Abstract

Ultrafast lasers have been used for high-precision processing of a wide range of materials, including dielectrics, semiconductors, metals and polymer composites, enabling numerous applications ranging from micromachining to photonics and life sciences. To make ultrafast laser materials processing compatible with the scale and throughput needed for industrial use, it is a common practice to run the laser at a high repetition rate and hence high average power. However, heat accumulation under such processing conditions will deteriorate the processing quality, especially for polymers, which typically have a low melting temperature. In this paper, an analytical solution to a transient, two-dimensional thermal model is developed using Duhamel’s theorem and the Hankel transform. This solution is used to understand the effect of laser parameters on ultrafast laser processing of polypropylene (PP). Laser cutting experiments are carried out on PP sheets to correlate with the theoretical calculation. This study shows that, in laser cutting, the total energy absorbed in the material and the intensity are two important figures of merit to predict the cutting performance. Heat accumulation is observed at low scanning speeds and high repetition rates, leading to significant heat-affected zone and even burning of the material, which is supported by experimental data and modelling results. It is found that heat accumulation can be avoided by a proper choice of the processing condition.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2018 (1)

2017 (1)

G. Chen, Y. Wang, J. Zhang, and J. Bi, “An analytical solution for two-dimensional modeling of repetitive long pulse laser heating material,” Int. J. Heat Mass Tran. 104, 503–509 (2017).
[Crossref]

2016 (2)

M. Malinauskas, A. Žukauskas, S. Hasegawa, Y. Hayasaki, V. Mizeikis, R. Buividas, and S. Juodkazis, “Ultrafast laser processing of materials: from science to industry,” Light Sci. Appl. 5(8), e16133 (2016).
[Crossref] [PubMed]

H. A. Maddah, “Polypropylene as a promising plastic: A Review,” Am. J. Pol. Sci. 6(1), 1–11 (2016).

2015 (4)

F. Bauer, A. Michalowski, T. Kiedrowski, and S. Nolte, “Heat accumulation in ultra-short pulsed scanning laser ablation of metals,” Opt. Express 23(2), 1035–1043 (2015).
[Crossref] [PubMed]

M. Hase, P. Fons, K. Mitrofanov, A. V. Kolobov, and J. Tominaga, “Femtosecond structural transformation of phase-change materials far from equilibrium monitored by coherent phonons,” Nat. Commun. 6(1), 8367 (2015).
[Crossref] [PubMed]

S. Mishra and V. Yadava, “Laser Beam Micro-Machining (LBMM) – A review,” Opt. Lasers Eng. 73, 89–122 (2015).
[Crossref]

K. C. Phillips, H. H. Gandhi, E. Mazur, and S. K. Sundaram, “Ultrafast laser processing of materials: a review,” Adv. Opt. Photonics 7(4), 684–712 (2015).
[Crossref]

2014 (2)

K. Sugioka and Y. Cheng, “Ultrafast Lasers – reliable tools for advanced material processing,” Light Sci. Appl. 3(4), e149 (2014).
[Crossref]

T. T. Lam, “A generalized heat conduction solution for ultrafast laser heating in metallic films,” Int. J. Heat Mass Tran. 73, 330–339 (2014).
[Crossref]

2012 (2)

A. K. Nath, A. Gupta, and F. Benny, “Theoretical and experimental study on laser surface hardening by repetitive laser pulses,” Surf. Coat. Tech. 206(8–9), 2602–2615 (2012).
[Crossref]

W. Sibbett, A. A. Lagatsky, and C. T. A. Brown, “The development and application of femtosecond laser systems,” Opt. Express 20(7), 6989–7001 (2012).
[Crossref] [PubMed]

2011 (1)

B. S. Yilbas, A. Y. Al-Dweik, and S. Bin Mansour, “Analytical solution of hyperbolic heat conduction equation in relation to laser short-pulse heating,” Physica B 406(8), 1550–1555 (2011).
[Crossref]

2008 (1)

R. R. Gattass and E. Mazur, “Femtosecond laser micromaching in transparent materials,” Nat. Photonics 2(4), 219–225 (2008).
[Crossref]

2006 (1)

B. S. Yilbas and M. Pakdemirli, “Analytical solution for temperature field in electron and lattice sub-systems during heating of solid film,” Physica B 382(1-2), 213–219 (2006).
[Crossref]

2005 (2)

M. Khenner and V. K. Henner, “Temperature of spatially modulated surface of solid film heated by repetitive laser pulses,” J. Phys. D Appl. Phys. 38(23), 4196–4201 (2005).
[Crossref]

S. Eaton, H. Zhang, P. Herman, F. Yoshino, L. Shah, J. Bovatsek, and A. Arai, “Heat accumulation effects in femtosecond laser-written waveguides with variable repetition rate,” Opt. Express 13(12), 4708–4716 (2005).
[Crossref] [PubMed]

2004 (2)

