Abstract

Ray-tracing is the commonly used technique to calculate the absorption of light in laser deep-penetration welding or drilling. Since new lasers with high brilliance enable small capillaries with high aspect ratios, diffraction might become important. To examine the applicability of the ray-tracing method, we studied the total absorptance and the absorbed intensity of polarized beams in several capillary geometries. The ray-tracing results are compared with more sophisticated simulations based on physical optics. The comparison shows that the simple ray-tracing is applicable to calculate the total absorptance in triangular grooves and in conical capillaries but not in rectangular grooves. To calculate the distribution of the absorbed intensity ray-tracing fails due to the neglected interference, diffraction, and the effects of beam propagation in the capillaries with sub-wavelength diameter. If diffraction is avoided e.g. with beams smaller than the entrance pupil of the capillary or with very shallow capillaries, the distribution of the absorbed intensity calculated by ray-tracing corresponds to the local average of the interference pattern found by physical optics.

© 2012 OSA

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References

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  1. V. G. Niziev and A. V. Nesterov, “Influence of beam polarization on laser cutting efficiency,” J. Phys. D Appl. Phys.32(13), 1455–1461 (1999).
    [CrossRef]
  2. M. Born and E. Wolf, Principles of Optics (Cambridge University Press, 2003), chap. 14.
  3. D. Bergström, J. Powell, and A. F. H. Kaplan, “Absorptance of nonferrous alloys to Nd:YLF and Nd:YAG laser light at room temperature,” Appl. Opt.46(8), 1290–1301 (2007).
    [CrossRef] [PubMed]
  4. K. Venkatakrishnan, B. Tan, P. Stanley, and N. R. Sivakumar, “The effect of polarization on ultrashort pulsed laser ablation of thin metal films,” J. Appl. Phys.92(3), 1604–1607 (2002).
    [CrossRef]
  5. S. Nolte, C. Momma, G. Kamlage, A. Ostendorf, C. Fallnich, F. von Alvensleben, and H. Welling, “Polarization effects in ultrashort-pulse laser drilling,” Appl. Phys., A Mater. Sci. Process.68(5), 563–567 (1999).
    [CrossRef]
  6. A. Weck, T. H. R. Crawford, D. S. Wilkinson, H. K. Haugen, and J. S. Preston, “Laser drilling of high aspect ratio holes in copper with femtosecond, picosecond and nanosecond pulses,” Appl. Phys., A Mater. Sci. Process.90(3), 537–543 (2008).
    [CrossRef]
  7. M. Meier, V. Romano, and T. Feurer, “Material processing with pulsed radially and azimuthally polarized laser radiation,” Appl. Phys., A Mater. Sci. Process.86(3), 329–334 (2007).
    [CrossRef]
  8. M. Schneider, L. Berthe, R. Fabbro, and M. Muller, “Measurement of laser absorptivity for operating parameters characteristic of laser drilling regime,” J. Phys. D Appl. Phys.41(15), 155502 (2008).
    [CrossRef]
  9. M. Kraus, M. A. Ahmed, A. Michalowski, A. Voss, R. Weber, and T. Graf, “Microdrilling in steel using ultrashort pulsed laser beams with radial and azimuthal polarization,” Opt. Express18(21), 22305–22313 (2010).
    [CrossRef] [PubMed]
  10. H. J. Allelein, R. Hecker, A. Max, Th. Overhoff, and D. Stöver, “Laser system for boring and sampling in coated-particle fuel,” J. Appl. Phys.50(10), 6162–6167 (1979).
    [CrossRef]
  11. A. G. Borkin, S. V. Drobyazko, E. B. Levchenko, Yu. M. Senatorov, and A. Yu. Turygin, “Self-focusing and waveguide propagation of radiation in the case of deep penetration of a metal by a laser beam,” Sov. J. Quantum Electron.15(11), 1515–1523 (1985).
    [CrossRef]
  12. M. F. Modest, “Effects of multiple reflections on hole formation during short-pulsed laser drilling,” J. Heat Transfer128(7), 653–661 (2006).
    [CrossRef]
  13. H. Ki, P. S. Mohanty, and J. Mazumder, “Multiple reflection and its influence on keyhole evolution,” J. Laser Appl.14(1), 39–45 (2002).
    [CrossRef]
  14. L. Li, C. Driver, J. Atkinson, R. Giedl-Wagner, and H. J. Helml, “Sequential laser and EDM micro-drilling for next generation fuel injection nozzle manufacture,” CIRP Ann-Manuf. Techn.55(1), 179–182 (2006).
  15. F. Dausinger, “Precise drilling with short-pulsed lasers,” Proc. SPIE3888, 180–187 (2000).
    [CrossRef]
  16. L. D. Landau, E. M. Lifshitz, and L. P. Pitaevskii, Electrodynamics of Continuous Media (Pergamon Press, 1984), chap. 10.
  17. A. Degiron, H. J. Lezec, N. Yamamoto, and T. W. Ebbesen, “Optical transmission properties of single subwavelength aperture in a real metal,” Opt. Commun.239(1–3), 61–66 (2004).
    [CrossRef]

