Abstract

The evolution of the shape and size of a bubble around a nanowire immersed in a liquid can be studied as a light absorption problem and consequently can directly be related to the distribution of the temperature around the nanowire. Such a physical phenomenon can be seen as the photo-thermal coupled problem of nanowire illuminated by an electromagnetic wave. The resolution of the multiphysic model allows to compute the variation of the temperature and consequently the evolution of the created bubble. An advanced adaptive remeshing process is developed to solve the numerical model using Finite Element Method. An optimization process is applied to solve the coupled problem and is used to detect the size of the produced bubble around nanowire under illumination. The adaptive remeshing process permits to control the convergence of the numerical solution relatively to the evolution of the temperature field. The process allows to study the evolution of the shape and size of the bubble. We show the influence of the laser parameters on the evolution of the bubble. The informations about the geometry of the nanowire can be deduced from the size and shape of the bubble.

© 2013 OSA

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  1. M. Boroski, A. C. Rodrigues, J. C. Garcia, L. C. Sampaio, J. Nozaki, and N. Hioka, “Combined electrocoagulation and TiO2photoassisted treatment applied to wastewater effluents from pharmaceutical and cosmetic industries original,” J. Hazard. Mater.162, 448–454 (2009).
    [CrossRef]
  2. D. Karamanis, A. N. Okte, E. Vardoulakis, and T. Vaimakis, “Water vapor adsorption and photocatalytic pollutant degradation with TiO2-sepiolite nanocomposites original,” Appl. Clay Sci.53, 181–187 (2011).
    [CrossRef]
  3. G. Bystrzejewska-Piotrowska, J. Golimowski, and P. L. Urban, “Nanoparticles: their potential toxicity, waste and environmental management,” Waste Manage.29, 2587–2595 (2009).
    [CrossRef]
  4. B. Nowack, “The behavior and effects of nanoparticles in the environment,” Environ. Pollut.157, 1063–1064 (2009).
    [CrossRef] [PubMed]
  5. D. Lapotko and E. Lukianova, “Laser-induced micro-bubbles in cells,” Int. J. Heat Mass Transf.48(1), 227–234 (2005).
    [CrossRef]
  6. D. Lapotko, E. Lukianova, and A. Shnip, “Photothermal responses of individual cells,” J. Biomed. Opt.10, 014006 (2004).
    [CrossRef]
  7. D. Barchiesi, T. Grosges, E. Kremer, and M. Lamy de la Chapelle, “Electromagnetic heat induced in meso-structures: computation of temperature in metallic dimers,” PIERS Online7, 406–410 (2011).
  8. T. Grosges, H. Borouchaki, and D. Barchiesi, “New adaptive mesh development for accurate near-field enhancement computation,” J. Microsc.229, 293–301 (2008).
    [CrossRef] [PubMed]
  9. M. Born and E. Wolf, Principle of Optics (Pergamon, 1993).
  10. J. Jin, The Finite Element Method in Electromagnetics (John Wiley and Sons, 1993).
  11. T. Grosges, S. Petit, D. Barchiesi, and S. Hudlet, “Numerical modeling of the subwavelength phase-change recording using an apertureless scanning near-field optical microscope,” Opt. Express12, 5987–5995 (2004).
    [CrossRef] [PubMed]
  12. T. Grosges, A. Vial, and D. Barchiesi, “Models of near field spectroscopic studies: comparison between finite element and finite difference methods,” Opt. Express13, 8483–8497 (2005).
    [CrossRef] [PubMed]
  13. R. Courant, “Variational methods for the solution of problems of equilibrium and vibrations,” Bull. Amer. Math. Soc.49, 1–23 (1943).
    [CrossRef]
  14. P. Silvester and G. Pelosi, Finite Elements for Wave Electromagnetics: Methods and Techniques (IEEE, 1994).
  15. D. Barchiesi, E. Kremer, A. Cherouat, T. Grosges, and H. Borouchaki, “Dilation of nanonatennas induced by an electromagnetic source,” Adv. Electromagn.1, 48–57 (2012).
    [CrossRef]
  16. I. Stakgold, Boundary Value Problems of Mathematical Physics (Macmillan, 1968), vol. I-II.
  17. P. G. Ciarlet, Basic Error Estimates for Elliptic Problems (North Holland, 1991).
  18. D. Xue and L. Demkowicz, “Modeling of electromagnetic absorption/scattering problems on curvilinear geometries using hp finite/infinite element method,” Finite Elem. Anal. Des.42, 570–579 (2006).
    [CrossRef]
  19. T. Grosges, H. Borouchaki, and D. Barchiesi, “Improved scheme for accurate computation of high electric near-field gradients,” Opt. Express15, 1307–1321 (2007).
    [CrossRef] [PubMed]
  20. R. Radovitzky and M. Ortiz, “Error estimation and adaptive meshing in strongly non-linear dynamic problems,” Comput. Meth. Appl. Mech. Eng.172, 203–240 (1999).
    [CrossRef]
  21. M. Ainsworth and J. T. Oden, “A posteriori error estimation in finite element analysis,” Comput. Meth. Appl. Mech. Eng.142, 1–88 (1997).
    [CrossRef]
  22. T. L. Brown and J. A. Rice, “The effect of laser wavelength and power density on the laser desorption mass spectrum of fulvic acid,” Org. Geochem.31, 627–634 (2000).
    [CrossRef]
  23. K. O’Connor, O. Morris, and E. Sokell, “Angular and energy distribution of Sn ion debris ejected from a laser-produced plasma source, for laser power densities in the range suitable for extreme ultraviolet lithography,” J. Appl. Phys.109, 073301 (2011).
    [CrossRef]
  24. D. Marquardt, “An algorithm for least-squares estimation of nonlinear parameters,” SIAM J. Appl. Math.11, 431–441 (1963).
    [CrossRef]
  25. P. E. Gill and W. Murray, “Algorithms for the solution of the nonlinear least-squares problem,” SIAM J. Numer. Anal.15, 977–992 (1978).
    [CrossRef]

