Abstract

A method of calculating radiation spectra of an asymmetric (ellipsoidal) laser-induced plasma plume is developed for two cases, when the radiation is collected by a lens and by an optical fiber. The lens receives the radiation coming from the entire plasma plume, while the view sight of an optical fiber is restricted to an acceptance cone so that only the radiation coming with an incident angle smaller than the cone angle is collected. The method incorporates the solution of the radiative transfer equation along the line of sight. An optimal number of lines is found to achieve the numerical convergence with a relative error <1%. Several practical simulations are carried out that include different placements and orientations of the lens and optic fiber. The effect of a motion of the center of the mass of the plasma plume on the radiation spectra is also investigated.

© 2008 Optical Society of America

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  1. J. D. Winefordner, I. B. Gornushkin, T. Correll, E. Gibb, B. W. Smith, and N. Omenetto, “Comparing several atomic spectrometric methods to the super stars: special emphasis on laser induced breakdown spectrometry, LIBS, a future super star,” J. Anal. At. Spectrom. 19, 1061-1083 (2004).
    [CrossRef]
  2. A. Bogaerts, Z. Chen, R. Gijbels, and A. Vertes, “Laser ablation for analytical sampling: what can we learn from modeling?,” Spectrochim. Acta Part B 58, 1867-1893 (2003).
    [CrossRef]
  3. S. I. Anisimov and B. S. Lukyanchuk, “Selected problems of laser ablation theory,” Usp. Fiz. Nauk 172, 301-333 (2002).
    [CrossRef]
  4. S. I. Anisimov, D. Buerle, and B. S. Lukyanchuk, “Gas dynamics and film profiles in pulsed-laser deposition of materials,” Phys. Rev. B 48, 12076-12081 (1993).
    [CrossRef]
  5. I. B. Gornushkin, J. Anzano, L. A. King, B. W. Smith, N. Omenetto, and J. D. Winefordner, “Curve of growth methodology applied to laser-induced plasma emission spectrometry,” Spectrochim. Acta Part B 54, 491-498 (1999).
    [CrossRef]
  6. J. A. Aguilera, C. Aragon, and J. Bengoechea, “Spatial characterization of laser-induced plasmas by deconvolution of spatially resolved spectra,” Appl. Opt. 42, 5938-5946 (2003).
    [CrossRef] [PubMed]
  7. A. Ciucci, M. Corsi, V. Palleschi, S. Rastelli, A. Salvetti, and E. Tognoni, “New procedure for quantitative elemental analysis by laser-induced plasma spectroscopy,” Appl. Spectrosc. 53, 960-964 (1999).
    [CrossRef]
  8. P. Yaroshchyk, D. Body, R. J. S. Morrison, and B. L. Chadwick, “A semi-quantitative standard-less analysis method for laser induced breakdown spectroscopy,” Spectrochim. Acta Part B 61, 200-209 (2006).
    [CrossRef]
  9. I. B. Gornushkin, A. Ya. Kazakov, N. Omenetto, B. W. Smith, and J. D. Winefordner, “Radiation dynamics of post-breakdown laser induced plasma,” Spectrochim. Acta Part B 59, 401-418 (2004).
    [CrossRef]
  10. I. B. Gornushkin, S. V. Shabanov, N. Omenetto, and J. D. Winefordner, “Theoretical modeling of a non-isothermal asymmetric expansion of laser induced plasma in vacuum,” J. Appl. Phys. 100, 073304 (2006).
    [CrossRef]
  11. J. J. MacFarlane, C. L. Rettig, P. Wang, I. E. Golovkin, and P. R. Woodruff, “Radiation hydrodynamics, spectral, and atomic physics modeling of laser-produced plasma EUVL lithography light sources,” Proc. SPIE Int. 5751, 588-600(2005).
    [CrossRef]
  12. Ya. B. Zel'dovich and Yu. P. Raizer, Physics of Shock Waves and High Temperature Hydrodynamics Phenomena (Academic, 1966), Vol. 1.
  13. B. C. Castle, A. K. Knight, K. Visser, B. W. Smith, and J. D. Winefordner, “Battery powered laser-induced plasma spectrometer for elemental determinations,” J. Anal. At. Spectrom. 13, 589-595 (1998).
    [CrossRef]
  14. V. Margetic, M. Bolshov, A. Stockhaus, K. Niemax, and R. Hergenrder, “Depth profiling of multi-layer samples using femtosecond laser ablation,” J. Anal. At. Spectrom. 16, 616-621 (2001).
    [CrossRef]
  15. D. N. Stratis, K. L. Eland, and S. M. Angel, “Effect of pulse delay time on a pre-ablation dual-pulse LIBS plasma,” Appl. Spectrosc. 55, 1297-1303 (2001).
    [CrossRef]
  16. Ocean Optics Product Catalogue, (Ocean Optics, Inc., 2004), p. 122.