2010 (1)

2008 (2)

M. Schneider, L. Berthe, R. Fabbro, and M. Muller, “Measurement of laser absorptivity for operating parameters characteristic of laser drilling regime,” J. Phys. D Appl. Phys.41(15), 155502 (2008).
[CrossRef]

A. Weck, T. H. R. Crawford, D. S. Wilkinson, H. K. Haugen, and J. S. Preston, “Laser drilling of high aspect ratio holes in copper with femtosecond, picosecond and nanosecond pulses,” Appl. Phys., A Mater. Sci. Process.90(3), 537–543 (2008).
[CrossRef]

2007 (2)

M. Meier, V. Romano, and T. Feurer, “Material processing with pulsed radially and azimuthally polarized laser radiation,” Appl. Phys., A Mater. Sci. Process.86(3), 329–334 (2007).
[CrossRef]

D. Bergström, J. Powell, and A. F. H. Kaplan, “Absorptance of nonferrous alloys to Nd:YLF and Nd:YAG laser light at room temperature,” Appl. Opt.46(8), 1290–1301 (2007).
[CrossRef] [PubMed]

2006 (2)

M. F. Modest, “Effects of multiple reflections on hole formation during short-pulsed laser drilling,” J. Heat Transfer128(7), 653–661 (2006).
[CrossRef]

L. Li, C. Driver, J. Atkinson, R. Giedl-Wagner, and H. J. Helml, “Sequential laser and EDM micro-drilling for next generation fuel injection nozzle manufacture,” CIRP Ann-Manuf. Techn.55(1), 179–182 (2006).

2004 (1)

A. Degiron, H. J. Lezec, N. Yamamoto, and T. W. Ebbesen, “Optical transmission properties of single subwavelength aperture in a real metal,” Opt. Commun.239(1–3), 61–66 (2004).
[CrossRef]

2002 (2)

H. Ki, P. S. Mohanty, and J. Mazumder, “Multiple reflection and its influence on keyhole evolution,” J. Laser Appl.14(1), 39–45 (2002).
[CrossRef]

K. Venkatakrishnan, B. Tan, P. Stanley, and N. R. Sivakumar, “The effect of polarization on ultrashort pulsed laser ablation of thin metal films,” J. Appl. Phys.92(3), 1604–1607 (2002).
[CrossRef]

2000 (1)

F. Dausinger, “Precise drilling with short-pulsed lasers,” Proc. SPIE3888, 180–187 (2000).
[CrossRef]

1999 (2)

S. Nolte, C. Momma, G. Kamlage, A. Ostendorf, C. Fallnich, F. von Alvensleben, and H. Welling, “Polarization effects in ultrashort-pulse laser drilling,” Appl. Phys., A Mater. Sci. Process.68(5), 563–567 (1999).
[CrossRef]

V. G. Niziev and A. V. Nesterov, “Influence of beam polarization on laser cutting efficiency,” J. Phys. D Appl. Phys.32(13), 1455–1461 (1999).
[CrossRef]

1985 (1)

A. G. Borkin, S. V. Drobyazko, E. B. Levchenko, Yu. M. Senatorov, and A. Yu. Turygin, “Self-focusing and waveguide propagation of radiation in the case of deep penetration of a metal by a laser beam,” Sov. J. Quantum Electron.15(11), 1515–1523 (1985).
[CrossRef]

1979 (1)

H. J. Allelein, R. Hecker, A. Max, Th. Overhoff, and D. Stöver, “Laser system for boring and sampling in coated-particle fuel,” J. Appl. Phys.50(10), 6162–6167 (1979).
[CrossRef]

Ahmed, M. A.