2012 (1)

D. Barchiesi, E. Kremer, A. Cherouat, T. Grosges, and H. Borouchaki, “Dilation of nanonatennas induced by an electromagnetic source,” Adv. Electromagn.1, 48–57 (2012).
[CrossRef]

2011 (3)

D. Karamanis, A. N. Okte, E. Vardoulakis, and T. Vaimakis, “Water vapor adsorption and photocatalytic pollutant degradation with TiO2-sepiolite nanocomposites original,” Appl. Clay Sci.53, 181–187 (2011).
[CrossRef]

D. Barchiesi, T. Grosges, E. Kremer, and M. Lamy de la Chapelle, “Electromagnetic heat induced in meso-structures: computation of temperature in metallic dimers,” PIERS Online7, 406–410 (2011).

K. O’Connor, O. Morris, and E. Sokell, “Angular and energy distribution of Sn ion debris ejected from a laser-produced plasma source, for laser power densities in the range suitable for extreme ultraviolet lithography,” J. Appl. Phys.109, 073301 (2011).
[CrossRef]

2009 (3)

M. Boroski, A. C. Rodrigues, J. C. Garcia, L. C. Sampaio, J. Nozaki, and N. Hioka, “Combined electrocoagulation and TiO2photoassisted treatment applied to wastewater effluents from pharmaceutical and cosmetic industries original,” J. Hazard. Mater.162, 448–454 (2009).
[CrossRef]

G. Bystrzejewska-Piotrowska, J. Golimowski, and P. L. Urban, “Nanoparticles: their potential toxicity, waste and environmental management,” Waste Manage.29, 2587–2595 (2009).
[CrossRef]

B. Nowack, “The behavior and effects of nanoparticles in the environment,” Environ. Pollut.157, 1063–1064 (2009).
[CrossRef] [PubMed]

2008 (1)

T. Grosges, H. Borouchaki, and D. Barchiesi, “New adaptive mesh development for accurate near-field enhancement computation,” J. Microsc.229, 293–301 (2008).
[CrossRef] [PubMed]

