Abstract

UV laser induced damage (LID) on exit surface of fused silica could cause modulation effect to transmitted beam and further influence downstream propagation properties. This paper presents our experimental and analytical studies on this topic. In experiment, a series of measurement instruments are applied, including beam profiler, interferometer, microscope, and optical coherent tomography (OCT). Creating and characterizing of LID on fused silica sample have been implemented. Morphological features are studied based on their particular modulation effects on transmitted beam. In theoretical investigation, analytical modeling and numerical simulation are performed. Modulation effects from amplitude, phase, and size factors are analyzed respectively. Furthermore, we have novelly designed a simplified polygon model to simulate actual damage site with multiform modulation features, and the simulation results demonstrate that the modeling is usable and representative.

©2013 Optical Society of America

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  1. F. O. Génin, M. D. Feit, M. R. Kozlowski, A. M. Rubenchik, A. Salleo, and J. Yoshiyama, “Rear-surface laser damage on 355-nm silica optics owing to Fresnel diffraction on front-surface contamination particles,” Appl. Opt. 39(21), 3654–3663 (2000).
    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
  4. S. Mainguy, I. Tovena-Pecault, and B. Le Garrec, “Propagation of LIL/LMJ beams under the interaction with contamination particles,” Proc. SPIE 5991, 59910G, 59910G-9 (2005).
    [Crossref]
  5. M. J. Matthews, L. L. Bass, G. M. Guss, C. C. Widmayer, and F. L. Ravizza, “Downstream Intensification Effects Associated with CO2 Laser Mitigation of Fused Silica,” Proc. SPIE 6720, 67200A, 67200A-9 (2007).
    [Crossref]
  6. J. R. Schmidt, M. J. Runkel, K. E. Martin, and C. J. Stolz, “Scattering-induced downstream beam modulation by plasma scalded mirrors,” Proc. SPIE 6720, 67201H, 67201H-10 (2007).
    [Crossref]
  7. B. Bertussi, P. Cormont, S. Palmier, P. Legros, and J. L. Rullier, “Initiation of laser-induced damage sites in fused silica optical components,” Opt. Express 17(14), 11469–11479 (2009).
    [Crossref] [PubMed]
  8. R. A. Negres, M. A. Norton, D. A. Cross, and C. W. Carr, “Growth behavior of laser-induced damage on fused silica optics under UV, ns laser irradiation,” Opt. Express 18(19), 19966–19976 (2010).
    [Crossref] [PubMed]
  9. C. W. Carr, J. B. Trenholme, and M. L. Spaeth, “Effect of temporal pulse shape on optical damage,” Appl. Phys. Lett. 90(4), 041110 (2007).
    [Crossref]
  10. M. R. Kozlowski, R. Mouser, S. Maricle, P. Wegner, and T. Weiland, “Laser damage performance of fused silica optical components measured on the Beamlet laser at 351nm,” Proc. SPIE 3578, 436–445 (1999).
    [Crossref]
  11. S. G. Demos, M. Staggs, and M. R. Kozlowski, “Investigation of processes leading to damage growth in optical materials for large-aperture lasers,” Appl. Opt. 41(18), 3628–3633 (2002).
    [Crossref] [PubMed]
  12. E. Mendez, K. M. Nowak, H. J. Baker, F. J. Villarreal, and D. R. Hall, “Localized CO2 laser damage repair of fused silica optics,” Appl. Opt. 45(21), 5358–5367 (2006).
    [Crossref] [PubMed]
  13. I. L. Bass, V. G. Draggoo, G. M. Guss, R. P. Hackel, and M. A. Norton, “Mitigation of laser damage growth in fused silica NIF optics with a galvanometer scanned CO2 laser,” Proc. SPIE 6261, 62612A, 62612A-10 (2006).
    [Crossref]
  14. S. T. Yang, M. J. Matthew, S. Elhadj, D. Cooke, G. M. Guss, V. G. Draggoo, and P. J. Wegner, “Comparing the use of mid-infrared versus far-infrared lasers for mitigating damage growth on fused silica,” Appl. Opt. 49(14), 2606–2616 (2010).
    [Crossref]
  15. J. T. Hunt, K. R. Manes, and P. A. Renard, “Hot images from obscurations,” Appl. Opt. 32(30), 5973–5982 (1993).
    [Crossref] [PubMed]
  16. M. D. Feit and A. M. Rubenchik, “Influence of subsurface cracks on laser induced surface damage,” Proc. SPIE 5273, 264–271 (2004).
    [Crossref]
  17. C. C. Widmayer, M. R. Nickels, and D. Milam, “Nonlinear holographic imaging of phase errors,” Appl. Opt. 37(21), 4801–4805 (1998).
    [Crossref] [PubMed]
  18. J. Wong, J. L. Ferriera, E. F. Lindsey, D. L. Haupt, I. D. Hutcheon, and J. H. Kinney, “Morphology and microstructure in fused silica induced by high fluence ultraviolet 3ω (355nm) laser pulses,” J. Non-Cryst. Solids 352(3), 255–272 (2006).
    [Crossref]
  19. S. G. Demos, M. Staggs, K. Minoshima, and J. Fujimoto, “Characterization of laser induced damage sites in optical components,” Opt. Express 10(25), 1444–1450 (2002).
    [Crossref] [PubMed]
  20. C. W. Carr, M. J. Matthews, J. D. Bude, and M. L. Spaeth, “The effect of laser pulse duration on laser-induced damage in KDP and SiO2,” Proc. SPIE 6403, 64030K, 64030K-9 (2006).
    [Crossref]