N. M. Bulgakova, R. Stoian, A. Rosenfeld, I. V. Hertel, and E. E. B. Campbell, “Electronic transport and consequences for material removal in ultrafast pulsed laser ablation of materials,” Phys. Rev. B Condens. Matter Mater. Phys. 69(5), 054102 (2004).
[Crossref]

S. Nolte, M. Will, J. Burghoff, and A. Tünnermann, “Ultrafast laser processing: New options for three-dimensional photonic structures,” J. Mod. Opt. 51(16-18), 2533–2542 (2004).
[Crossref]

2003 (2)

S. J. Kalita, S. Bose, H. L. Hosick, and A. Bandyopadhyay, “Development of controlled porosity polymer-ceramic composite scaffolds via fused deposition modeling,” Mater. Sci. Eng. C 23(5), 611–620 (2003).
[Crossref]

S. Zhang and A. R. Horrocks, “A review of flame retardant polypropylene fibres,” Prog. Polym. Sci. 28(11), 1517–1538 (2003).
[Crossref]

1999 (1)

B. S. Yilbas and S. Z. Shuja, “Laser short-pulse heating of surfaces,” J. Phys. D Appl. Phys. 32(16), 1947–1954 (1999).
[Crossref]

1997 (1)

A. Kar, J. A. Rothenflue, and W. P. Latham, “Scaling laws for thick-section cutting with a chemical oxygen-iodine laser,” J. Laser Appl. 9(6), 279–286 (1997).
[Crossref]

1996 (1)

1995 (1)

V. I. Mazhukin, I. Smurov, C. Surry, and G. Flamant, “Overheated metastable states in polymer sublimation by laser radiation,” Appl. Surf. Sci. 86(1-4), 7–12 (1995).
[Crossref]

1990 (1)

A. Kar and J. Mazumder, “Two-dimensional model for material damage due to melting and vaporization during laser irradiation,” J. Appl. Phys. 68(8), 3884–3891 (1990).
[Crossref]

Al-Dweik, A. Y.

B. S. Yilbas, A. Y. Al-Dweik, and S. Bin Mansour, “Analytical solution of hyperbolic heat conduction equation in relation to laser short-pulse heating,” Physica B 406(8), 1550–1555 (2011).
[Crossref]

Arai, A.

Bandyopadhyay, A.

S. J. Kalita, S. Bose, H. L. Hosick, and A. Bandyopadhyay, “Development of controlled porosity polymer-ceramic composite scaffolds via fused deposition modeling,” Mater. Sci. Eng. C 23(5), 611–620 (2003).
[Crossref]

Bauer, F.

Benny, F.

A. K. Nath, A. Gupta, and F. Benny, “Theoretical and experimental study on laser surface hardening by repetitive laser pulses,” Surf. Coat. Tech. 206(8–9), 2602–2615 (2012).
[Crossref]

Bi, J.

G. Chen, Y. Wang, J. Zhang, and J. Bi, “An analytical solution for two-dimensional modeling of repetitive long pulse laser heating material,” Int. J. Heat Mass Tran. 104, 503–509 (2017).
[Crossref]

Bin Mansour, S.

B. S. Yilbas, A. Y. Al-Dweik, and S. Bin Mansour, “Analytical solution of hyperbolic heat conduction equation in relation to laser short-pulse heating,” Physica B 406(8), 1550–1555 (2011).
[Crossref]

Bose, S.

S. J. Kalita, S. Bose, H. L. Hosick, and A. Bandyopadhyay, “Development of controlled porosity polymer-ceramic composite scaffolds via fused deposition modeling,” Mater. Sci. Eng. C 23(5), 611–620 (2003).
[Crossref]

Bovatsek, J.

Brown, C. T. A.

Buividas, R.

M. Malinauskas, A. Žukauskas, S. Hasegawa, Y. Hayasaki, V. Mizeikis, R. Buividas, and S. Juodkazis, “Ultrafast laser processing of materials: from science to industry,” Light Sci. Appl. 5(8), e16133 (2016).
[Crossref] [PubMed]

Bulgakova, N. M.

N. M. Bulgakova, R. Stoian, A. Rosenfeld, I. V. Hertel, and E. E. B. Campbell, “Electronic transport and consequences for material removal in ultrafast pulsed laser ablation of materials,” Phys. Rev. B Condens. Matter Mater. Phys. 69(5), 054102 (2004).
[Crossref]

Burghoff, J.

S. Nolte, M. Will, J. Burghoff, and A. Tünnermann, “Ultrafast laser processing: New options for three-dimensional photonic structures,” J. Mod. Opt. 51(16-18), 2533–2542 (2004).
[Crossref]

Campbell, E. E. B.

N. M. Bulgakova, R. Stoian, A. Rosenfeld, I. V. Hertel, and E. E. B. Campbell, “Electronic transport and consequences for material removal in ultrafast pulsed laser ablation of materials,” Phys. Rev. B Condens. Matter Mater. Phys. 69(5), 054102 (2004).
[Crossref]

Chen, G.

