F. Anselmi, A. Begue, V. de Sars, J. Glückstad, E. Y. Isacoff, and V. Emiliani, “Scanless two-photon excitation of channelrhodopsin-2,” Nat. Methods 7(10), 848–854 (2010).
[Crossref] [PubMed]

Bernet, S.

C. Maurer, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “What Spatial Light modulators can do for optical microscopy,” Laser Photon. Rev. 5(1), 81–101 (2011).
[Crossref]

Bøggild, P.

Brandstetter, R.

R. Brandstetter and K. Leib, “Fabrication of a binary phase only filter (BPOF) on transparency film,” Opt. Laser Technol. 23(4), 247–250 (1991).
[Crossref]

Caley, A. J.

Cordingley, J.

Daria, V. R.

de Sars, V.

E. Papagiakoumou, F. Anselmi, A. Begue, V. de Sars, J. Glückstad, E. Y. Isacoff, and V. Emiliani, “Scanless two-photon excitation of channelrhodopsin-2,” Nat. Methods 7(10), 848–854 (2010).
[Crossref] [PubMed]

Dearden, G.

Z. Kuang, W. Perrie, J. Leach, M. Sharp, S. P. Edwardson, M. Padgett, G. Dearden, and K. G. Watkins, “High throughput diffractive multi-beam femtosecond laser processing using a spatial light modulator,” Appl. Surf. Sci. 255(5), 2284–2289 (2008).
[Crossref]

Deng, X.

Dong, B. Z.

Dorrer, C.

Edwardson, S. P.

Z. Kuang, W. Perrie, J. Leach, M. Sharp, S. P. Edwardson, M. Padgett, G. Dearden, and K. G. Watkins, “High throughput diffractive multi-beam femtosecond laser processing using a spatial light modulator,” Appl. Surf. Sci. 255(5), 2284–2289 (2008).
[Crossref]

Emiliani, V.

E. Papagiakoumou, F. Anselmi, A. Begue, V. de Sars, J. Glückstad, E. Y. Isacoff, and V. Emiliani, “Scanless two-photon excitation of channelrhodopsin-2,” Nat. Methods 7(10), 848–854 (2010).
[Crossref] [PubMed]

Eriksen, R. L.

P. C. Mogensen, R. L. Eriksen, and J. Glückstad, “High capacity optical encryption system using ferro-electric spatial light modulators,” J. Opt. A, Pure Appl. Opt. 3(1), 10–15 (2001).
[Crossref]

Fan, D.

Gammelgaard, L.

Glückstad, J.

E. Papagiakoumou, F. Anselmi, A. Begue, V. de Sars, J. Glückstad, E. Y. Isacoff, and V. Emiliani, “Scanless two-photon excitation of channelrhodopsin-2,” Nat. Methods 7(10), 848–854 (2010).
[Crossref] [PubMed]

D. Palima and J. Glückstad, “Multi-wavelength spatial light shaping using generalized phase contrast,” Opt. Express 16(2), 1331–1342 (2008).
[Crossref] [PubMed]

P. J. Rodrigo, D. Palima, and J. Glückstad, “Accurate quantitative phase imaging using generalized phase contrast,” Opt. Express 16(4), 2740–2751 (2008).
[Crossref] [PubMed]

D. Palima and J. Glückstad, “Gaussian to uniform intensity shaper based on generalized phase contrast,” Opt. Express 16(3), 1507–1516 (2008).
[Crossref] [PubMed]

D. Palima, C. A. Alonzo, P. J. Rodrigo, and J. Glückstad, “Generalized phase contrast matched to Gaussian illumination,” Opt. Express 15(19), 11971–11977 (2007).
[Crossref] [PubMed]

P. J. Rodrigo, L. Gammelgaard, P. Bøggild, I. Perch-Nielsen, and J. Glückstad, “Actuation of microfabricated tools using multiple GPC-based counterpropagating-beam traps,” Opt. Express 13(18), 6899–6904 (2005).
[Crossref] [PubMed]

V. R. Daria, P. J. Rodrigo, and J. Glückstad, “Dynamic array of dark optical traps,” Appl. Phys. Lett. 84(3), 323–325 (2004).
[Crossref]

P. J. Rodrigo, V. R. Daria, and J. Glückstad, “Real-time interactive optical micromanipulation of a mixture of high-and low-index particles,” Opt. Express 12(7), 1417–1425 (2004).
[Crossref] [PubMed]

P. C. Mogensen and J. Glückstad, “Phase-only optical decryption of a fixed mask,” Appl. Opt. 40(8), 1226–1235 (2001).
[Crossref]

P. C. Mogensen, R. L. Eriksen, and J. Glückstad, “High capacity optical encryption system using ferro-electric spatial light modulators,” J. Opt. A, Pure Appl. Opt. 3(1), 10–15 (2001).
[Crossref]

J. Glückstad and P. C. Mogensen, “Reconfigurable ternary-phase array illuminator based on the generalised phase contrast method,” Opt. Commun. 173(1-6), 169–175 (2000).
[Crossref]

Gu, B. Y.