Allelein, H. J.

H. J. Allelein, R. Hecker, A. Max, Th. Overhoff, and D. Stöver, “Laser system for boring and sampling in coated-particle fuel,” J. Appl. Phys.50(10), 6162–6167 (1979).
[CrossRef]

Atkinson, J.

L. Li, C. Driver, J. Atkinson, R. Giedl-Wagner, and H. J. Helml, “Sequential laser and EDM micro-drilling for next generation fuel injection nozzle manufacture,” CIRP Ann-Manuf. Techn.55(1), 179–182 (2006).

Bergström, D.

Berthe, L.

M. Schneider, L. Berthe, R. Fabbro, and M. Muller, “Measurement of laser absorptivity for operating parameters characteristic of laser drilling regime,” J. Phys. D Appl. Phys.41(15), 155502 (2008).
[CrossRef]

Borkin, A. G.

A. G. Borkin, S. V. Drobyazko, E. B. Levchenko, Yu. M. Senatorov, and A. Yu. Turygin, “Self-focusing and waveguide propagation of radiation in the case of deep penetration of a metal by a laser beam,” Sov. J. Quantum Electron.15(11), 1515–1523 (1985).
[CrossRef]

Crawford, T. H. R.

A. Weck, T. H. R. Crawford, D. S. Wilkinson, H. K. Haugen, and J. S. Preston, “Laser drilling of high aspect ratio holes in copper with femtosecond, picosecond and nanosecond pulses,” Appl. Phys., A Mater. Sci. Process.90(3), 537–543 (2008).
[CrossRef]

Dausinger, F.

F. Dausinger, “Precise drilling with short-pulsed lasers,” Proc. SPIE3888, 180–187 (2000).
[CrossRef]

Degiron, A.

A. Degiron, H. J. Lezec, N. Yamamoto, and T. W. Ebbesen, “Optical transmission properties of single subwavelength aperture in a real metal,” Opt. Commun.239(1–3), 61–66 (2004).
[CrossRef]

Driver, C.

L. Li, C. Driver, J. Atkinson, R. Giedl-Wagner, and H. J. Helml, “Sequential laser and EDM micro-drilling for next generation fuel injection nozzle manufacture,” CIRP Ann-Manuf. Techn.55(1), 179–182 (2006).

Drobyazko, S. V.

A. G. Borkin, S. V. Drobyazko, E. B. Levchenko, Yu. M. Senatorov, and A. Yu. Turygin, “Self-focusing and waveguide propagation of radiation in the case of deep penetration of a metal by a laser beam,” Sov. J. Quantum Electron.15(11), 1515–1523 (1985).
[CrossRef]

Ebbesen, T. W.

A. Degiron, H. J. Lezec, N. Yamamoto, and T. W. Ebbesen, “Optical transmission properties of single subwavelength aperture in a real metal,” Opt. Commun.239(1–3), 61–66 (2004).
[CrossRef]

Fabbro, R.

M. Schneider, L. Berthe, R. Fabbro, and M. Muller, “Measurement of laser absorptivity for operating parameters characteristic of laser drilling regime,” J. Phys. D Appl. Phys.41(15), 155502 (2008).
[CrossRef]

Fallnich, C.

S. Nolte, C. Momma, G. Kamlage, A. Ostendorf, C. Fallnich, F. von Alvensleben, and H. Welling, “Polarization effects in ultrashort-pulse laser drilling,” Appl. Phys., A Mater. Sci. Process.68(5), 563–567 (1999).
[CrossRef]

Feurer, T.

M. Meier, V. Romano, and T. Feurer, “Material processing with pulsed radially and azimuthally polarized laser radiation,” Appl. Phys., A Mater. Sci. Process.86(3), 329–334 (2007).
[CrossRef]

Giedl-Wagner, R.