2010 (2)

2009 (1)

2007 (3)

M. J. Matthews, L. L. Bass, G. M. Guss, C. C. Widmayer, and F. L. Ravizza, “Downstream Intensification Effects Associated with CO2 Laser Mitigation of Fused Silica,” Proc. SPIE 6720, 67200A, 67200A-9 (2007).
[Crossref]

J. R. Schmidt, M. J. Runkel, K. E. Martin, and C. J. Stolz, “Scattering-induced downstream beam modulation by plasma scalded mirrors,” Proc. SPIE 6720, 67201H, 67201H-10 (2007).
[Crossref]

C. W. Carr, J. B. Trenholme, and M. L. Spaeth, “Effect of temporal pulse shape on optical damage,” Appl. Phys. Lett. 90(4), 041110 (2007).
[Crossref]

2006 (4)

I. L. Bass, V. G. Draggoo, G. M. Guss, R. P. Hackel, and M. A. Norton, “Mitigation of laser damage growth in fused silica NIF optics with a galvanometer scanned CO2 laser,” Proc. SPIE 6261, 62612A, 62612A-10 (2006).
[Crossref]

J. Wong, J. L. Ferriera, E. F. Lindsey, D. L. Haupt, I. D. Hutcheon, and J. H. Kinney, “Morphology and microstructure in fused silica induced by high fluence ultraviolet 3ω (355nm) laser pulses,” J. Non-Cryst. Solids 352(3), 255–272 (2006).
[Crossref]

C. W. Carr, M. J. Matthews, J. D. Bude, and M. L. Spaeth, “The effect of laser pulse duration on laser-induced damage in KDP and SiO2,” Proc. SPIE 6403, 64030K, 64030K-9 (2006).
[Crossref]

E. Mendez, K. M. Nowak, H. J. Baker, F. J. Villarreal, and D. R. Hall, “Localized CO2 laser damage repair of fused silica optics,” Appl. Opt. 45(21), 5358–5367 (2006).
[Crossref] [PubMed]

2005 (2)

S. Mainguy, B. Le Garrec, and M. Josse, “Downstream impact of flaws on the LIL/LMJ laser lines,” Proc. SPIE 5991, 599105, 599105-9 (2005).
[Crossref]

S. Mainguy, I. Tovena-Pecault, and B. Le Garrec, “Propagation of LIL/LMJ beams under the interaction with contamination particles,” Proc. SPIE 5991, 59910G, 59910G-9 (2005).
[Crossref]

2004 (1)