Hanafi, A. M.

Hussain, F.

Isacoff, E. Y.

E. Papagiakoumou, F. Anselmi, A. Begue, V. de Sars, J. Glückstad, E. Y. Isacoff, and V. Emiliani, “Scanless two-photon excitation of channelrhodopsin-2,” Nat. Methods 7(10), 848–854 (2010).
[Crossref] [PubMed]

Jesacher, A.

C. Maurer, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “What Spatial Light modulators can do for optical microscopy,” Laser Photon. Rev. 5(1), 81–101 (2011).
[Crossref]

Karim, M. A.

Kessler, T. J.

Kuang, Z.

Z. Kuang, W. Perrie, J. Leach, M. Sharp, S. P. Edwardson, M. Padgett, G. Dearden, and K. G. Watkins, “High throughput diffractive multi-beam femtosecond laser processing using a spatial light modulator,” Appl. Surf. Sci. 255(5), 2284–2289 (2008).
[Crossref]

Lawrence, G. N.

Leach, J.

Z. Kuang, W. Perrie, J. Leach, M. Sharp, S. P. Edwardson, M. Padgett, G. Dearden, and K. G. Watkins, “High throughput diffractive multi-beam femtosecond laser processing using a spatial light modulator,” Appl. Surf. Sci. 255(5), 2284–2289 (2008).
[Crossref]

Leib, K.

R. Brandstetter and K. Leib, “Fabrication of a binary phase only filter (BPOF) on transparency film,” Opt. Laser Technol. 23(4), 247–250 (1991).
[Crossref]

Li, Y.

Lin, Y.

Liu, J.

Liu, J. S.

Maurer, C.

C. Maurer, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “What Spatial Light modulators can do for optical microscopy,” Laser Photon. Rev. 5(1), 81–101 (2011).
[Crossref]

Mogensen, P. C.

P. C. Mogensen, R. L. Eriksen, and J. Glückstad, “High capacity optical encryption system using ferro-electric spatial light modulators,” J. Opt. A, Pure Appl. Opt. 3(1), 10–15 (2001).
[Crossref]

P. C. Mogensen and J. Glückstad, “Phase-only optical decryption of a fixed mask,” Appl. Opt. 40(8), 1226–1235 (2001).
[Crossref]

J. Glückstad and P. C. Mogensen, “Reconfigurable ternary-phase array illuminator based on the generalised phase contrast method,” Opt. Commun. 173(1-6), 169–175 (2000).
[Crossref]

Mustafa, S.

Padgett, M.

Z. Kuang, W. Perrie, J. Leach, M. Sharp, S. P. Edwardson, M. Padgett, G. Dearden, and K. G. Watkins, “High throughput diffractive multi-beam femtosecond laser processing using a spatial light modulator,” Appl. Surf. Sci. 255(5), 2284–2289 (2008).
[Crossref]

Palima, D.

Papagiakoumou, E.

E. Papagiakoumou, F. Anselmi, A. Begue, V. de Sars, J. Glückstad, E. Y. Isacoff, and V. Emiliani, “Scanless two-photon excitation of channelrhodopsin-2,” Nat. Methods 7(10), 848–854 (2010).
[Crossref] [PubMed]

Perch-Nielsen, I.

Perrie, W.

Z. Kuang, W. Perrie, J. Leach, M. Sharp, S. P. Edwardson, M. Padgett, G. Dearden, and K. G. Watkins, “High throughput diffractive multi-beam femtosecond laser processing using a spatial light modulator,” Appl. Surf. Sci. 255(5), 2284–2289 (2008).
[Crossref]

Qiu, Y.

Ritsch-Marte, M.

C. Maurer, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “What Spatial Light modulators can do for optical microscopy,” Laser Photon. Rev. 5(1), 81–101 (2011).
[Crossref]

Rodrigo, P. J.

Samberid, Z.

Sharp, M.

Z. Kuang, W. Perrie, J. Leach, M. Sharp, S. P. Edwardson, M. Padgett, G. Dearden, and K. G. Watkins, “High throughput diffractive multi-beam femtosecond laser processing using a spatial light modulator,” Appl. Surf. Sci. 255(5), 2284–2289 (2008).
[Crossref]

Taghizadeh, M. R.

Tan, X.

Thomson, M. J.

Veldkamp, W. B.

W. B. Veldkamp, “Laser beam profile shaping with binary diffraction grating,” Opt. Commun. 38(5-6), 381–386 (1981).
[Crossref]

Waddie, A. J.

Wang, M.

J. Yang and M. Wang, “Analysis and optimization on single-zone binary flat-top beam shaper,” Opt. Eng. 42(11), 3106–3113 (2003).
[Crossref]

Watkins, K. G.

Z. Kuang, W. Perrie, J. Leach, M. Sharp, S. P. Edwardson, M. Padgett, G. Dearden, and K. G. Watkins, “High throughput diffractive multi-beam femtosecond laser processing using a spatial light modulator,” Appl. Surf. Sci. 255(5), 2284–2289 (2008).
[Crossref]

Yang, G. Z.