G. Chen, Y. Wang, J. Zhang, and J. Bi, “An analytical solution for two-dimensional modeling of repetitive long pulse laser heating material,” Int. J. Heat Mass Tran. 104, 503–509 (2017).
[Crossref]

Cheng, Y.

K. Sugioka and Y. Cheng, “Ultrafast Lasers – reliable tools for advanced material processing,” Light Sci. Appl. 3(4), e149 (2014).
[Crossref]

Eaton, S.

Feit, M. D.

Flamant, G.

V. I. Mazhukin, I. Smurov, C. Surry, and G. Flamant, “Overheated metastable states in polymer sublimation by laser radiation,” Appl. Surf. Sci. 86(1-4), 7–12 (1995).
[Crossref]

Fons, P.

M. Hase, P. Fons, K. Mitrofanov, A. V. Kolobov, and J. Tominaga, “Femtosecond structural transformation of phase-change materials far from equilibrium monitored by coherent phonons,” Nat. Commun. 6(1), 8367 (2015).
[Crossref] [PubMed]

Gandhi, H. H.

K. C. Phillips, H. H. Gandhi, E. Mazur, and S. K. Sundaram, “Ultrafast laser processing of materials: a review,” Adv. Opt. Photonics 7(4), 684–712 (2015).
[Crossref]

Gattass, R. R.

R. R. Gattass and E. Mazur, “Femtosecond laser micromaching in transparent materials,” Nat. Photonics 2(4), 219–225 (2008).
[Crossref]

Gupta, A.

A. K. Nath, A. Gupta, and F. Benny, “Theoretical and experimental study on laser surface hardening by repetitive laser pulses,” Surf. Coat. Tech. 206(8–9), 2602–2615 (2012).
[Crossref]

Hase, M.

M. Hase, P. Fons, K. Mitrofanov, A. V. Kolobov, and J. Tominaga, “Femtosecond structural transformation of phase-change materials far from equilibrium monitored by coherent phonons,” Nat. Commun. 6(1), 8367 (2015).
[Crossref] [PubMed]

Hasegawa, S.

M. Malinauskas, A. Žukauskas, S. Hasegawa, Y. Hayasaki, V. Mizeikis, R. Buividas, and S. Juodkazis, “Ultrafast laser processing of materials: from science to industry,” Light Sci. Appl. 5(8), e16133 (2016).
[Crossref] [PubMed]

Hayasaki, Y.

M. Malinauskas, A. Žukauskas, S. Hasegawa, Y. Hayasaki, V. Mizeikis, R. Buividas, and S. Juodkazis, “Ultrafast laser processing of materials: from science to industry,” Light Sci. Appl. 5(8), e16133 (2016).
[Crossref] [PubMed]

Henner, V. K.

M. Khenner and V. K. Henner, “Temperature of spatially modulated surface of solid film heated by repetitive laser pulses,” J. Phys. D Appl. Phys. 38(23), 4196–4201 (2005).
[Crossref]

Herman, P.

Herman, S.

Hertel, I. V.

N. M. Bulgakova, R. Stoian, A. Rosenfeld, I. V. Hertel, and E. E. B. Campbell, “Electronic transport and consequences for material removal in ultrafast pulsed laser ablation of materials,” Phys. Rev. B Condens. Matter Mater. Phys. 69(5), 054102 (2004).
[Crossref]

Horrocks, A. R.

S. Zhang and A. R. Horrocks, “A review of flame retardant polypropylene fibres,” Prog. Polym. Sci. 28(11), 1517–1538 (2003).
[Crossref]

Hosick, H. L.

S. J. Kalita, S. Bose, H. L. Hosick, and A. Bandyopadhyay, “Development of controlled porosity polymer-ceramic composite scaffolds via fused deposition modeling,” Mater. Sci. Eng. C 23(5), 611–620 (2003).
[Crossref]

Juodkazis, S.

M. Malinauskas, A. Žukauskas, S. Hasegawa, Y. Hayasaki, V. Mizeikis, R. Buividas, and S. Juodkazis, “Ultrafast laser processing of materials: from science to industry,” Light Sci. Appl. 5(8), e16133 (2016).
[Crossref] [PubMed]

Kalita, S. J.

S. J. Kalita, S. Bose, H. L. Hosick, and A. Bandyopadhyay, “Development of controlled porosity polymer-ceramic composite scaffolds via fused deposition modeling,” Mater. Sci. Eng. C 23(5), 611–620 (2003).
[Crossref]

Kar, A.

A. Kar, J. A. Rothenflue, and W. P. Latham, “Scaling laws for thick-section cutting with a chemical oxygen-iodine laser,” J. Laser Appl. 9(6), 279–286 (1997).
[Crossref]

A. Kar and J. Mazumder, “Two-dimensional model for material damage due to melting and vaporization during laser irradiation,” J. Appl. Phys. 68(8), 3884–3891 (1990).
[Crossref]

Khenner, M.