M. D. Feit and A. M. Rubenchik, “Influence of subsurface cracks on laser induced surface damage,” Proc. SPIE 5273, 264–271 (2004).
[Crossref]

2003 (1)

O. Morice, “Miro: Complete modeling and software for pulse amplification and propagation in high-power laser system,” Opt. Eng. 42(6), 1530–1541 (2003).
[Crossref]

2002 (2)

2000 (1)

1999 (1)

M. R. Kozlowski, R. Mouser, S. Maricle, P. Wegner, and T. Weiland, “Laser damage performance of fused silica optical components measured on the Beamlet laser at 351nm,” Proc. SPIE 3578, 436–445 (1999).
[Crossref]

1998 (1)

1993 (1)

Baker, H. J.

Bass, I. L.

I. L. Bass, V. G. Draggoo, G. M. Guss, R. P. Hackel, and M. A. Norton, “Mitigation of laser damage growth in fused silica NIF optics with a galvanometer scanned CO2 laser,” Proc. SPIE 6261, 62612A, 62612A-10 (2006).
[Crossref]

Bass, L. L.

M. J. Matthews, L. L. Bass, G. M. Guss, C. C. Widmayer, and F. L. Ravizza, “Downstream Intensification Effects Associated with CO2 Laser Mitigation of Fused Silica,” Proc. SPIE 6720, 67200A, 67200A-9 (2007).
[Crossref]

Bertussi, B.

Bude, J. D.

C. W. Carr, M. J. Matthews, J. D. Bude, and M. L. Spaeth, “The effect of laser pulse duration on laser-induced damage in KDP and SiO2,” Proc. SPIE 6403, 64030K, 64030K-9 (2006).
[Crossref]

Carr, C. W.

R. A. Negres, M. A. Norton, D. A. Cross, and C. W. Carr, “Growth behavior of laser-induced damage on fused silica optics under UV, ns laser irradiation,” Opt. Express 18(19), 19966–19976 (2010).
[Crossref] [PubMed]

C. W. Carr, J. B. Trenholme, and M. L. Spaeth, “Effect of temporal pulse shape on optical damage,” Appl. Phys. Lett. 90(4), 041110 (2007).
[Crossref]

C. W. Carr, M. J. Matthews, J. D. Bude, and M. L. Spaeth, “The effect of laser pulse duration on laser-induced damage in KDP and SiO2,” Proc. SPIE 6403, 64030K, 64030K-9 (2006).
[Crossref]

Cooke, D.

Cormont, P.

Cross, D. A.

Demos, S. G.

Draggoo, V. G.

S. T. Yang, M. J. Matthew, S. Elhadj, D. Cooke, G. M. Guss, V. G. Draggoo, and P. J. Wegner, “Comparing the use of mid-infrared versus far-infrared lasers for mitigating damage growth on fused silica,” Appl. Opt. 49(14), 2606–2616 (2010).
[Crossref]

I. L. Bass, V. G. Draggoo, G. M. Guss, R. P. Hackel, and M. A. Norton, “Mitigation of laser damage growth in fused silica NIF optics with a galvanometer scanned CO2 laser,” Proc. SPIE 6261, 62612A, 62612A-10 (2006).
[Crossref]

Elhadj, S.

Feit, M. D.

Ferriera, J. L.

J. Wong, J. L. Ferriera, E. F. Lindsey, D. L. Haupt, I. D. Hutcheon, and J. H. Kinney, “Morphology and microstructure in fused silica induced by high fluence ultraviolet 3ω (355nm) laser pulses,” J. Non-Cryst. Solids 352(3), 255–272 (2006).
[Crossref]

Fujimoto, J.

Génin, F. O.

Guss, G. M.