2006 (2)

P. Yaroshchyk, D. Body, R. J. S. Morrison, and B. L. Chadwick, “A semi-quantitative standard-less analysis method for laser induced breakdown spectroscopy,” Spectrochim. Acta Part B 61, 200-209 (2006).
[CrossRef]

I. B. Gornushkin, S. V. Shabanov, N. Omenetto, and J. D. Winefordner, “Theoretical modeling of a non-isothermal asymmetric expansion of laser induced plasma in vacuum,” J. Appl. Phys. 100, 073304 (2006).
[CrossRef]

2005 (1)

J. J. MacFarlane, C. L. Rettig, P. Wang, I. E. Golovkin, and P. R. Woodruff, “Radiation hydrodynamics, spectral, and atomic physics modeling of laser-produced plasma EUVL lithography light sources,” Proc. SPIE Int. 5751, 588-600(2005).
[CrossRef]

2004 (2)

I. B. Gornushkin, A. Ya. Kazakov, N. Omenetto, B. W. Smith, and J. D. Winefordner, “Radiation dynamics of post-breakdown laser induced plasma,” Spectrochim. Acta Part B 59, 401-418 (2004).
[CrossRef]

J. D. Winefordner, I. B. Gornushkin, T. Correll, E. Gibb, B. W. Smith, and N. Omenetto, “Comparing several atomic spectrometric methods to the super stars: special emphasis on laser induced breakdown spectrometry, LIBS, a future super star,” J. Anal. At. Spectrom. 19, 1061-1083 (2004).
[CrossRef]

2003 (2)

A. Bogaerts, Z. Chen, R. Gijbels, and A. Vertes, “Laser ablation for analytical sampling: what can we learn from modeling?,” Spectrochim. Acta Part B 58, 1867-1893 (2003).
[CrossRef]

J. A. Aguilera, C. Aragon, and J. Bengoechea, “Spatial characterization of laser-induced plasmas by deconvolution of spatially resolved spectra,” Appl. Opt. 42, 5938-5946 (2003).
[CrossRef] [PubMed]

2002 (1)

S. I. Anisimov and B. S. Lukyanchuk, “Selected problems of laser ablation theory,” Usp. Fiz. Nauk 172, 301-333 (2002).
[CrossRef]

2001 (2)

V. Margetic, M. Bolshov, A. Stockhaus, K. Niemax, and R. Hergenrder, “Depth profiling of multi-layer samples using femtosecond laser ablation,” J. Anal. At. Spectrom. 16, 616-621 (2001).
[CrossRef]

D. N. Stratis, K. L. Eland, and S. M. Angel, “Effect of pulse delay time on a pre-ablation dual-pulse LIBS plasma,” Appl. Spectrosc. 55, 1297-1303 (2001).
[CrossRef]

1999 (2)

I. B. Gornushkin, J. Anzano, L. A. King, B. W. Smith, N. Omenetto, and J. D. Winefordner, “Curve of growth methodology applied to laser-induced plasma emission spectrometry,” Spectrochim. Acta Part B 54, 491-498 (1999).
[CrossRef]

A. Ciucci, M. Corsi, V. Palleschi, S. Rastelli, A. Salvetti, and E. Tognoni, “New procedure for quantitative elemental analysis by laser-induced plasma spectroscopy,” Appl. Spectrosc. 53, 960-964 (1999).
[CrossRef]

1998 (1)

B. C. Castle, A. K. Knight, K. Visser, B. W. Smith, and J. D. Winefordner, “Battery powered laser-induced plasma spectrometer for elemental determinations,” J. Anal. At. Spectrom. 13, 589-595 (1998).
[CrossRef]

1993 (1)

S. I. Anisimov, D. Buerle, and B. S. Lukyanchuk, “Gas dynamics and film profiles in pulsed-laser deposition of materials,” Phys. Rev. B 48, 12076-12081 (1993).
[CrossRef]

Aguilera, J. A.

Angel, S. M.

Anisimov, S. I.

S. I. Anisimov and B. S. Lukyanchuk, “Selected problems of laser ablation theory,” Usp. Fiz. Nauk 172, 301-333 (2002).
[CrossRef]

S. I. Anisimov, D. Buerle, and B. S. Lukyanchuk, “Gas dynamics and film profiles in pulsed-laser deposition of materials,” Phys. Rev. B 48, 12076-12081 (1993).
[CrossRef]

Anzano, J.