2007 (1)

2006 (1)

D. Xue and L. Demkowicz, “Modeling of electromagnetic absorption/scattering problems on curvilinear geometries using hp finite/infinite element method,” Finite Elem. Anal. Des.42, 570–579 (2006).
[CrossRef]

2005 (2)

2004 (2)

2000 (1)

T. L. Brown and J. A. Rice, “The effect of laser wavelength and power density on the laser desorption mass spectrum of fulvic acid,” Org. Geochem.31, 627–634 (2000).
[CrossRef]

1999 (1)

R. Radovitzky and M. Ortiz, “Error estimation and adaptive meshing in strongly non-linear dynamic problems,” Comput. Meth. Appl. Mech. Eng.172, 203–240 (1999).
[CrossRef]

1997 (1)

M. Ainsworth and J. T. Oden, “A posteriori error estimation in finite element analysis,” Comput. Meth. Appl. Mech. Eng.142, 1–88 (1997).
[CrossRef]

1978 (1)

P. E. Gill and W. Murray, “Algorithms for the solution of the nonlinear least-squares problem,” SIAM J. Numer. Anal.15, 977–992 (1978).
[CrossRef]

1963 (1)

D. Marquardt, “An algorithm for least-squares estimation of nonlinear parameters,” SIAM J. Appl. Math.11, 431–441 (1963).
[CrossRef]

1943 (1)

R. Courant, “Variational methods for the solution of problems of equilibrium and vibrations,” Bull. Amer. Math. Soc.49, 1–23 (1943).
[CrossRef]

Ainsworth, M.

M. Ainsworth and J. T. Oden, “A posteriori error estimation in finite element analysis,” Comput. Meth. Appl. Mech. Eng.142, 1–88 (1997).
[CrossRef]

Barchiesi, D.

D. Barchiesi, E. Kremer, A. Cherouat, T. Grosges, and H. Borouchaki, “Dilation of nanonatennas induced by an electromagnetic source,” Adv. Electromagn.1, 48–57 (2012).
[CrossRef]

D. Barchiesi, T. Grosges, E. Kremer, and M. Lamy de la Chapelle, “Electromagnetic heat induced in meso-structures: computation of temperature in metallic dimers,” PIERS Online7, 406–410 (2011).

T. Grosges, H. Borouchaki, and D. Barchiesi, “New adaptive mesh development for accurate near-field enhancement computation,” J. Microsc.229, 293–301 (2008).
[CrossRef] [PubMed]

T. Grosges, H. Borouchaki, and D. Barchiesi, “Improved scheme for accurate computation of high electric near-field gradients,” Opt. Express15, 1307–1321 (2007).
[CrossRef] [PubMed]

T. Grosges, A. Vial, and D. Barchiesi, “Models of near field spectroscopic studies: comparison between finite element and finite difference methods,” Opt. Express13, 8483–8497 (2005).
[CrossRef] [PubMed]

T. Grosges, S. Petit, D. Barchiesi, and S. Hudlet, “Numerical modeling of the subwavelength phase-change recording using an apertureless scanning near-field optical microscope,” Opt. Express12, 5987–5995 (2004).
[CrossRef] [PubMed]

Born, M.

M. Born and E. Wolf, Principle of Optics (Pergamon, 1993).

Boroski, M.

M. Boroski, A. C. Rodrigues, J. C. Garcia, L. C. Sampaio, J. Nozaki, and N. Hioka, “Combined electrocoagulation and TiO2photoassisted treatment applied to wastewater effluents from pharmaceutical and cosmetic industries original,” J. Hazard. Mater.162, 448–454 (2009).
[CrossRef]

Borouchaki, H.

D. Barchiesi, E. Kremer, A. Cherouat, T. Grosges, and H. Borouchaki, “Dilation of nanonatennas induced by an electromagnetic source,” Adv. Electromagn.1, 48–57 (2012).
[CrossRef]

T. Grosges, H. Borouchaki, and D. Barchiesi, “New adaptive mesh development for accurate near-field enhancement computation,” J. Microsc.229, 293–301 (2008).
[CrossRef] [PubMed]

T. Grosges, H. Borouchaki, and D. Barchiesi, “Improved scheme for accurate computation of high electric near-field gradients,” Opt. Express15, 1307–1321 (2007).
[CrossRef] [PubMed]

Brown, T. L.