M. Khenner and V. K. Henner, “Temperature of spatially modulated surface of solid film heated by repetitive laser pulses,” J. Phys. D Appl. Phys. 38(23), 4196–4201 (2005).
[Crossref]

Kiedrowski, T.

Kolobov, A. V.

M. Hase, P. Fons, K. Mitrofanov, A. V. Kolobov, and J. Tominaga, “Femtosecond structural transformation of phase-change materials far from equilibrium monitored by coherent phonons,” Nat. Commun. 6(1), 8367 (2015).
[Crossref] [PubMed]

Lagatsky, A. A.

Lam, T. T.

T. T. Lam, “A generalized heat conduction solution for ultrafast laser heating in metallic films,” Int. J. Heat Mass Tran. 73, 330–339 (2014).
[Crossref]

Latham, W. P.

A. Kar, J. A. Rothenflue, and W. P. Latham, “Scaling laws for thick-section cutting with a chemical oxygen-iodine laser,” J. Laser Appl. 9(6), 279–286 (1997).
[Crossref]

Maddah, H. A.

H. A. Maddah, “Polypropylene as a promising plastic: A Review,” Am. J. Pol. Sci. 6(1), 1–11 (2016).

Malinauskas, M.

M. Malinauskas, A. Žukauskas, S. Hasegawa, Y. Hayasaki, V. Mizeikis, R. Buividas, and S. Juodkazis, “Ultrafast laser processing of materials: from science to industry,” Light Sci. Appl. 5(8), e16133 (2016).
[Crossref] [PubMed]

Mazhukin, V. I.

V. I. Mazhukin, I. Smurov, C. Surry, and G. Flamant, “Overheated metastable states in polymer sublimation by laser radiation,” Appl. Surf. Sci. 86(1-4), 7–12 (1995).
[Crossref]

Mazumder, J.

A. Kar and J. Mazumder, “Two-dimensional model for material damage due to melting and vaporization during laser irradiation,” J. Appl. Phys. 68(8), 3884–3891 (1990).
[Crossref]

Mazur, E.

K. C. Phillips, H. H. Gandhi, E. Mazur, and S. K. Sundaram, “Ultrafast laser processing of materials: a review,” Adv. Opt. Photonics 7(4), 684–712 (2015).
[Crossref]

R. R. Gattass and E. Mazur, “Femtosecond laser micromaching in transparent materials,” Nat. Photonics 2(4), 219–225 (2008).
[Crossref]

Michalowski, A.

Mishra, S.

S. Mishra and V. Yadava, “Laser Beam Micro-Machining (LBMM) – A review,” Opt. Lasers Eng. 73, 89–122 (2015).
[Crossref]

Mitrofanov, K.

M. Hase, P. Fons, K. Mitrofanov, A. V. Kolobov, and J. Tominaga, “Femtosecond structural transformation of phase-change materials far from equilibrium monitored by coherent phonons,” Nat. Commun. 6(1), 8367 (2015).
[Crossref] [PubMed]

Mizeikis, V.

M. Malinauskas, A. Žukauskas, S. Hasegawa, Y. Hayasaki, V. Mizeikis, R. Buividas, and S. Juodkazis, “Ultrafast laser processing of materials: from science to industry,” Light Sci. Appl. 5(8), e16133 (2016).
[Crossref] [PubMed]

Nath, A. K.

A. K. Nath, A. Gupta, and F. Benny, “Theoretical and experimental study on laser surface hardening by repetitive laser pulses,” Surf. Coat. Tech. 206(8–9), 2602–2615 (2012).
[Crossref]

Nolte, S.

F. Bauer, A. Michalowski, T. Kiedrowski, and S. Nolte, “Heat accumulation in ultra-short pulsed scanning laser ablation of metals,” Opt. Express 23(2), 1035–1043 (2015).
[Crossref] [PubMed]

S. Nolte, M. Will, J. Burghoff, and A. Tünnermann, “Ultrafast laser processing: New options for three-dimensional photonic structures,” J. Mod. Opt. 51(16-18), 2533–2542 (2004).
[Crossref]

Pakdemirli, M.

B. S. Yilbas and M. Pakdemirli, “Analytical solution for temperature field in electron and lattice sub-systems during heating of solid film,” Physica B 382(1-2), 213–219 (2006).
[Crossref]

Perry, M. D.

Phillips, K. C.

K. C. Phillips, H. H. Gandhi, E. Mazur, and S. K. Sundaram, “Ultrafast laser processing of materials: a review,” Adv. Opt. Photonics 7(4), 684–712 (2015).
[Crossref]

Qiao, J.

Rosenfeld, A.

N. M. Bulgakova, R. Stoian, A. Rosenfeld, I. V. Hertel, and E. E. B. Campbell, “Electronic transport and consequences for material removal in ultrafast pulsed laser ablation of materials,” Phys. Rev. B Condens. Matter Mater. Phys. 69(5), 054102 (2004).
[Crossref]

Rothenflue, J. A.