I. B. Gornushkin, J. Anzano, L. A. King, B. W. Smith, N. Omenetto, and J. D. Winefordner, “Curve of growth methodology applied to laser-induced plasma emission spectrometry,” Spectrochim. Acta Part B 54, 491-498 (1999).
[CrossRef]

Aragon, C.

Bengoechea, J.

Body, D.

P. Yaroshchyk, D. Body, R. J. S. Morrison, and B. L. Chadwick, “A semi-quantitative standard-less analysis method for laser induced breakdown spectroscopy,” Spectrochim. Acta Part B 61, 200-209 (2006).
[CrossRef]

Bogaerts, A.

A. Bogaerts, Z. Chen, R. Gijbels, and A. Vertes, “Laser ablation for analytical sampling: what can we learn from modeling?,” Spectrochim. Acta Part B 58, 1867-1893 (2003).
[CrossRef]

Bolshov, M.

V. Margetic, M. Bolshov, A. Stockhaus, K. Niemax, and R. Hergenrder, “Depth profiling of multi-layer samples using femtosecond laser ablation,” J. Anal. At. Spectrom. 16, 616-621 (2001).
[CrossRef]

Buerle, D.

S. I. Anisimov, D. Buerle, and B. S. Lukyanchuk, “Gas dynamics and film profiles in pulsed-laser deposition of materials,” Phys. Rev. B 48, 12076-12081 (1993).
[CrossRef]

Castle, B. C.

B. C. Castle, A. K. Knight, K. Visser, B. W. Smith, and J. D. Winefordner, “Battery powered laser-induced plasma spectrometer for elemental determinations,” J. Anal. At. Spectrom. 13, 589-595 (1998).
[CrossRef]

Chadwick, B. L.

P. Yaroshchyk, D. Body, R. J. S. Morrison, and B. L. Chadwick, “A semi-quantitative standard-less analysis method for laser induced breakdown spectroscopy,” Spectrochim. Acta Part B 61, 200-209 (2006).
[CrossRef]

Chen, Z.

A. Bogaerts, Z. Chen, R. Gijbels, and A. Vertes, “Laser ablation for analytical sampling: what can we learn from modeling?,” Spectrochim. Acta Part B 58, 1867-1893 (2003).
[CrossRef]

Ciucci, A.

Correll, T.

J. D. Winefordner, I. B. Gornushkin, T. Correll, E. Gibb, B. W. Smith, and N. Omenetto, “Comparing several atomic spectrometric methods to the super stars: special emphasis on laser induced breakdown spectrometry, LIBS, a future super star,” J. Anal. At. Spectrom. 19, 1061-1083 (2004).
[CrossRef]

Corsi, M.

Eland, K. L.

Gibb, E.

J. D. Winefordner, I. B. Gornushkin, T. Correll, E. Gibb, B. W. Smith, and N. Omenetto, “Comparing several atomic spectrometric methods to the super stars: special emphasis on laser induced breakdown spectrometry, LIBS, a future super star,” J. Anal. At. Spectrom. 19, 1061-1083 (2004).
[CrossRef]

Gijbels, R.

A. Bogaerts, Z. Chen, R. Gijbels, and A. Vertes, “Laser ablation for analytical sampling: what can we learn from modeling?,” Spectrochim. Acta Part B 58, 1867-1893 (2003).
[CrossRef]

Golovkin, I. E.

J. J. MacFarlane, C. L. Rettig, P. Wang, I. E. Golovkin, and P. R. Woodruff, “Radiation hydrodynamics, spectral, and atomic physics modeling of laser-produced plasma EUVL lithography light sources,” Proc. SPIE Int. 5751, 588-600(2005).
[CrossRef]

Gornushkin, I. B.

I. B. Gornushkin, S. V. Shabanov, N. Omenetto, and J. D. Winefordner, “Theoretical modeling of a non-isothermal asymmetric expansion of laser induced plasma in vacuum,” J. Appl. Phys. 100, 073304 (2006).
[CrossRef]

I. B. Gornushkin, A. Ya. Kazakov, N. Omenetto, B. W. Smith, and J. D. Winefordner, “Radiation dynamics of post-breakdown laser induced plasma,” Spectrochim. Acta Part B 59, 401-418 (2004).
[CrossRef]

J. D. Winefordner, I. B. Gornushkin, T. Correll, E. Gibb, B. W. Smith, and N. Omenetto, “Comparing several atomic spectrometric methods to the super stars: special emphasis on laser induced breakdown spectrometry, LIBS, a future super star,” J. Anal. At. Spectrom. 19, 1061-1083 (2004).
[CrossRef]

I. B. Gornushkin, J. Anzano, L. A. King, B. W. Smith, N. Omenetto, and J. D. Winefordner, “Curve of growth methodology applied to laser-induced plasma emission spectrometry,” Spectrochim. Acta Part B 54, 491-498 (1999).
[CrossRef]

Hergenrder, R.