S. T. Yang, M. J. Matthew, S. Elhadj, D. Cooke, G. M. Guss, V. G. Draggoo, and P. J. Wegner, “Comparing the use of mid-infrared versus far-infrared lasers for mitigating damage growth on fused silica,” Appl. Opt. 49(14), 2606–2616 (2010).
[Crossref]

M. J. Matthews, L. L. Bass, G. M. Guss, C. C. Widmayer, and F. L. Ravizza, “Downstream Intensification Effects Associated with CO2 Laser Mitigation of Fused Silica,” Proc. SPIE 6720, 67200A, 67200A-9 (2007).
[Crossref]

I. L. Bass, V. G. Draggoo, G. M. Guss, R. P. Hackel, and M. A. Norton, “Mitigation of laser damage growth in fused silica NIF optics with a galvanometer scanned CO2 laser,” Proc. SPIE 6261, 62612A, 62612A-10 (2006).
[Crossref]

Hackel, R. P.

I. L. Bass, V. G. Draggoo, G. M. Guss, R. P. Hackel, and M. A. Norton, “Mitigation of laser damage growth in fused silica NIF optics with a galvanometer scanned CO2 laser,” Proc. SPIE 6261, 62612A, 62612A-10 (2006).
[Crossref]

Hall, D. R.

Haupt, D. L.

J. Wong, J. L. Ferriera, E. F. Lindsey, D. L. Haupt, I. D. Hutcheon, and J. H. Kinney, “Morphology and microstructure in fused silica induced by high fluence ultraviolet 3ω (355nm) laser pulses,” J. Non-Cryst. Solids 352(3), 255–272 (2006).
[Crossref]

Hunt, J. T.

Hutcheon, I. D.

J. Wong, J. L. Ferriera, E. F. Lindsey, D. L. Haupt, I. D. Hutcheon, and J. H. Kinney, “Morphology and microstructure in fused silica induced by high fluence ultraviolet 3ω (355nm) laser pulses,” J. Non-Cryst. Solids 352(3), 255–272 (2006).
[Crossref]

Josse, M.

S. Mainguy, B. Le Garrec, and M. Josse, “Downstream impact of flaws on the LIL/LMJ laser lines,” Proc. SPIE 5991, 599105, 599105-9 (2005).
[Crossref]

Kinney, J. H.

J. Wong, J. L. Ferriera, E. F. Lindsey, D. L. Haupt, I. D. Hutcheon, and J. H. Kinney, “Morphology and microstructure in fused silica induced by high fluence ultraviolet 3ω (355nm) laser pulses,” J. Non-Cryst. Solids 352(3), 255–272 (2006).
[Crossref]

Kozlowski, M. R.

Le Garrec, B.

S. Mainguy, I. Tovena-Pecault, and B. Le Garrec, “Propagation of LIL/LMJ beams under the interaction with contamination particles,” Proc. SPIE 5991, 59910G, 59910G-9 (2005).
[Crossref]

S. Mainguy, B. Le Garrec, and M. Josse, “Downstream impact of flaws on the LIL/LMJ laser lines,” Proc. SPIE 5991, 599105, 599105-9 (2005).
[Crossref]

Legros, P.

Lindsey, E. F.

J. Wong, J. L. Ferriera, E. F. Lindsey, D. L. Haupt, I. D. Hutcheon, and J. H. Kinney, “Morphology and microstructure in fused silica induced by high fluence ultraviolet 3ω (355nm) laser pulses,” J. Non-Cryst. Solids 352(3), 255–272 (2006).
[Crossref]

Mainguy, S.

S. Mainguy, B. Le Garrec, and M. Josse, “Downstream impact of flaws on the LIL/LMJ laser lines,” Proc. SPIE 5991, 599105, 599105-9 (2005).
[Crossref]

S. Mainguy, I. Tovena-Pecault, and B. Le Garrec, “Propagation of LIL/LMJ beams under the interaction with contamination particles,” Proc. SPIE 5991, 59910G, 59910G-9 (2005).
[Crossref]

Manes, K. R.

Maricle, S.

M. R. Kozlowski, R. Mouser, S. Maricle, P. Wegner, and T. Weiland, “Laser damage performance of fused silica optical components measured on the Beamlet laser at 351nm,” Proc. SPIE 3578, 436–445 (1999).
[Crossref]

Martin, K. E.