A. Kar, J. A. Rothenflue, and W. P. Latham, “Scaling laws for thick-section cutting with a chemical oxygen-iodine laser,” J. Laser Appl. 9(6), 279–286 (1997).
[Crossref]

Rubenchik, A. M.

Scott, R. E.

Shah, L.

Shore, B. W.

Shuja, S. Z.

B. S. Yilbas and S. Z. Shuja, “Laser short-pulse heating of surfaces,” J. Phys. D Appl. Phys. 32(16), 1947–1954 (1999).
[Crossref]

Sibbett, W.

Smurov, I.

V. I. Mazhukin, I. Smurov, C. Surry, and G. Flamant, “Overheated metastable states in polymer sublimation by laser radiation,” Appl. Surf. Sci. 86(1-4), 7–12 (1995).
[Crossref]

Stoian, R.

N. M. Bulgakova, R. Stoian, A. Rosenfeld, I. V. Hertel, and E. E. B. Campbell, “Electronic transport and consequences for material removal in ultrafast pulsed laser ablation of materials,” Phys. Rev. B Condens. Matter Mater. Phys. 69(5), 054102 (2004).
[Crossref]

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K. C. Phillips, H. H. Gandhi, E. Mazur, and S. K. Sundaram, “Ultrafast laser processing of materials: a review,” Adv. Opt. Photonics 7(4), 684–712 (2015).
[Crossref]

Surry, C.

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M. Hase, P. Fons, K. Mitrofanov, A. V. Kolobov, and J. Tominaga, “Femtosecond structural transformation of phase-change materials far from equilibrium monitored by coherent phonons,” Nat. Commun. 6(1), 8367 (2015).
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S. Nolte, M. Will, J. Burghoff, and A. Tünnermann, “Ultrafast laser processing: New options for three-dimensional photonic structures,” J. Mod. Opt. 51(16-18), 2533–2542 (2004).
[Crossref]

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G. Chen, Y. Wang, J. Zhang, and J. Bi, “An analytical solution for two-dimensional modeling of repetitive long pulse laser heating material,” Int. J. Heat Mass Tran. 104, 503–509 (2017).
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S. Mishra and V. Yadava, “Laser Beam Micro-Machining (LBMM) – A review,” Opt. Lasers Eng. 73, 89–122 (2015).
[Crossref]

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B. S. Yilbas, A. Y. Al-Dweik, and S. Bin Mansour, “Analytical solution of hyperbolic heat conduction equation in relation to laser short-pulse heating,” Physica B 406(8), 1550–1555 (2011).
[Crossref]

B. S. Yilbas and M. Pakdemirli, “Analytical solution for temperature field in electron and lattice sub-systems during heating of solid film,” Physica B 382(1-2), 213–219 (2006).
[Crossref]

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[Crossref]

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[Crossref]

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M. Malinauskas, A. Žukauskas, S. Hasegawa, Y. Hayasaki, V. Mizeikis, R. Buividas, and S. Juodkazis, “Ultrafast laser processing of materials: from science to industry,” Light Sci. Appl. 5(8), e16133 (2016).
[Crossref] [PubMed]

Adv. Opt. Photonics (1)

K. C. Phillips, H. H. Gandhi, E. Mazur, and S. K. Sundaram, “Ultrafast laser processing of materials: a review,” Adv. Opt. Photonics 7(4), 684–712 (2015).
[Crossref]

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V. I. Mazhukin, I. Smurov, C. Surry, and G. Flamant, “Overheated metastable states in polymer sublimation by laser radiation,” Appl. Surf. Sci. 86(1-4), 7–12 (1995).
[Crossref]

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T. T. Lam, “A generalized heat conduction solution for ultrafast laser heating in metallic films,” Int. J. Heat Mass Tran. 73, 330–339 (2014).
[Crossref]

G. Chen, Y. Wang, J. Zhang, and J. Bi, “An analytical solution for two-dimensional modeling of repetitive long pulse laser heating material,” Int. J. Heat Mass Tran. 104, 503–509 (2017).
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A. Kar and J. Mazumder, “Two-dimensional model for material damage due to melting and vaporization during laser irradiation,” J. Appl. Phys. 68(8), 3884–3891 (1990).
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[Crossref]

J. Mod. Opt. (1)

S. Nolte, M. Will, J. Burghoff, and A. Tünnermann, “Ultrafast laser processing: New options for three-dimensional photonic structures,” J. Mod. Opt. 51(16-18), 2533–2542 (2004).
[Crossref]

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

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

B. S. Yilbas and S. Z. Shuja, “Laser short-pulse heating of surfaces,” J. Phys. D Appl. Phys. 32(16), 1947–1954 (1999).
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M. Khenner and V. K. Henner, “Temperature of spatially modulated surface of solid film heated by repetitive laser pulses,” J. Phys. D Appl. Phys. 38(23), 4196–4201 (2005).
[Crossref]