L. Li, C. Driver, J. Atkinson, R. Giedl-Wagner, and H. J. Helml, “Sequential laser and EDM micro-drilling for next generation fuel injection nozzle manufacture,” CIRP Ann-Manuf. Techn.55(1), 179–182 (2006).

Graf, T.

Haugen, H. K.

A. Weck, T. H. R. Crawford, D. S. Wilkinson, H. K. Haugen, and J. S. Preston, “Laser drilling of high aspect ratio holes in copper with femtosecond, picosecond and nanosecond pulses,” Appl. Phys., A Mater. Sci. Process.90(3), 537–543 (2008).
[CrossRef]

Hecker, R.

H. J. Allelein, R. Hecker, A. Max, Th. Overhoff, and D. Stöver, “Laser system for boring and sampling in coated-particle fuel,” J. Appl. Phys.50(10), 6162–6167 (1979).
[CrossRef]

Helml, H. J.

L. Li, C. Driver, J. Atkinson, R. Giedl-Wagner, and H. J. Helml, “Sequential laser and EDM micro-drilling for next generation fuel injection nozzle manufacture,” CIRP Ann-Manuf. Techn.55(1), 179–182 (2006).

Kamlage, G.

S. Nolte, C. Momma, G. Kamlage, A. Ostendorf, C. Fallnich, F. von Alvensleben, and H. Welling, “Polarization effects in ultrashort-pulse laser drilling,” Appl. Phys., A Mater. Sci. Process.68(5), 563–567 (1999).
[CrossRef]

Kaplan, A. F. H.

Ki, H.

H. Ki, P. S. Mohanty, and J. Mazumder, “Multiple reflection and its influence on keyhole evolution,” J. Laser Appl.14(1), 39–45 (2002).
[CrossRef]

Kraus, M.

Levchenko, E. B.

A. G. Borkin, S. V. Drobyazko, E. B. Levchenko, Yu. M. Senatorov, and A. Yu. Turygin, “Self-focusing and waveguide propagation of radiation in the case of deep penetration of a metal by a laser beam,” Sov. J. Quantum Electron.15(11), 1515–1523 (1985).
[CrossRef]

Lezec, H. J.

A. Degiron, H. J. Lezec, N. Yamamoto, and T. W. Ebbesen, “Optical transmission properties of single subwavelength aperture in a real metal,” Opt. Commun.239(1–3), 61–66 (2004).
[CrossRef]

Li, L.

L. Li, C. Driver, J. Atkinson, R. Giedl-Wagner, and H. J. Helml, “Sequential laser and EDM micro-drilling for next generation fuel injection nozzle manufacture,” CIRP Ann-Manuf. Techn.55(1), 179–182 (2006).

Max, A.

H. J. Allelein, R. Hecker, A. Max, Th. Overhoff, and D. Stöver, “Laser system for boring and sampling in coated-particle fuel,” J. Appl. Phys.50(10), 6162–6167 (1979).
[CrossRef]

Mazumder, J.

H. Ki, P. S. Mohanty, and J. Mazumder, “Multiple reflection and its influence on keyhole evolution,” J. Laser Appl.14(1), 39–45 (2002).
[CrossRef]

Meier, M.

M. Meier, V. Romano, and T. Feurer, “Material processing with pulsed radially and azimuthally polarized laser radiation,” Appl. Phys., A Mater. Sci. Process.86(3), 329–334 (2007).
[CrossRef]

Michalowski, A.

Modest, M. F.

M. F. Modest, “Effects of multiple reflections on hole formation during short-pulsed laser drilling,” J. Heat Transfer128(7), 653–661 (2006).
[CrossRef]

Mohanty, P. S.

H. Ki, P. S. Mohanty, and J. Mazumder, “Multiple reflection and its influence on keyhole evolution,” J. Laser Appl.14(1), 39–45 (2002).
[CrossRef]

Momma, C.

S. Nolte, C. Momma, G. Kamlage, A. Ostendorf, C. Fallnich, F. von Alvensleben, and H. Welling, “Polarization effects in ultrashort-pulse laser drilling,” Appl. Phys., A Mater. Sci. Process.68(5), 563–567 (1999).
[CrossRef]

Muller, M.