V. Margetic, M. Bolshov, A. Stockhaus, K. Niemax, and R. Hergenrder, “Depth profiling of multi-layer samples using femtosecond laser ablation,” J. Anal. At. Spectrom. 16, 616-621 (2001).
[CrossRef]

Kazakov, A. Ya.

I. B. Gornushkin, A. Ya. Kazakov, N. Omenetto, B. W. Smith, and J. D. Winefordner, “Radiation dynamics of post-breakdown laser induced plasma,” Spectrochim. Acta Part B 59, 401-418 (2004).
[CrossRef]

King, L. A.

I. B. Gornushkin, J. Anzano, L. A. King, B. W. Smith, N. Omenetto, and J. D. Winefordner, “Curve of growth methodology applied to laser-induced plasma emission spectrometry,” Spectrochim. Acta Part B 54, 491-498 (1999).
[CrossRef]

Knight, A. K.

B. C. Castle, A. K. Knight, K. Visser, B. W. Smith, and J. D. Winefordner, “Battery powered laser-induced plasma spectrometer for elemental determinations,” J. Anal. At. Spectrom. 13, 589-595 (1998).
[CrossRef]

Lukyanchuk, B. S.

S. I. Anisimov and B. S. Lukyanchuk, “Selected problems of laser ablation theory,” Usp. Fiz. Nauk 172, 301-333 (2002).
[CrossRef]

S. I. Anisimov, D. Buerle, and B. S. Lukyanchuk, “Gas dynamics and film profiles in pulsed-laser deposition of materials,” Phys. Rev. B 48, 12076-12081 (1993).
[CrossRef]

MacFarlane, J. J.

J. J. MacFarlane, C. L. Rettig, P. Wang, I. E. Golovkin, and P. R. Woodruff, “Radiation hydrodynamics, spectral, and atomic physics modeling of laser-produced plasma EUVL lithography light sources,” Proc. SPIE Int. 5751, 588-600(2005).
[CrossRef]

Margetic, V.

V. Margetic, M. Bolshov, A. Stockhaus, K. Niemax, and R. Hergenrder, “Depth profiling of multi-layer samples using femtosecond laser ablation,” J. Anal. At. Spectrom. 16, 616-621 (2001).
[CrossRef]

Niemax, K.

V. Margetic, M. Bolshov, A. Stockhaus, K. Niemax, and R. Hergenrder, “Depth profiling of multi-layer samples using femtosecond laser ablation,” J. Anal. At. Spectrom. 16, 616-621 (2001).
[CrossRef]

Omenetto, N.

I. B. Gornushkin, S. V. Shabanov, N. Omenetto, and J. D. Winefordner, “Theoretical modeling of a non-isothermal asymmetric expansion of laser induced plasma in vacuum,” J. Appl. Phys. 100, 073304 (2006).
[CrossRef]

I. B. Gornushkin, A. Ya. Kazakov, N. Omenetto, B. W. Smith, and J. D. Winefordner, “Radiation dynamics of post-breakdown laser induced plasma,” Spectrochim. Acta Part B 59, 401-418 (2004).
[CrossRef]

J. D. Winefordner, I. B. Gornushkin, T. Correll, E. Gibb, B. W. Smith, and N. Omenetto, “Comparing several atomic spectrometric methods to the super stars: special emphasis on laser induced breakdown spectrometry, LIBS, a future super star,” J. Anal. At. Spectrom. 19, 1061-1083 (2004).
[CrossRef]

I. B. Gornushkin, J. Anzano, L. A. King, B. W. Smith, N. Omenetto, and J. D. Winefordner, “Curve of growth methodology applied to laser-induced plasma emission spectrometry,” Spectrochim. Acta Part B 54, 491-498 (1999).
[CrossRef]

Palleschi, V.

Raizer, Yu. P.

Ya. B. Zel'dovich and Yu. P. Raizer, Physics of Shock Waves and High Temperature Hydrodynamics Phenomena (Academic, 1966), Vol. 1.

Rastelli, S.

Rettig, C. L.