J. R. Schmidt, M. J. Runkel, K. E. Martin, and C. J. Stolz, “Scattering-induced downstream beam modulation by plasma scalded mirrors,” Proc. SPIE 6720, 67201H, 67201H-10 (2007).
[Crossref]

Matthew, M. J.

Matthews, M. J.

M. J. Matthews, L. L. Bass, G. M. Guss, C. C. Widmayer, and F. L. Ravizza, “Downstream Intensification Effects Associated with CO2 Laser Mitigation of Fused Silica,” Proc. SPIE 6720, 67200A, 67200A-9 (2007).
[Crossref]

C. W. Carr, M. J. Matthews, J. D. Bude, and M. L. Spaeth, “The effect of laser pulse duration on laser-induced damage in KDP and SiO2,” Proc. SPIE 6403, 64030K, 64030K-9 (2006).
[Crossref]

Mendez, E.

Milam, D.

Minoshima, K.

Morice, O.

O. Morice, “Miro: Complete modeling and software for pulse amplification and propagation in high-power laser system,” Opt. Eng. 42(6), 1530–1541 (2003).
[Crossref]

Mouser, R.

M. R. Kozlowski, R. Mouser, S. Maricle, P. Wegner, and T. Weiland, “Laser damage performance of fused silica optical components measured on the Beamlet laser at 351nm,” Proc. SPIE 3578, 436–445 (1999).
[Crossref]

Negres, R. A.

Nickels, M. R.

Norton, M. A.

R. A. Negres, M. A. Norton, D. A. Cross, and C. W. Carr, “Growth behavior of laser-induced damage on fused silica optics under UV, ns laser irradiation,” Opt. Express 18(19), 19966–19976 (2010).
[Crossref] [PubMed]

I. L. Bass, V. G. Draggoo, G. M. Guss, R. P. Hackel, and M. A. Norton, “Mitigation of laser damage growth in fused silica NIF optics with a galvanometer scanned CO2 laser,” Proc. SPIE 6261, 62612A, 62612A-10 (2006).
[Crossref]

Nowak, K. M.

Palmier, S.

Ravizza, F. L.

M. J. Matthews, L. L. Bass, G. M. Guss, C. C. Widmayer, and F. L. Ravizza, “Downstream Intensification Effects Associated with CO2 Laser Mitigation of Fused Silica,” Proc. SPIE 6720, 67200A, 67200A-9 (2007).
[Crossref]

Renard, P. A.

Rubenchik, A. M.

Rullier, J. L.

Runkel, M. J.

J. R. Schmidt, M. J. Runkel, K. E. Martin, and C. J. Stolz, “Scattering-induced downstream beam modulation by plasma scalded mirrors,” Proc. SPIE 6720, 67201H, 67201H-10 (2007).
[Crossref]

Salleo, A.

Schmidt, J. R.

J. R. Schmidt, M. J. Runkel, K. E. Martin, and C. J. Stolz, “Scattering-induced downstream beam modulation by plasma scalded mirrors,” Proc. SPIE 6720, 67201H, 67201H-10 (2007).
[Crossref]

Spaeth, M. L.

C. W. Carr, J. B. Trenholme, and M. L. Spaeth, “Effect of temporal pulse shape on optical damage,” Appl. Phys. Lett. 90(4), 041110 (2007).
[Crossref]

C. W. Carr, M. J. Matthews, J. D. Bude, and M. L. Spaeth, “The effect of laser pulse duration on laser-induced damage in KDP and SiO2,” Proc. SPIE 6403, 64030K, 64030K-9 (2006).
[Crossref]

Staggs, M.

Stolz, C. J.

J. R. Schmidt, M. J. Runkel, K. E. Martin, and C. J. Stolz, “Scattering-induced downstream beam modulation by plasma scalded mirrors,” Proc. SPIE 6720, 67201H, 67201H-10 (2007).
[Crossref]

Tovena-Pecault, I.

S. Mainguy, I. Tovena-Pecault, and B. Le Garrec, “Propagation of LIL/LMJ beams under the interaction with contamination particles,” Proc. SPIE 5991, 59910G, 59910G-9 (2005).
[Crossref]

Trenholme, J. B.