Light Sci. Appl. (2)

M. Malinauskas, A. Žukauskas, S. Hasegawa, Y. Hayasaki, V. Mizeikis, R. Buividas, and S. Juodkazis, “Ultrafast laser processing of materials: from science to industry,” Light Sci. Appl. 5(8), e16133 (2016).
[Crossref] [PubMed]

K. Sugioka and Y. Cheng, “Ultrafast Lasers – reliable tools for advanced material processing,” Light Sci. Appl. 3(4), e149 (2014).
[Crossref]

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S. J. Kalita, S. Bose, H. L. Hosick, and A. Bandyopadhyay, “Development of controlled porosity polymer-ceramic composite scaffolds via fused deposition modeling,” Mater. Sci. Eng. C 23(5), 611–620 (2003).
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Nat. Commun. (1)

M. Hase, P. Fons, K. Mitrofanov, A. V. Kolobov, and J. Tominaga, “Femtosecond structural transformation of phase-change materials far from equilibrium monitored by coherent phonons,” Nat. Commun. 6(1), 8367 (2015).
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Nat. Photonics (1)

R. R. Gattass and E. Mazur, “Femtosecond laser micromaching in transparent materials,” Nat. Photonics 2(4), 219–225 (2008).
[Crossref]

Opt. Express (3)

Opt. Lasers Eng. (1)

S. Mishra and V. Yadava, “Laser Beam Micro-Machining (LBMM) – A review,” Opt. Lasers Eng. 73, 89–122 (2015).
[Crossref]

Opt. Mater. Express (1)

Phys. Rev. B Condens. Matter Mater. Phys. (1)

N. M. Bulgakova, R. Stoian, A. Rosenfeld, I. V. Hertel, and E. E. B. Campbell, “Electronic transport and consequences for material removal in ultrafast pulsed laser ablation of materials,” Phys. Rev. B Condens. Matter Mater. Phys. 69(5), 054102 (2004).
[Crossref]

Physica B (2)

B. S. Yilbas and M. Pakdemirli, “Analytical solution for temperature field in electron and lattice sub-systems during heating of solid film,” Physica B 382(1-2), 213–219 (2006).
[Crossref]

B. S. Yilbas, A. Y. Al-Dweik, and S. Bin Mansour, “Analytical solution of hyperbolic heat conduction equation in relation to laser short-pulse heating,” Physica B 406(8), 1550–1555 (2011).
[Crossref]

Prog. Polym. Sci. (1)

S. Zhang and A. R. Horrocks, “A review of flame retardant polypropylene fibres,” Prog. Polym. Sci. 28(11), 1517–1538 (2003).
[Crossref]

Surf. Coat. Tech. (1)

A. K. Nath, A. Gupta, and F. Benny, “Theoretical and experimental study on laser surface hardening by repetitive laser pulses,” Surf. Coat. Tech. 206(8–9), 2602–2615 (2012).
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Figures (12)

Fig. 1
Fig. 1 Schematic of ultrashort pulse laser heating model in cylindrical coordinates with boundary conditions at four locations as BC1, BC2, BC3 and BC4 at the upper and lower surfaces, center of the cylinder and r = Rc, respectively.
Fig. 2
Fig. 2 Results from the thermal model for various laser parameters, (a) radially symmetric temperature distribution at the surface of the workpiece, z = 0, and (b) axial distribution of temperature at the center of the laser beam, r = 0, to examine the maximum depth of the workpiece that can be vaporized using different laser parameters.
Fig. 3
Fig. 3 2D contour plot of temperature distribution in the workpiece, showing isotherms to indicate the removal of materials above the isotherm of vaporization temperature marked by 601 K contour.
Fig. 4
Fig. 4 Temperature distribution over time for different energies at the surface of the workpiece (z = 0, r = 0) and the decomposition temperature of PP indicated by a horizontal dash line, (a) heat accumulation with different pulses and (b) heat accumulation with 2 µJ pulse energy.
Fig. 5
Fig. 5 Schematics of the experimental setup for laser cutting.
Fig. 6
Fig. 6 Effect of different pulse repetition rates on the laser cutting process for different pulse energies with the same average powers, showing a variety of cut quality such as partial-depth cutting, through cutting and burning of the workpiece.
Fig. 7
Fig. 7 Microscopic examination of the cut quality, (a) illustration of heat accumulation at a high (1 MHz) repetition rate, (b) optical microscopic images of laser cut PP sheets at 1 MHz and 100 kHz with the same average power 1.5 W and (c) SEM images of the sheets in (b) for analyzing the cut quality at a higher magnification.
Fig. 8
Fig. 8 Comparison between the experimental kerf profile and the model result obtained at the cutting speed of 20 mm/s with a laser of pulse energy 20 µJ and 100 kHz repetition rate.
Fig. 9
Fig. 9 A process parameter map containing theoretical isotherms and experimental results to delineate different physical effects such as through cut and burning observed during the interaction between the ultrafast laser and PP workpiece.
Fig. 10
Fig. 10 Estimation of absorptivity by fitting the theoretical results to experimental data on partial cut depths at r = 0 for different cutting speeds.
Fig. 11
Fig. 11 Experimental data for the depth of cavity formed during laser cutting at different speeds and repetition rates, showing that the cut depths follow the same trend as a function of absorbed intensity.
Fig. 12
Fig. 12 Comparison between the experimental data for the material removal rate as a function of absorbed average power during laser cutting and the corresponding linear trend predicted by an overall energy balance model.