M. Schneider, L. Berthe, R. Fabbro, and M. Muller, “Measurement of laser absorptivity for operating parameters characteristic of laser drilling regime,” J. Phys. D Appl. Phys.41(15), 155502 (2008).
[CrossRef]

Nesterov, A. V.

V. G. Niziev and A. V. Nesterov, “Influence of beam polarization on laser cutting efficiency,” J. Phys. D Appl. Phys.32(13), 1455–1461 (1999).
[CrossRef]

Niziev, V. G.

V. G. Niziev and A. V. Nesterov, “Influence of beam polarization on laser cutting efficiency,” J. Phys. D Appl. Phys.32(13), 1455–1461 (1999).
[CrossRef]

Nolte, S.

S. Nolte, C. Momma, G. Kamlage, A. Ostendorf, C. Fallnich, F. von Alvensleben, and H. Welling, “Polarization effects in ultrashort-pulse laser drilling,” Appl. Phys., A Mater. Sci. Process.68(5), 563–567 (1999).
[CrossRef]

Ostendorf, A.

S. Nolte, C. Momma, G. Kamlage, A. Ostendorf, C. Fallnich, F. von Alvensleben, and H. Welling, “Polarization effects in ultrashort-pulse laser drilling,” Appl. Phys., A Mater. Sci. Process.68(5), 563–567 (1999).
[CrossRef]

Overhoff, Th.

H. J. Allelein, R. Hecker, A. Max, Th. Overhoff, and D. Stöver, “Laser system for boring and sampling in coated-particle fuel,” J. Appl. Phys.50(10), 6162–6167 (1979).
[CrossRef]

Powell, J.

Preston, J. S.

A. Weck, T. H. R. Crawford, D. S. Wilkinson, H. K. Haugen, and J. S. Preston, “Laser drilling of high aspect ratio holes in copper with femtosecond, picosecond and nanosecond pulses,” Appl. Phys., A Mater. Sci. Process.90(3), 537–543 (2008).
[CrossRef]

Romano, V.

M. Meier, V. Romano, and T. Feurer, “Material processing with pulsed radially and azimuthally polarized laser radiation,” Appl. Phys., A Mater. Sci. Process.86(3), 329–334 (2007).
[CrossRef]

Schneider, M.

M. Schneider, L. Berthe, R. Fabbro, and M. Muller, “Measurement of laser absorptivity for operating parameters characteristic of laser drilling regime,” J. Phys. D Appl. Phys.41(15), 155502 (2008).
[CrossRef]

Senatorov, Yu. M.

A. G. Borkin, S. V. Drobyazko, E. B. Levchenko, Yu. M. Senatorov, and A. Yu. Turygin, “Self-focusing and waveguide propagation of radiation in the case of deep penetration of a metal by a laser beam,” Sov. J. Quantum Electron.15(11), 1515–1523 (1985).
[CrossRef]

Sivakumar, N. R.

K. Venkatakrishnan, B. Tan, P. Stanley, and N. R. Sivakumar, “The effect of polarization on ultrashort pulsed laser ablation of thin metal films,” J. Appl. Phys.92(3), 1604–1607 (2002).
[CrossRef]

Stanley, P.

K. Venkatakrishnan, B. Tan, P. Stanley, and N. R. Sivakumar, “The effect of polarization on ultrashort pulsed laser ablation of thin metal films,” J. Appl. Phys.92(3), 1604–1607 (2002).
[CrossRef]

Stöver, D.

H. J. Allelein, R. Hecker, A. Max, Th. Overhoff, and D. Stöver, “Laser system for boring and sampling in coated-particle fuel,” J. Appl. Phys.50(10), 6162–6167 (1979).
[CrossRef]

Tan, B.

K. Venkatakrishnan, B. Tan, P. Stanley, and N. R. Sivakumar, “The effect of polarization on ultrashort pulsed laser ablation of thin metal films,” J. Appl. Phys.92(3), 1604–1607 (2002).
[CrossRef]

Turygin, A. Yu.

A. G. Borkin, S. V. Drobyazko, E. B. Levchenko, Yu. M. Senatorov, and A. Yu. Turygin, “Self-focusing and waveguide propagation of radiation in the case of deep penetration of a metal by a laser beam,” Sov. J. Quantum Electron.15(11), 1515–1523 (1985).
[CrossRef]

Venkatakrishnan, K.