C. W. Carr, J. B. Trenholme, and M. L. Spaeth, “Effect of temporal pulse shape on optical damage,” Appl. Phys. Lett. 90(4), 041110 (2007).
[Crossref]

Villarreal, F. J.

Wegner, P.

M. R. Kozlowski, R. Mouser, S. Maricle, P. Wegner, and T. Weiland, “Laser damage performance of fused silica optical components measured on the Beamlet laser at 351nm,” Proc. SPIE 3578, 436–445 (1999).
[Crossref]

Wegner, P. J.

Weiland, T.

M. R. Kozlowski, R. Mouser, S. Maricle, P. Wegner, and T. Weiland, “Laser damage performance of fused silica optical components measured on the Beamlet laser at 351nm,” Proc. SPIE 3578, 436–445 (1999).
[Crossref]

Widmayer, C. C.

M. J. Matthews, L. L. Bass, G. M. Guss, C. C. Widmayer, and F. L. Ravizza, “Downstream Intensification Effects Associated with CO2 Laser Mitigation of Fused Silica,” Proc. SPIE 6720, 67200A, 67200A-9 (2007).
[Crossref]

C. C. Widmayer, M. R. Nickels, and D. Milam, “Nonlinear holographic imaging of phase errors,” Appl. Opt. 37(21), 4801–4805 (1998).
[Crossref] [PubMed]

Wong, J.

J. Wong, J. L. Ferriera, E. F. Lindsey, D. L. Haupt, I. D. Hutcheon, and J. H. Kinney, “Morphology and microstructure in fused silica induced by high fluence ultraviolet 3ω (355nm) laser pulses,” J. Non-Cryst. Solids 352(3), 255–272 (2006).
[Crossref]

Yang, S. T.

Yoshiyama, J.

Appl. Opt. (6)

Appl. Phys. Lett. (1)

C. W. Carr, J. B. Trenholme, and M. L. Spaeth, “Effect of temporal pulse shape on optical damage,” Appl. Phys. Lett. 90(4), 041110 (2007).
[Crossref]

J. Non-Cryst. Solids (1)

J. Wong, J. L. Ferriera, E. F. Lindsey, D. L. Haupt, I. D. Hutcheon, and J. H. Kinney, “Morphology and microstructure in fused silica induced by high fluence ultraviolet 3ω (355nm) laser pulses,” J. Non-Cryst. Solids 352(3), 255–272 (2006).
[Crossref]

Opt. Eng. (1)

O. Morice, “Miro: Complete modeling and software for pulse amplification and propagation in high-power laser system,” Opt. Eng. 42(6), 1530–1541 (2003).
[Crossref]

Opt. Express (3)

Proc. SPIE (8)

C. W. Carr, M. J. Matthews, J. D. Bude, and M. L. Spaeth, “The effect of laser pulse duration on laser-induced damage in KDP and SiO2,” Proc. SPIE 6403, 64030K, 64030K-9 (2006).
[Crossref]

M. D. Feit and A. M. Rubenchik, “Influence of subsurface cracks on laser induced surface damage,” Proc. SPIE 5273, 264–271 (2004).
[Crossref]

I. L. Bass, V. G. Draggoo, G. M. Guss, R. P. Hackel, and M. A. Norton, “Mitigation of laser damage growth in fused silica NIF optics with a galvanometer scanned CO2 laser,” Proc. SPIE 6261, 62612A, 62612A-10 (2006).
[Crossref]

M. R. Kozlowski, R. Mouser, S. Maricle, P. Wegner, and T. Weiland, “Laser damage performance of fused silica optical components measured on the Beamlet laser at 351nm,” Proc. SPIE 3578, 436–445 (1999).
[Crossref]

S. Mainguy, B. Le Garrec, and M. Josse, “Downstream impact of flaws on the LIL/LMJ laser lines,” Proc. SPIE 5991, 599105, 599105-9 (2005).
[Crossref]

S. Mainguy, I. Tovena-Pecault, and B. Le Garrec, “Propagation of LIL/LMJ beams under the interaction with contamination particles,” Proc. SPIE 5991, 59910G, 59910G-9 (2005).
[Crossref]