Tables (1)

Tables Icon

Table 1 Thermophysical properties of PP [24–26] and laser irradiation parameters for thermal modeling

Equations (52)

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I( r,t )=A I o   e 2 r 2 ω o 2 φ(t)
φ ( t )= { t( n p 1 ) t p    t pk            for ( n p 1 ) t p t  ( n p 1 ) t p + t pk  ( n p 1 ) t p + t on t t on   t pk          for ( n p 1 ) t p + t pk  <t( n p 1 ) t p + t on                     0                          for ( n p 1 ) t p + t on  <t ( n p 1 ) t p + t p
2  T( r,z,t ) r 2 +  1 r   T(r,z,t) r +  k zr 2  T( r,z,t ) z 2 =  1 α r   T(r,z,t) t
BC1:  k z T(r,z,t) z | z=0   =AI(r,t).
BC2:  k z   T(r,z,t) z | z=L   =h( T L   T ).
BC3:  T(r,z,t) r | r=0   =0.
 BC4:T( R c ,z,t )= T
IC :T( r,z,0 )=  T o
r * =  r ω o   z * =  z ω o
t * =  α r t ω o 2 T * (  r * , z * ,  t * )= T( r,z,t ) T T o T
1 r *   r *  ( r *   T * (  r * , z * ,  t * ) r *   )+ k zr 2 T * (  r * , z * ,  t * ) z * 2 =  1 α r     T * (  r * , z * ,  t * ) t *  
 BC1:    T * (  r * , z * ,  t * ) z * | z * =0 = A k z  I( r * , t * )
BC2:    T * (  r * , z * ,  t * ) z * | z * = L * = Bi  T * (  r * , z * ,  t * )| z * = L *
 BC3:    T * (  r * , z * ,  t * ) r * | r * =0 =0
BC4:  T * (   R c * , z * ,  t * )=0
IC:  T * (   r * , z * ,0 )=  T i
T * (   r * ,  z *  ,  t *   ) = m=1  J o ( λ m * r * ) N H  (   λ m *   ) ψ ¯ ss * (   λ m *  ,  z *  ,  τ *   )  + m=1  J o ( λ m * r * ) N H  (   λ m *   ) n=1  cos( γ n * z * ) N F  (   γ n *   ) T ¯ ˜ ι * ( λ m *  ,  γ n *  ) eat* m=1  J o ( λ m * r * ) N H  (   λ m *   ) n=1  cos( γ n * z * ) N F  (   γ n *   ) G ¯ ˜ ( λ m *  ,  γ n *  ) 0 t * e a( t * τ) d φ * ( τ * ) d τ * d τ *
1 N H ( λ m * ) =   2 R * 2 J 1 2 ( λ m * R * )
G ¯ ˜  ( λ m * ,  γ n * )=  0 L * ψ ¯ ss *  ( λ m * , z * )cos( γ n * z * ) d z *
 T( r,z,t )=( T o T ) T * (   r * ,  z *  ,  t *   )+ T
D=b( I a I a o ) 
v w k D=  1 H e ( A E p N p )  H l H e
k zr    d 2 T ¯ * ( λ m * , z * , t * ) d z * 2   λ m * 2   T ¯ * ( λ m * , z * , t * )= d T ¯ * ( λ m * , z * , t * ) d t *
BC1:  d T ¯ * ( λ m * , z * , t * ) d z * | z * =0 =  A k z   I ¯ ( λ m * , t * )
BC2: d T ¯ * ( λ m * , z * , t * ) d z * | z * = L * = Bi  T ¯ * ( λ m * , z * , t * )| z * = L *
 IC:  T ¯ * ( λ m * , z * ,0 )=  T ¯ i ( λ m * )
I ¯ ( λ m * , t * )=  0 R c * r * J o ( λ m * r * )I( r * , t * )d r *
T ¯ i ( λ m * )=  0 R c * r * J o ( λ m * r * ) T i  d r *
k zr    d 2 ψ ¯ * ( λ m * , z * , t * , τ * ) d z * 2   λ m * 2   ψ ¯ * ( λ m * , z * , t * , τ * )= d ψ ¯ * ( λ m * , z * , t * , τ * ) d t *
BC1:  d ψ ¯ * ( λ m *  , z * , t * , τ * ) d z * | z * =0 =  A k z   I ¯ ( λ m * , τ * )