T. L. Brown and J. A. Rice, “The effect of laser wavelength and power density on the laser desorption mass spectrum of fulvic acid,” Org. Geochem.31, 627–634 (2000).
[CrossRef]

Bystrzejewska-Piotrowska, G.

G. Bystrzejewska-Piotrowska, J. Golimowski, and P. L. Urban, “Nanoparticles: their potential toxicity, waste and environmental management,” Waste Manage.29, 2587–2595 (2009).
[CrossRef]

Cherouat, A.

D. Barchiesi, E. Kremer, A. Cherouat, T. Grosges, and H. Borouchaki, “Dilation of nanonatennas induced by an electromagnetic source,” Adv. Electromagn.1, 48–57 (2012).
[CrossRef]

Ciarlet, P. G.

P. G. Ciarlet, Basic Error Estimates for Elliptic Problems (North Holland, 1991).

Courant, R.

R. Courant, “Variational methods for the solution of problems of equilibrium and vibrations,” Bull. Amer. Math. Soc.49, 1–23 (1943).
[CrossRef]

Demkowicz, L.

D. Xue and L. Demkowicz, “Modeling of electromagnetic absorption/scattering problems on curvilinear geometries using hp finite/infinite element method,” Finite Elem. Anal. Des.42, 570–579 (2006).
[CrossRef]

Garcia, J. C.

M. Boroski, A. C. Rodrigues, J. C. Garcia, L. C. Sampaio, J. Nozaki, and N. Hioka, “Combined electrocoagulation and TiO2photoassisted treatment applied to wastewater effluents from pharmaceutical and cosmetic industries original,” J. Hazard. Mater.162, 448–454 (2009).
[CrossRef]

Gill, P. E.

P. E. Gill and W. Murray, “Algorithms for the solution of the nonlinear least-squares problem,” SIAM J. Numer. Anal.15, 977–992 (1978).
[CrossRef]

Golimowski, J.

G. Bystrzejewska-Piotrowska, J. Golimowski, and P. L. Urban, “Nanoparticles: their potential toxicity, waste and environmental management,” Waste Manage.29, 2587–2595 (2009).
[CrossRef]

Grosges, T.

D. Barchiesi, E. Kremer, A. Cherouat, T. Grosges, and H. Borouchaki, “Dilation of nanonatennas induced by an electromagnetic source,” Adv. Electromagn.1, 48–57 (2012).
[CrossRef]

D. Barchiesi, T. Grosges, E. Kremer, and M. Lamy de la Chapelle, “Electromagnetic heat induced in meso-structures: computation of temperature in metallic dimers,” PIERS Online7, 406–410 (2011).

T. Grosges, H. Borouchaki, and D. Barchiesi, “New adaptive mesh development for accurate near-field enhancement computation,” J. Microsc.229, 293–301 (2008).
[CrossRef] [PubMed]

T. Grosges, H. Borouchaki, and D. Barchiesi, “Improved scheme for accurate computation of high electric near-field gradients,” Opt. Express15, 1307–1321 (2007).
[CrossRef] [PubMed]

T. Grosges, A. Vial, and D. Barchiesi, “Models of near field spectroscopic studies: comparison between finite element and finite difference methods,” Opt. Express13, 8483–8497 (2005).
[CrossRef] [PubMed]

T. Grosges, S. Petit, D. Barchiesi, and S. Hudlet, “Numerical modeling of the subwavelength phase-change recording using an apertureless scanning near-field optical microscope,” Opt. Express12, 5987–5995 (2004).
[CrossRef] [PubMed]

Hioka, N.

M. Boroski, A. C. Rodrigues, J. C. Garcia, L. C. Sampaio, J. Nozaki, and N. Hioka, “Combined electrocoagulation and TiO2photoassisted treatment applied to wastewater effluents from pharmaceutical and cosmetic industries original,” J. Hazard. Mater.162, 448–454 (2009).
[CrossRef]

Hudlet, S.