Yang, J.

J. Yang and M. Wang, “Analysis and optimization on single-zone binary flat-top beam shaper,” Opt. Eng. 42(11), 3106–3113 (2003).
[Crossref]

Zain, N. M.

Zernike, F.

F. Zernike, “How I discovered phase contrast,” Science 121(3141), 345–349 (1955).
[Crossref] [PubMed]

Appl. Opt. (3)

Appl. Phys. Lett. (1)

V. R. Daria, P. J. Rodrigo, and J. Glückstad, “Dynamic array of dark optical traps,” Appl. Phys. Lett. 84(3), 323–325 (2004).
[Crossref]

Appl. Surf. Sci. (1)

Z. Kuang, W. Perrie, J. Leach, M. Sharp, S. P. Edwardson, M. Padgett, G. Dearden, and K. G. Watkins, “High throughput diffractive multi-beam femtosecond laser processing using a spatial light modulator,” Appl. Surf. Sci. 255(5), 2284–2289 (2008).
[Crossref]

J. Opt. A, Pure Appl. Opt. (1)

P. C. Mogensen, R. L. Eriksen, and J. Glückstad, “High capacity optical encryption system using ferro-electric spatial light modulators,” J. Opt. A, Pure Appl. Opt. 3(1), 10–15 (2001).
[Crossref]

Laser Photon. Rev. (1)

C. Maurer, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “What Spatial Light modulators can do for optical microscopy,” Laser Photon. Rev. 5(1), 81–101 (2011).
[Crossref]

Nat. Methods (1)

E. Papagiakoumou, F. Anselmi, A. Begue, V. de Sars, J. Glückstad, E. Y. Isacoff, and V. Emiliani, “Scanless two-photon excitation of channelrhodopsin-2,” Nat. Methods 7(10), 848–854 (2010).
[Crossref] [PubMed]

Opt. Commun. (2)

W. B. Veldkamp, “Laser beam profile shaping with binary diffraction grating,” Opt. Commun. 38(5-6), 381–386 (1981).
[Crossref]

J. Glückstad and P. C. Mogensen, “Reconfigurable ternary-phase array illuminator based on the generalised phase contrast method,” Opt. Commun. 173(1-6), 169–175 (2000).
[Crossref]

Opt. Eng. (1)

J. Yang and M. Wang, “Analysis and optimization on single-zone binary flat-top beam shaper,” Opt. Eng. 42(11), 3106–3113 (2003).
[Crossref]

Opt. Express (7)

Opt. Laser Technol. (1)

R. Brandstetter and K. Leib, “Fabrication of a binary phase only filter (BPOF) on transparency film,” Opt. Laser Technol. 23(4), 247–250 (1991).
[Crossref]

Opt. Lett. (5)

Science (1)

F. Zernike, “How I discovered phase contrast,” Science 121(3141), 345–349 (1955).
[Crossref] [PubMed]

Other (3)

J. Glückstad, and D. Palima, “Generalized Phase Contrast: Applications in Optics and Photonics,” Springer Series in Optical Sciences146, (2009) 310.

F. M. Dickey, and S. C. Holswade, Laser Beam Shaping: Theory and Techniques (Marcel Dekker, New York, 2000).

H. Herzig, Micro-Optics: Elements, Systems & Applications (Taylor and Francis Ltd, London (1997).

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Figures (5)

Fig. 1
Fig. 1 A typical Gaussian beam-shaping Generalized Phase Contrast (GPC) setup. An optimized phase contrast filter (PCF) simultaneously creates an image of the phase object and a co-propagating reference wave that transform this into a high-contrast interference pattern. Without any intrinsic randomness, this image-and-interfere scheme is inherently speckle-free.

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Fig. 2
Fig. 2 Efficiency and beam uniformity in GPC-based Gaussian beam shaping: (a) Efficiency of different beam patterns vs. PCF size. The displayed legend shows experimentally obtained beam patterns for a 40μm PCF size. (b) Radial variation of the intensity for a circular beam shows a 30% intensity rolloff. This rolloff is reduced to 14%, without losing efficiency, using input phase corrections.

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Fig. 3
Fig. 3 Schematic diagram of the GPC beam-shaping setup. The input beam is expanded by lenses L1 (f1 = –100mm) and L2 (f2 = +250mm). Fourier lenses L3 and L4 both have focal lengths of 200 mm. The PCF is a phase-only filter that creates a π-phase shift over an on-axis circular region (diameter, 2R ~ 40µm) in the spatial Fourier plane.

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Fig. 4
Fig. 4 Shaping of a Gaussian into a near top-hat beam: (a) Output image when the filter in the Fourier plane (FP) is removed; (b) Output image when an optimal filter is inserted to shape the beam into a top-hat; (c) Line scans through Figs. 4a (black) and 4b (red), respectively.

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Fig. 5
Fig. 5 a) and c) are square and rectangular profiles obtained by shaping the circular Gaussian beam. 5b and 5d are the line scans through the respective images. The red line indicates the horizontal scan through the reshaped profile and the black trace is that of the input Gaussian.

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