K. Venkatakrishnan, B. Tan, P. Stanley, and N. R. Sivakumar, “The effect of polarization on ultrashort pulsed laser ablation of thin metal films,” J. Appl. Phys.92(3), 1604–1607 (2002).
[CrossRef]

von Alvensleben, F.

S. Nolte, C. Momma, G. Kamlage, A. Ostendorf, C. Fallnich, F. von Alvensleben, and H. Welling, “Polarization effects in ultrashort-pulse laser drilling,” Appl. Phys., A Mater. Sci. Process.68(5), 563–567 (1999).
[CrossRef]

Voss, A.

Weber, R.

Weck, A.

A. Weck, T. H. R. Crawford, D. S. Wilkinson, H. K. Haugen, and J. S. Preston, “Laser drilling of high aspect ratio holes in copper with femtosecond, picosecond and nanosecond pulses,” Appl. Phys., A Mater. Sci. Process.90(3), 537–543 (2008).
[CrossRef]

Welling, H.

S. Nolte, C. Momma, G. Kamlage, A. Ostendorf, C. Fallnich, F. von Alvensleben, and H. Welling, “Polarization effects in ultrashort-pulse laser drilling,” Appl. Phys., A Mater. Sci. Process.68(5), 563–567 (1999).
[CrossRef]

Wilkinson, D. S.

A. Weck, T. H. R. Crawford, D. S. Wilkinson, H. K. Haugen, and J. S. Preston, “Laser drilling of high aspect ratio holes in copper with femtosecond, picosecond and nanosecond pulses,” Appl. Phys., A Mater. Sci. Process.90(3), 537–543 (2008).
[CrossRef]

Yamamoto, N.

A. Degiron, H. J. Lezec, N. Yamamoto, and T. W. Ebbesen, “Optical transmission properties of single subwavelength aperture in a real metal,” Opt. Commun.239(1–3), 61–66 (2004).
[CrossRef]

Appl. Opt. (1)

Appl. Phys., A Mater. Sci. Process. (3)

S. Nolte, C. Momma, G. Kamlage, A. Ostendorf, C. Fallnich, F. von Alvensleben, and H. Welling, “Polarization effects in ultrashort-pulse laser drilling,” Appl. Phys., A Mater. Sci. Process.68(5), 563–567 (1999).
[CrossRef]

A. Weck, T. H. R. Crawford, D. S. Wilkinson, H. K. Haugen, and J. S. Preston, “Laser drilling of high aspect ratio holes in copper with femtosecond, picosecond and nanosecond pulses,” Appl. Phys., A Mater. Sci. Process.90(3), 537–543 (2008).
[CrossRef]

M. Meier, V. Romano, and T. Feurer, “Material processing with pulsed radially and azimuthally polarized laser radiation,” Appl. Phys., A Mater. Sci. Process.86(3), 329–334 (2007).
[CrossRef]

CIRP Ann-Manuf. Techn. (1)

L. Li, C. Driver, J. Atkinson, R. Giedl-Wagner, and H. J. Helml, “Sequential laser and EDM micro-drilling for next generation fuel injection nozzle manufacture,” CIRP Ann-Manuf. Techn.55(1), 179–182 (2006).

J. Appl. Phys. (2)

K. Venkatakrishnan, B. Tan, P. Stanley, and N. R. Sivakumar, “The effect of polarization on ultrashort pulsed laser ablation of thin metal films,” J. Appl. Phys.92(3), 1604–1607 (2002).
[CrossRef]

H. J. Allelein, R. Hecker, A. Max, Th. Overhoff, and D. Stöver, “Laser system for boring and sampling in coated-particle fuel,” J. Appl. Phys.50(10), 6162–6167 (1979).
[CrossRef]

J. Heat Transfer (1)

M. F. Modest, “Effects of multiple reflections on hole formation during short-pulsed laser drilling,” J. Heat Transfer128(7), 653–661 (2006).
[CrossRef]

J. Laser Appl. (1)

H. Ki, P. S. Mohanty, and J. Mazumder, “Multiple reflection and its influence on keyhole evolution,” J. Laser Appl.14(1), 39–45 (2002).
[CrossRef]