J. J. MacFarlane, C. L. Rettig, P. Wang, I. E. Golovkin, and P. R. Woodruff, “Radiation hydrodynamics, spectral, and atomic physics modeling of laser-produced plasma EUVL lithography light sources,” Proc. SPIE Int. 5751, 588-600(2005).
[CrossRef]

S. Morrison, R. J.

P. Yaroshchyk, D. Body, R. J. S. Morrison, and B. L. Chadwick, “A semi-quantitative standard-less analysis method for laser induced breakdown spectroscopy,” Spectrochim. Acta Part B 61, 200-209 (2006).
[CrossRef]

Salvetti, A.

Shabanov, S. V.

I. B. Gornushkin, S. V. Shabanov, N. Omenetto, and J. D. Winefordner, “Theoretical modeling of a non-isothermal asymmetric expansion of laser induced plasma in vacuum,” J. Appl. Phys. 100, 073304 (2006).
[CrossRef]

Smith, B. W.

I. B. Gornushkin, A. Ya. Kazakov, N. Omenetto, B. W. Smith, and J. D. Winefordner, “Radiation dynamics of post-breakdown laser induced plasma,” Spectrochim. Acta Part B 59, 401-418 (2004).
[CrossRef]

J. D. Winefordner, I. B. Gornushkin, T. Correll, E. Gibb, B. W. Smith, and N. Omenetto, “Comparing several atomic spectrometric methods to the super stars: special emphasis on laser induced breakdown spectrometry, LIBS, a future super star,” J. Anal. At. Spectrom. 19, 1061-1083 (2004).
[CrossRef]

I. B. Gornushkin, J. Anzano, L. A. King, B. W. Smith, N. Omenetto, and J. D. Winefordner, “Curve of growth methodology applied to laser-induced plasma emission spectrometry,” Spectrochim. Acta Part B 54, 491-498 (1999).
[CrossRef]

B. C. Castle, A. K. Knight, K. Visser, B. W. Smith, and J. D. Winefordner, “Battery powered laser-induced plasma spectrometer for elemental determinations,” J. Anal. At. Spectrom. 13, 589-595 (1998).
[CrossRef]

Stockhaus, A.

V. Margetic, M. Bolshov, A. Stockhaus, K. Niemax, and R. Hergenrder, “Depth profiling of multi-layer samples using femtosecond laser ablation,” J. Anal. At. Spectrom. 16, 616-621 (2001).
[CrossRef]

Stratis, D. N.

Tognoni, E.

Vertes, A.

A. Bogaerts, Z. Chen, R. Gijbels, and A. Vertes, “Laser ablation for analytical sampling: what can we learn from modeling?,” Spectrochim. Acta Part B 58, 1867-1893 (2003).
[CrossRef]

Visser, K.

B. C. Castle, A. K. Knight, K. Visser, B. W. Smith, and J. D. Winefordner, “Battery powered laser-induced plasma spectrometer for elemental determinations,” J. Anal. At. Spectrom. 13, 589-595 (1998).
[CrossRef]

Wang, P.

J. J. MacFarlane, C. L. Rettig, P. Wang, I. E. Golovkin, and P. R. Woodruff, “Radiation hydrodynamics, spectral, and atomic physics modeling of laser-produced plasma EUVL lithography light sources,” Proc. SPIE Int. 5751, 588-600(2005).
[CrossRef]

Winefordner, J. D.

I. B. Gornushkin, S. V. Shabanov, N. Omenetto, and J. D. Winefordner, “Theoretical modeling of a non-isothermal asymmetric expansion of laser induced plasma in vacuum,” J. Appl. Phys. 100, 073304 (2006).
[CrossRef]

I. B. Gornushkin, A. Ya. Kazakov, N. Omenetto, B. W. Smith, and J. D. Winefordner, “Radiation dynamics of post-breakdown laser induced plasma,” Spectrochim. Acta Part B 59, 401-418 (2004).
[CrossRef]

J. D. Winefordner, I. B. Gornushkin, T. Correll, E. Gibb, B. W. Smith, and N. Omenetto, “Comparing several atomic spectrometric methods to the super stars: special emphasis on laser induced breakdown spectrometry, LIBS, a future super star,” J. Anal. At. Spectrom. 19, 1061-1083 (2004).
[CrossRef]

I. B. Gornushkin, J. Anzano, L. A. King, B. W. Smith, N. Omenetto, and J. D. Winefordner, “Curve of growth methodology applied to laser-induced plasma emission spectrometry,” Spectrochim. Acta Part B 54, 491-498 (1999).
[CrossRef]

B. C. Castle, A. K. Knight, K. Visser, B. W. Smith, and J. D. Winefordner, “Battery powered laser-induced plasma spectrometer for elemental determinations,” J. Anal. At. Spectrom. 13, 589-595 (1998).
[CrossRef]

Woodruff, P. R.