Jin, J.

J. Jin, The Finite Element Method in Electromagnetics (John Wiley and Sons, 1993).

Karamanis, D.

D. Karamanis, A. N. Okte, E. Vardoulakis, and T. Vaimakis, “Water vapor adsorption and photocatalytic pollutant degradation with TiO2-sepiolite nanocomposites original,” Appl. Clay Sci.53, 181–187 (2011).
[CrossRef]

Kremer, E.

D. Barchiesi, E. Kremer, A. Cherouat, T. Grosges, and H. Borouchaki, “Dilation of nanonatennas induced by an electromagnetic source,” Adv. Electromagn.1, 48–57 (2012).
[CrossRef]

D. Barchiesi, T. Grosges, E. Kremer, and M. Lamy de la Chapelle, “Electromagnetic heat induced in meso-structures: computation of temperature in metallic dimers,” PIERS Online7, 406–410 (2011).

Lamy de la Chapelle, M.

D. Barchiesi, T. Grosges, E. Kremer, and M. Lamy de la Chapelle, “Electromagnetic heat induced in meso-structures: computation of temperature in metallic dimers,” PIERS Online7, 406–410 (2011).

Lapotko, D.

D. Lapotko and E. Lukianova, “Laser-induced micro-bubbles in cells,” Int. J. Heat Mass Transf.48(1), 227–234 (2005).
[CrossRef]

D. Lapotko, E. Lukianova, and A. Shnip, “Photothermal responses of individual cells,” J. Biomed. Opt.10, 014006 (2004).
[CrossRef]

Lukianova, E.

D. Lapotko and E. Lukianova, “Laser-induced micro-bubbles in cells,” Int. J. Heat Mass Transf.48(1), 227–234 (2005).
[CrossRef]

D. Lapotko, E. Lukianova, and A. Shnip, “Photothermal responses of individual cells,” J. Biomed. Opt.10, 014006 (2004).
[CrossRef]

Marquardt, D.

D. Marquardt, “An algorithm for least-squares estimation of nonlinear parameters,” SIAM J. Appl. Math.11, 431–441 (1963).
[CrossRef]

Morris, O.

K. O’Connor, O. Morris, and E. Sokell, “Angular and energy distribution of Sn ion debris ejected from a laser-produced plasma source, for laser power densities in the range suitable for extreme ultraviolet lithography,” J. Appl. Phys.109, 073301 (2011).
[CrossRef]

Murray, W.

P. E. Gill and W. Murray, “Algorithms for the solution of the nonlinear least-squares problem,” SIAM J. Numer. Anal.15, 977–992 (1978).
[CrossRef]

Nowack, B.

B. Nowack, “The behavior and effects of nanoparticles in the environment,” Environ. Pollut.157, 1063–1064 (2009).
[CrossRef] [PubMed]

Nozaki, J.

M. Boroski, A. C. Rodrigues, J. C. Garcia, L. C. Sampaio, J. Nozaki, and N. Hioka, “Combined electrocoagulation and TiO2photoassisted treatment applied to wastewater effluents from pharmaceutical and cosmetic industries original,” J. Hazard. Mater.162, 448–454 (2009).
[CrossRef]

O’Connor, K.

K. O’Connor, O. Morris, and E. Sokell, “Angular and energy distribution of Sn ion debris ejected from a laser-produced plasma source, for laser power densities in the range suitable for extreme ultraviolet lithography,” J. Appl. Phys.109, 073301 (2011).
[CrossRef]

Oden, J. T.

M. Ainsworth and J. T. Oden, “A posteriori error estimation in finite element analysis,” Comput. Meth. Appl. Mech. Eng.142, 1–88 (1997).
[CrossRef]

Okte, A. N.

D. Karamanis, A. N. Okte, E. Vardoulakis, and T. Vaimakis, “Water vapor adsorption and photocatalytic pollutant degradation with TiO2-sepiolite nanocomposites original,” Appl. Clay Sci.53, 181–187 (2011).
[CrossRef]

Ortiz, M.