J. Phys. D Appl. Phys. (2)

M. Schneider, L. Berthe, R. Fabbro, and M. Muller, “Measurement of laser absorptivity for operating parameters characteristic of laser drilling regime,” J. Phys. D Appl. Phys.41(15), 155502 (2008).
[CrossRef]

V. G. Niziev and A. V. Nesterov, “Influence of beam polarization on laser cutting efficiency,” J. Phys. D Appl. Phys.32(13), 1455–1461 (1999).
[CrossRef]

Opt. Commun. (1)

A. Degiron, H. J. Lezec, N. Yamamoto, and T. W. Ebbesen, “Optical transmission properties of single subwavelength aperture in a real metal,” Opt. Commun.239(1–3), 61–66 (2004).
[CrossRef]

Opt. Express (1)

Proc. SPIE (1)

F. Dausinger, “Precise drilling with short-pulsed lasers,” Proc. SPIE3888, 180–187 (2000).
[CrossRef]

Sov. J. Quantum Electron. (1)

A. G. Borkin, S. V. Drobyazko, E. B. Levchenko, Yu. M. Senatorov, and A. Yu. Turygin, “Self-focusing and waveguide propagation of radiation in the case of deep penetration of a metal by a laser beam,” Sov. J. Quantum Electron.15(11), 1515–1523 (1985).
[CrossRef]

Other (2)

L. D. Landau, E. M. Lifshitz, and L. P. Pitaevskii, Electrodynamics of Continuous Media (Pergamon Press, 1984), chap. 10.

M. Born and E. Wolf, Principles of Optics (Cambridge University Press, 2003), chap. 14.

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Figures (10)

Fig. 1
Fig. 1

The examined model geometries in 2D Cartesian (case A and B) and axial (case C) coordinates. The incident fields are plane-wave (A, B) and ring-mode (C), respectively.

Fig. 2
Fig. 2

Absorptivity (a) and absorbed intensity (b) of CrNi steel at 1030 nm. For TM polarization steep change occurs near to grazing incidence (>83°).

Fig. 3
Fig. 3

Experimental set up of the absorptivity measurement: (1) linearly polarized cw laser, (2) and (3) mirror, (4) aperture, (5) half-wave plate, (6) focusing lens, (7) sample, (8) thermal paste, (9) and (11) temperature sensor, (10) rotating working table, (12) control unit, (13) PC, (14) thermal shielding.

Fig. 4
Fig. 4

Flow chart of ray-tracing method.

Fig. 5
Fig. 5

Total absorptance in the rectangular groove for TE (a) and TM (b) polarization. The dash-dotted line shows the total absorptance calculated by means of the ray-tracing. The other lines show the results from the physical optics simulations.

Fig. 6
Fig. 6

The contour charts of the normalized absorbed intensity obtained by ray-tracing (a) and physical optics(PO) (b, c). The aspect ratio of the rectangular groove is 5.

Fig. 7
Fig. 7

Total absorptance of a linearly polarized beam propagating in a triangular groove obtained by ray-tracing (RT) and physical optics (PO).

Fig. 8
Fig. 8

Distribution of the absorbed intensity along the wall of the triangular grooves with different aspect ratio for TE (a)-(c) and TM (d)-(f) polarization.

Fig. 9
Fig. 9

Distribution of the absorbed intensity along the wall of the conical capillary with different aspect ratio. The incident beams are polarized azimuthally (a, b) and radially (c).

Fig. 10
Fig. 10

Distribution of the absorbed intensity along the wall of the conical capillary with the different beam radii. The incident beam is radially polarized. The aspect ratio of the conical capillary is 5. The results obtained with physical optics were averaged over the interference pattern to better visualize the influence of the diffraction.

Equations (6)

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I( r,z )= 16 r 2 π ω 4 ( z ) exp( 4 r 2 ω 2 ( z ) ),
ω( z )= ω 0 1+ ( z z f ) 2 z 0 2
I abs = P abs_triangle s tri ,
I abs ( x,z )= I abs, x ( x,z )cosα+ I abs ,z ( x,z )sinα,
P abs = wall I abs ( x,z )dl
P abs = wall I abs ( r,z )2πrdl

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