J. J. MacFarlane, C. L. Rettig, P. Wang, I. E. Golovkin, and P. R. Woodruff, “Radiation hydrodynamics, spectral, and atomic physics modeling of laser-produced plasma EUVL lithography light sources,” Proc. SPIE Int. 5751, 588-600(2005).
[CrossRef]

Yaroshchyk, P.

P. Yaroshchyk, D. Body, R. J. S. Morrison, and B. L. Chadwick, “A semi-quantitative standard-less analysis method for laser induced breakdown spectroscopy,” Spectrochim. Acta Part B 61, 200-209 (2006).
[CrossRef]

Zel'dovich, Ya. B.

Ya. B. Zel'dovich and Yu. P. Raizer, Physics of Shock Waves and High Temperature Hydrodynamics Phenomena (Academic, 1966), Vol. 1.

Appl. Opt. (1)

Appl. Spectrosc. (2)

J. Anal. At. Spectrom. (3)

B. C. Castle, A. K. Knight, K. Visser, B. W. Smith, and J. D. Winefordner, “Battery powered laser-induced plasma spectrometer for elemental determinations,” J. Anal. At. Spectrom. 13, 589-595 (1998).
[CrossRef]

V. Margetic, M. Bolshov, A. Stockhaus, K. Niemax, and R. Hergenrder, “Depth profiling of multi-layer samples using femtosecond laser ablation,” J. Anal. At. Spectrom. 16, 616-621 (2001).
[CrossRef]

J. D. Winefordner, I. B. Gornushkin, T. Correll, E. Gibb, B. W. Smith, and N. Omenetto, “Comparing several atomic spectrometric methods to the super stars: special emphasis on laser induced breakdown spectrometry, LIBS, a future super star,” J. Anal. At. Spectrom. 19, 1061-1083 (2004).
[CrossRef]

J. Appl. Phys. (1)

I. B. Gornushkin, S. V. Shabanov, N. Omenetto, and J. D. Winefordner, “Theoretical modeling of a non-isothermal asymmetric expansion of laser induced plasma in vacuum,” J. Appl. Phys. 100, 073304 (2006).
[CrossRef]

Phys. Rev. B (1)

S. I. Anisimov, D. Buerle, and B. S. Lukyanchuk, “Gas dynamics and film profiles in pulsed-laser deposition of materials,” Phys. Rev. B 48, 12076-12081 (1993).
[CrossRef]

Proc. SPIE Int. (1)

J. J. MacFarlane, C. L. Rettig, P. Wang, I. E. Golovkin, and P. R. Woodruff, “Radiation hydrodynamics, spectral, and atomic physics modeling of laser-produced plasma EUVL lithography light sources,” Proc. SPIE Int. 5751, 588-600(2005).
[CrossRef]

Spectrochim. Acta Part B (4)

I. B. Gornushkin, J. Anzano, L. A. King, B. W. Smith, N. Omenetto, and J. D. Winefordner, “Curve of growth methodology applied to laser-induced plasma emission spectrometry,” Spectrochim. Acta Part B 54, 491-498 (1999).
[CrossRef]

A. Bogaerts, Z. Chen, R. Gijbels, and A. Vertes, “Laser ablation for analytical sampling: what can we learn from modeling?,” Spectrochim. Acta Part B 58, 1867-1893 (2003).
[CrossRef]

P. Yaroshchyk, D. Body, R. J. S. Morrison, and B. L. Chadwick, “A semi-quantitative standard-less analysis method for laser induced breakdown spectroscopy,” Spectrochim. Acta Part B 61, 200-209 (2006).
[CrossRef]

I. B. Gornushkin, A. Ya. Kazakov, N. Omenetto, B. W. Smith, and J. D. Winefordner, “Radiation dynamics of post-breakdown laser induced plasma,” Spectrochim. Acta Part B 59, 401-418 (2004).
[CrossRef]

Usp. Fiz. Nauk (1)

S. I. Anisimov and B. S. Lukyanchuk, “Selected problems of laser ablation theory,” Usp. Fiz. Nauk 172, 301-333 (2002).
[CrossRef]

Other (2)

Ya. B. Zel'dovich and Yu. P. Raizer, Physics of Shock Waves and High Temperature Hydrodynamics Phenomena (Academic, 1966), Vol. 1.

Ocean Optics Product Catalogue, (Ocean Optics, Inc., 2004), p. 122.