R. Radovitzky and M. Ortiz, “Error estimation and adaptive meshing in strongly non-linear dynamic problems,” Comput. Meth. Appl. Mech. Eng.172, 203–240 (1999).
[CrossRef]

Pelosi, G.

P. Silvester and G. Pelosi, Finite Elements for Wave Electromagnetics: Methods and Techniques (IEEE, 1994).

Petit, S.

Radovitzky, R.

R. Radovitzky and M. Ortiz, “Error estimation and adaptive meshing in strongly non-linear dynamic problems,” Comput. Meth. Appl. Mech. Eng.172, 203–240 (1999).
[CrossRef]

Rice, J. A.

T. L. Brown and J. A. Rice, “The effect of laser wavelength and power density on the laser desorption mass spectrum of fulvic acid,” Org. Geochem.31, 627–634 (2000).
[CrossRef]

Rodrigues, A. C.

M. Boroski, A. C. Rodrigues, J. C. Garcia, L. C. Sampaio, J. Nozaki, and N. Hioka, “Combined electrocoagulation and TiO2photoassisted treatment applied to wastewater effluents from pharmaceutical and cosmetic industries original,” J. Hazard. Mater.162, 448–454 (2009).
[CrossRef]

Sampaio, L. C.

M. Boroski, A. C. Rodrigues, J. C. Garcia, L. C. Sampaio, J. Nozaki, and N. Hioka, “Combined electrocoagulation and TiO2photoassisted treatment applied to wastewater effluents from pharmaceutical and cosmetic industries original,” J. Hazard. Mater.162, 448–454 (2009).
[CrossRef]

Shnip, A.

D. Lapotko, E. Lukianova, and A. Shnip, “Photothermal responses of individual cells,” J. Biomed. Opt.10, 014006 (2004).
[CrossRef]

Silvester, P.

P. Silvester and G. Pelosi, Finite Elements for Wave Electromagnetics: Methods and Techniques (IEEE, 1994).

Sokell, E.

K. O’Connor, O. Morris, and E. Sokell, “Angular and energy distribution of Sn ion debris ejected from a laser-produced plasma source, for laser power densities in the range suitable for extreme ultraviolet lithography,” J. Appl. Phys.109, 073301 (2011).
[CrossRef]

Stakgold, I.

I. Stakgold, Boundary Value Problems of Mathematical Physics (Macmillan, 1968), vol. I-II.

Urban, P. L.

G. Bystrzejewska-Piotrowska, J. Golimowski, and P. L. Urban, “Nanoparticles: their potential toxicity, waste and environmental management,” Waste Manage.29, 2587–2595 (2009).
[CrossRef]

Vaimakis, T.

D. Karamanis, A. N. Okte, E. Vardoulakis, and T. Vaimakis, “Water vapor adsorption and photocatalytic pollutant degradation with TiO2-sepiolite nanocomposites original,” Appl. Clay Sci.53, 181–187 (2011).
[CrossRef]

Vardoulakis, E.

D. Karamanis, A. N. Okte, E. Vardoulakis, and T. Vaimakis, “Water vapor adsorption and photocatalytic pollutant degradation with TiO2-sepiolite nanocomposites original,” Appl. Clay Sci.53, 181–187 (2011).
[CrossRef]

Vial, A.

Wolf, E.

M. Born and E. Wolf, Principle of Optics (Pergamon, 1993).

Xue, D.