BC2:  d ψ ¯ * ( λ m * ,   z * , t * , τ * ) d z * | z * = L * = Bi  ψ ¯ * ( λ m * ,  z * , t * , τ * )| z * = L *
 IC:  ψ ¯ * ( λ m * , z * ,0, τ * )=  T ¯ i ( λ m * )
ψ ¯ * ( λ m * , z * , t * , τ * )= ψ ¯ H *  ( λ m * , z * , t * )+ ψ ¯ ss *  ( λ m * , z * , τ * ) 
  k zr  d 2 ψ ¯ H * ( λ m * , z * , t * ) d z * 2   λ m * 2   ψ ¯ H * ( λ m * , z * , t * )= d ψ ¯ H * ( λ m * , z * , t * ) d t *
d ψ ¯ H * ( λ m * , z * , t * ) d z * | z * =0 =0
d ψ ¯ H * ( λ m * ,   z * , t * ) d z * | z * = L * +Bi  ψ ¯ H * ( λ m * ,  z * , t * )| z * = L * =0
  ψ ¯ H * ( λ m * , z * ,0 )=  T ¯ i ( λ m * )  ψ ¯ ss * ( λ m * , z * , τ * )
  d 2 ψ ¯ ss * ( λ m * , z * , τ * ) d z * 2 λ m * 2 k zr  ψ ¯ ss * ( λ m * , z * , τ * )=0 
d ψ ¯ ss * ( λ m * , z * , τ * ) d z * | z * =0 = I ¯ ( λ m * , τ * )
d ψ ¯ ss * ( λ m * ,   z * , τ * ) d z * | z * = L * +Bi  ψ ¯ ss * ( λ m * ,  z * , τ * )| z * = L * =0
ψ ¯ ss * ( λ m *  ,  z *  ,  τ *   )= C 3  [ { Bi sinh( λ m * k zr   L * )+ λ m * k zr  cosh( λ m * k zr   L * )   λ m * k zr sinh( λ m * k zr   L * )+Bicosh( λ m * k zr   L * )    }cosh( λ m * k zr   z * )+  sinh( λ m * k zr   z * ) ]
  ψ ¯ ˜ H * ( λ m * , γ n * , t * )= 0 L * cos( γ n * z * )   ψ ¯ H * ( λ m * , z * , t * )d z *
d ψ ¯ ˜ H * ( λ m * , γ n * , t * ) d t * +( k zr  γ n * 2 + λ m * 2 ) ψ ¯ ˜ H * ( λ m * , γ n * , t * )=0
  ψ ¯ ˜ H * ( λ m * , γ n * ,0 )=  T ¯ ˜ i ( λ m * )  ψ ¯ ˜ ss * ( λ m * , γ n * , τ * )
ψ ¯ ˜ H * ( λ m * ,, γ n * , t * )= ψ ¯ ˜ H * ( λ m * ,, γ n * ,0 ) e ( k zr  γ n * 2 + λ m * 2 ) t *
ψ ¯ * ( λ m * , z * , t * , τ * )=  n=1  cos( γ n * z * )  N F  (   γ n *   )  [ T ¯ ˜ i ( λ m * , γ n * ) ψ ¯ ˜ ss * ( λ m * , γ n * , τ * ) ] e ( k zr  γ n * 2 + λ m * 2 ) t * +  ψ ¯ ss * ( λ m *  ,  z *  ,  τ *   )
1 N F  ( γ n * ) = 2 ( γ n *2 +B i 2 ) L * ( γ n *2 +B i 2 )+Bi
T ¯ * ( λ m * , z * , t * )=  0 t * ψ ¯ * ( λ m * , z * , t * , τ * ) t *  d τ *  
T ¯ * ( λ m * , z * , t * )=  ψ ¯ ss * ( λ m *  ,  z *  ,  τ *   )+ n=1  cos( γ n * z * )  N F  (   γ n *   ) T ¯ ˜ i ( λ m * , γ n * ) e a t * n=1  cos( γ n * z * )  N F  (   γ n *   )  [ ψ ¯ ˜ ss *  ( λ m * , z * ,0 ) e a t * 0 t * e a( t * τ * ) d d τ * { ψ ¯ ss * ( λ m *  ,  γ n *  ,  τ *   ) }d τ * ]
N p  E p  At= 1 2 v  w k D ρ [ c p  ( T m T o )+  H m + H v + c p ( T f T m ) ]t  +k  ( T f T o ) α t on  v  t on 2 N p d p t+k  ( T f T o ) 2 α t off  v( t on + t off )  d p t off N p t
H e =  1 2  ρ [ c P ( T f T o )+ H m + H v ];
H l =  kρ c P ( T f T o ) 4 v 2 D ω o [ 2 t on 3/2 + t off 3/2 + t on t off ]

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