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Figures (5)

Fig. 1
Fig. 1

Ellipsoid oriented along the coordinate axes. A generally oriented ellipsoid is obtained by three rotations as explained in Appendix A.

Fig. 2
Fig. 2

Parameterization of the plasma ellipsoid E and lens L as explained in the text. The shaded crosssections form the family of planes P ( η ) normal to A ξ p . The part E p of the ellipsoid surface E visible from the point p is the union of the ellipses being the intersections of planes P ( η ) with E . The ellipses are shown by dashed curves, and the dashed straight lines indicate the direction of the plasma radiation collected by the lens surface element d σ at the point p.

Fig. 3
Fig. 3

(a) Light collection geometry for the lens and (b) spectra calculated for different positions of the collection lens.

Fig. 4
Fig. 4

(a) Series of images illustrating the motion of the center of the mass of a plasma plume in vacuum (the recoil motion). The vertical axis is the distance in centimeters from the target surface where the ablation takes place, the horizontal axis is time in nanoseconds. The images were recorded for the brass plasma in vacuum [10]. (b) Dependence of the distance traveled by the plume upon the delay time. The slope is used to determine the speed of the center of the mass.

Fig. 5
Fig. 5

(a) Light collection geometry for the optical fiber. Two otherwise identical plasma plume have different speeds v of the center of the mass. Plasma plumes are schematically shown by ellipses, the larger ellipse corresponds to a later time. If v = 0 (left), the ellipses have the same center, not so for v 0 (right). This causes the difference in the radiation data collected by the fiber (black rectangle) within its sight cone (between two straight rays outgoing from the fiber). (b) Mg 285.21 nm line calculated for the two cases shown in (a). The solid curve represents the result for v = 0 (the center of the mass at rest), the dashed curve represents the result for the moving center of the mass.

Equations (53)