D. Xue and L. Demkowicz, “Modeling of electromagnetic absorption/scattering problems on curvilinear geometries using hp finite/infinite element method,” Finite Elem. Anal. Des.42, 570–579 (2006).
[CrossRef]

Adv. Electromagn. (1)

D. Barchiesi, E. Kremer, A. Cherouat, T. Grosges, and H. Borouchaki, “Dilation of nanonatennas induced by an electromagnetic source,” Adv. Electromagn.1, 48–57 (2012).
[CrossRef]

Appl. Clay Sci. (1)

D. Karamanis, A. N. Okte, E. Vardoulakis, and T. Vaimakis, “Water vapor adsorption and photocatalytic pollutant degradation with TiO2-sepiolite nanocomposites original,” Appl. Clay Sci.53, 181–187 (2011).
[CrossRef]

Bull. Amer. Math. Soc. (1)

R. Courant, “Variational methods for the solution of problems of equilibrium and vibrations,” Bull. Amer. Math. Soc.49, 1–23 (1943).
[CrossRef]

Comput. Meth. Appl. Mech. Eng. (2)

R. Radovitzky and M. Ortiz, “Error estimation and adaptive meshing in strongly non-linear dynamic problems,” Comput. Meth. Appl. Mech. Eng.172, 203–240 (1999).
[CrossRef]

M. Ainsworth and J. T. Oden, “A posteriori error estimation in finite element analysis,” Comput. Meth. Appl. Mech. Eng.142, 1–88 (1997).
[CrossRef]

Environ. Pollut. (1)

B. Nowack, “The behavior and effects of nanoparticles in the environment,” Environ. Pollut.157, 1063–1064 (2009).
[CrossRef] [PubMed]

Finite Elem. Anal. Des. (1)

D. Xue and L. Demkowicz, “Modeling of electromagnetic absorption/scattering problems on curvilinear geometries using hp finite/infinite element method,” Finite Elem. Anal. Des.42, 570–579 (2006).
[CrossRef]

Int. J. Heat Mass Transf. (1)

D. Lapotko and E. Lukianova, “Laser-induced micro-bubbles in cells,” Int. J. Heat Mass Transf.48(1), 227–234 (2005).
[CrossRef]

J. Appl. Phys. (1)

K. O’Connor, O. Morris, and E. Sokell, “Angular and energy distribution of Sn ion debris ejected from a laser-produced plasma source, for laser power densities in the range suitable for extreme ultraviolet lithography,” J. Appl. Phys.109, 073301 (2011).
[CrossRef]

J. Biomed. Opt. (1)

D. Lapotko, E. Lukianova, and A. Shnip, “Photothermal responses of individual cells,” J. Biomed. Opt.10, 014006 (2004).
[CrossRef]

J. Hazard. Mater. (1)

M. Boroski, A. C. Rodrigues, J. C. Garcia, L. C. Sampaio, J. Nozaki, and N. Hioka, “Combined electrocoagulation and TiO2photoassisted treatment applied to wastewater effluents from pharmaceutical and cosmetic industries original,” J. Hazard. Mater.162, 448–454 (2009).
[CrossRef]

J. Microsc. (1)

T. Grosges, H. Borouchaki, and D. Barchiesi, “New adaptive mesh development for accurate near-field enhancement computation,” J. Microsc.229, 293–301 (2008).
[CrossRef] [PubMed]

Opt. Express (3)

Org. Geochem. (1)

T. L. Brown and J. A. Rice, “The effect of laser wavelength and power density on the laser desorption mass spectrum of fulvic acid,” Org. Geochem.31, 627–634 (2000).
[CrossRef]

PIERS Online (1)

D. Barchiesi, T. Grosges, E. Kremer, and M. Lamy de la Chapelle, “Electromagnetic heat induced in meso-structures: computation of temperature in metallic dimers,” PIERS Online7, 406–410 (2011).

SIAM J. Appl. Math. (1)

D. Marquardt, “An algorithm for least-squares estimation of nonlinear parameters,” SIAM J. Appl. Math.11, 431–441 (1963).
[CrossRef]

SIAM J. Numer. Anal. (1)

P. E. Gill and W. Murray, “Algorithms for the solution of the nonlinear least-squares problem,” SIAM J. Numer. Anal.15, 977–992 (1978).
[CrossRef]

Waste Manage. (1)

G. Bystrzejewska-Piotrowska, J. Golimowski, and P. L. Urban, “Nanoparticles: their potential toxicity, waste and environmental management,” Waste Manage.29, 2587–2595 (2009).
[CrossRef]

Other (5)

M. Born and E. Wolf, Principle of Optics (Pergamon, 1993).

J. Jin, The Finite Element Method in Electromagnetics (John Wiley and Sons, 1993).

P. Silvester and G. Pelosi, Finite Elements for Wave Electromagnetics: Methods and Techniques (IEEE, 1994).

I. Stakgold, Boundary Value Problems of Mathematical Physics (Macmillan, 1968), vol. I-II.

P. G. Ciarlet, Basic Error Estimates for Elliptic Problems (North Holland, 1991).

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Figures (7)

Fig. 1
Fig. 1

Optimization process and remeshing loops.