M. J. Matthews, L. L. Bass, G. M. Guss, C. C. Widmayer, and F. L. Ravizza, “Downstream Intensification Effects Associated with CO2 Laser Mitigation of Fused Silica,” Proc. SPIE 6720, 67200A, 67200A-9 (2007).
[Crossref]

J. R. Schmidt, M. J. Runkel, K. E. Martin, and C. J. Stolz, “Scattering-induced downstream beam modulation by plasma scalded mirrors,” Proc. SPIE 6720, 67201H, 67201H-10 (2007).
[Crossref]

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Figures (11)

Fig. 1
Fig. 1 Sketch map of experimental setup. A series of measurement instruments are applied for DIME characterization.

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Fig. 2
Fig. 2 DIME characterizations: (a) microscope observation, (b) surface form measured by interferometer, (c) OCT image of lateral morphology, and (d) Transmitted beam profile at 5mm downstream distance.

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Fig. 3
Fig. 3 SEM micrograph of the damage site. In center, crater core with sub-micron structures is formed. Around, the cracks and flaws indicate the existence of sub-surface fracturing and peeling.

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Fig. 4
Fig. 4 Modulated profiles of transmitted beam at different downstream distances.

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Fig. 5
Fig. 5 Evolution curves of on-axis intensity of two different size cases.

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Fig. 6
Fig. 6 Schematic diagram of transmitted beam modulation and propagation.

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Fig. 7
Fig. 7 Simulation results of small size case (100μm). Beam profiles under amplitude (upper-line) and phase (lower-line) factors are exhibited and ranged according to the propagation distance. Left panels exhibit the initial parameters.

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Fig. 8
Fig. 8 Simulation results of large size case (500μm). Beam profiles under amplitude (upper-line) and phase (lower-line) factors are exhibited and ranged according to the propagation distance. Left panels exhibit the initial parameters.

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Fig. 9
Fig. 9 Evolution curves of the intensity parameters along with propagation distance.

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Fig. 10
Fig. 10 Pentagon DIME model with crater-like morphological features.

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Fig. 11
Fig. 11 Numerical simulation of the simplified DIME model with crater-like pentagon pattern.

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Equations (6)

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U( x 0 , y 0 ,Z=0 )= u 0 h( x 0 , y 0 ),
h( x 0 , y 0 )={ 1 ∉ s t( x 0 , y 0 )exp[ jϕ( x 0 , y 0 ) ] ∈ s ,
U( x,y,Z=z )= 1 jλz exp(jkz) ∬ ∞ U( x 0 , y 0 ,Z=0 ) exp{ j k 2z [ ( x− x 0 ) 2 + ( y− y 0 ) 2 ] }d x 0 d y 0 .
U( x,y,Z=z )= 1 jλz exp(jkz)[ ∬ ( x 0 , y 0 )∈s u 0 h( x 0 , y 0 ) exp{ j k 2z [ ( x− x 0 ) 2 + ( y− y 0 ) 2 ] }d x 0 d y 0 + ∬ ( x 0 , y 0 )∉s u 0 h( x 0 , y 0 ) exp{ j k 2z [ ( x− x 0 ) 2 + ( y− y 0 ) 2 ] }d x 0 d y 0 ]. = 1 jλz exp(jkz) ∬ ( x 0 , y 0 )∈s t( x 0 , y 0 )exp { j k 2z [ ( x− x 0 ) 2 + ( y− y 0 ) 2 ]+jϕ( x 0 , y 0 ) }d x 0 d y 0 + 1 jλz exp(jkz) ∬ ( x 0 , y 0 )∉s exp{ j k 2z [ ( x− x 0 ) 2 + ( y− y 0 ) 2 ] }d x 0 d y 0
I( x,y,Z=z )= | U( x,y,Z=z ) | 2 .
h( x 0 , y 0 )={ 0 ∈ s 0 a i exp(j ϕ i ) ∈ s i (i=1,2,...,5) 1 ∈else .

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