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( r , A ξ r ) = 1 ,
I ν ( p , r , t ) ( l , d S ) d Ω σ ,
I ν ( p , r , t ) ( r p , n ) | p r | 3 cos θ p d S d σ .
I ν tot ( t ) = L E p I ν ( p , r , t ) ( r p , n ) | p r | 3 cos θ p d S d σ ,
( r , A ξ p ) 1 ,
( r , A ξ p ) = η , η [ 1 , λ ] .
λ = ( p , A ξ p ) .
( e i , A ξ e j ) = δ i j , ( e j , A ξ p ) = 0 , i , j = 1 , 2.
r U = ξ 1 sin ϕ cos φ , ξ 2 sin ϕ sin φ , ξ 3 cos ϕ , ϕ [ 0 , π ] , φ [ 0 , 2 π ) .
e 1 U = ( r U ϕ ) λ = ξ 1 cos ϕ λ cos φ λ , ξ 2 cos ϕ λ sin φ λ , - ξ 3 sin ϕ λ ,
e 2 U = 1 sin ϕ λ ( r U φ ) λ = - ξ 1 sin φ λ , ξ 2 cos φ λ , 0 ,
e j = U T e j U .
r = η λ 2 p + q 1 e 1 + q 2 e 2 ,
q 1 2 + q 2 2 = 1 - η 2 λ 2 ,
r = r ( p , η , θ ) = η λ 2 p + 1 - η 2 λ 2 ( cos θ e 1 + sin θ e 2 ) , η [ 1 , λ ] , θ [ 0 , 2 π ) .
η s ( η ) = η - 2 ( η - 1 ) ( λ 2 - η ) 1 + λ 2 - 2 η .
r l ( u ) = ( 1 - u ) r ( p , η s , θ ) + u r ( p , η , θ ) , u [ 0 , 1 ] .
I ν ( p , r , t ) = 0 1 B ν ( r l ( u ) , t ) κ ν ( r l ( u ) , t ) exp [ - u 1 κ ( r l ( u ) , t ) d u ] d u ,
d S d η d θ = r η × r θ = 1 - η 2 / λ 2 λ 2 ( - sin θ p × e 1 + cos θ p × e 2 ) - η λ 2 e 1 × e 2 .
L = η - η s λ 2 p + { 1 - η 2 / λ 2 - 1 - η s 2 / λ 2 } ( cos θ e 1 + sin θ e 2 ) ,
cos θ p d S = | ( L , d S ) | | L | J ( p , η , θ ) d η d θ ,
J ( p , η , θ ) = { ( η - η s ) η + λ 2 - η 2 - ( λ 2 - η 2 ) ( λ 2 - η s 2 ) } | ( p , e 1 × e 2 ) | | L | λ 4 .
p = p ( r , α ) = p 0 + r ( cos α u 1 + sin α u 2 ) , r [ 0 , R ] , α [ 0 , 2 π ) .
( r - p , n ) | r - p | 3 = ( r , n ) - ( p 0 , n ) | r - p | 3 Ω ( p , η , θ ) ,
I ν t o t ( t ) = 0 2 π 0 R 1 λ 0 2 π I ν ( p , r , t ) Ω ( p , η , θ ) J ( p , η , θ ) r d θ d η d r d α .
λ 2 = ( p , A ξ p ) A ξ | p | 2 A ξ ( | p 0 | + R ) 2 ,
λ max = | p 0 | + R min ( ξ 1 , ξ 2 , ξ 3 ) .
N η = 1 + [ λ - 1 Δ λ ] ,
r j + 1 = r j + Δ r , α j + 1 = α j + Δ α ,
p j k = p ( r j , α k ) , λ j k = ( p j k , A ξ p j k ) 1 / 2 , N η ; j k = 1 + [ ( λ j k - 1 ) / Δ λ ] .
Δ η l = { ( λ j k - 1 ) / ln N η ; j k } ln { ( l + 1 ) / l } ,
η l + 1 = η l + Δ η l , η 1 = Δ η 1 / 2 , η s , l = η s ( η l ) ,
θ m + 1 = θ m + Δ θ , r l m = r ( p j k , η l , θ m ) , r s , l m = r ( p j k , η s , l , θ m ) .
r j , k ; l , m q = ( 1 - u q ) r s , l m + u q r l m , I j , k ; l , m = q = 1 N u B ν ( r j , k ; l , m q , t ) κ ν ( r j , k ; l , m q , t ) exp [ - q = q N u κ ν ( r j , k ; l , m q , t ) Δ u ] Δ u .
Ω j , k ; l , m = Ω ( p j k , η l , θ m ) , J j , k ; l , m = J ( p j k , η l , θ m ) .
I ν tot ( t ) = j = 1 N r r j { k = 1 N α { l = 1 N η ; j k { m = 1 N θ I j , k ; l , m Ω j , k ; l , m J j , k ; l , m Δ θ } Δ η } Δ α } Δ r .
I ν t o t ( t ) = σ 0 E β 0 I ν ( p 0 , r , t ) ( r - p 0 , n ) | r - p 0 | 3 ( l 0 , d S ) ,
- ( l 0 , n ) cos β 0 , l 0 = L 0 / | L 0 | , L 0 = p 0 - r .
I ν tot ( t ) = σ 0 l , m I 0 ; l , m Ω 0 ; l , m J 0 ; l , m Δ θ Δ η ,
U = U z ( θ E ) U y ( ϕ E ) U z ( φ E ) , r U = U r ,
U z ( β ) = [ cos β - sin β 0 sin β cos β 0 0 0 1 ] , U y ( β ) = [ cos β 0 - sin β 0 1 0 sin β 0 cos β ] .
n = U z ( ψ ) U y ( ϕ ) n 0 , u 1 , 2 = U z ( ψ ) U y ( ϕ ) u 01 , 02 .
v ( β , α ) = n cos β + ( u 1 cos α + u 2 sin α ) sin β n cos β + u α sin β ,
1 = ( r u , A ξ r u ) = ( p 0 , A ξ p 0 ) + 2 u ( p 0 , A ξ v ) + u 2 ( v , A ξ v ) ,
( v , M 0 v ) ( v , A ξ p 0 ) 2 - [ ( p 0 , A ξ p 0 ) - 1 ] ( v , A ξ v ) 0.
sin ( 2 β + γ α ) - c n + a α ( c n - a α ) 2 + 4 b α 2 ,
β [ β 1 * , β 2 * ] , β 1 * = max ( - β 0 , β 1 ) , β 2 * = min ( β 0 , β 2 ) .
if     c n = ( n , M 0 n ) 0 , then     α [ 0 , π ] .
h 1 q 1 2 + h 2 q 2 2 + 2 b q 1 q 2 = 1 ,
h 1 q 1 2 + h 2 q 2 2 - f 1 q 1 - f 2 q 2 = 0 ,
u = u ± ( β , α ) = - ( v , A ξ p 0 ) ± ( v , M 0 v ) ( v , A ξ v ) .
( l 0 , d S ) = | r - - p 0 | 2 | sin β | d β d α = u - 2 ( β , α ) | sin β | d β d α .
I ν tot ( t ) = σ 0 α 1 α 2 β 1 * β 2 * I ν ( p 0 , r - ( β , α ) , t ) cos β | sin β | d β d α .

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