Fig. 2
Fig. 2

Adapted meshes MF (a, b) and temperature maps T (c, d) for TEy and TMy mode, respectively.

Fig. 3
Fig. 3

Evolution of the mean temperature as function of the nanowire aspect ratio Rn after creation of the bubble for the four illumination modes.

Fig. 4
Fig. 4

Evolution of (a) the size ratio of the bubble Rb as function of the aspect ratio of the nanowire Rn for three laser power density of laser and (b) the volume of the bubble Vb as function of the volume of the nanowire Vn.

Fig. 5
Fig. 5

Evolution of the fit parameters (a) B and C, (b) C* as function of the power laser density Ps.

Fig. 6
Fig. 6

Evolution of (a) the size ratio of the bubble Rb as function of the aspect ratio of the nanowire Rn for three different inial temperature and (b) the volume of the bubble Vb as function of the volume of the nanowire Vn.

Fig. 7
Fig. 7

Evolution of the fit parameters (a) B and C, (b) C* as function of the initial temperature T0.

Tables (4)

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Table 1 Fit parameters of functions f and g and associated residual variance σ̂2.

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Table 2 Fit parameters of the functions L1, L2 and L 2 * and associated residual variance σ̂2.

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Table 3 Fit parameters of functions f and g and associated residual variance σ̂2.

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Table 4 Fit parameters of function L1, L2 and L 2 * and associated residual variance σ̂2.

Equations (25)

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[ . ( 1 ε r ) + k 0 2 ] H z ( x , y ) = 0 , ( x , y ) Ω , ( TM )
Δ E z ( x , y ) + ε r k 0 2 E z ( x , y ) = 0 , ( x , y ) Ω , ( TE )
1 ε r H z ( x , y ) n = j k 0 [ H z ( x , y ) ( n y 1 ) H i ( x , y ) ] , ( x , y ) Γ , ( TM )
E z ( x , y ) n = j k 0 ε r [ E z ( x , y ) ( n y 1 ) E i ( x , y ) ] , ( x , y ) Γ , ( TE )
E ( x , y ) = j ω ε r ε 0 [ × H ( x , y ) ] , ( x , y ) Ω ,
Q ( x , y ) = ω 2 ε 0 Im ( ε r ) | E ( x , y ) | 2 , ( x , y ) Ω .
[ . ( κ ( x , y ) ) ] T ( x , y ) = Q ( x , y ) , ( x , y ) Ω ,
Ω [ . ( 1 ε r H z ( x , y ) ) + ω 2 c 2 H z ( x , y ) ] . ν 1 d Ω = 0 ,
Ω [ Δ E z ( x , y ) + ε r ω 2 c 2 E z ( x , y ) ] . ν 2 d Ω = 0 ,
Ω [ . ( κ ( x , y ) ) T ( x , y ) Q ( x , y ) ] . ν 3 d Ω = 0 ,
C p ( Ω ) = { h p ( x , y ) } , ( x , y ) Ω ,
h min h p ( x , y ) = γ η ( x , y ) h max
f ( x ) = A + B ( x C ) 2 and g ( x ) = A * B * x C * ,
L 1 ( x ) = a 1 x + b 1 , L 2 ( x ) = a 2 x + b 2 and L 2 * ( x ) = a 2 * x + b 2 *
R b = [ A + a 1 P s + b 1 ( R n a 2 P s b 2 ) 2 ] = F ( R n , P s )
ln ( V b ) = [ A * B * ln ( V n ) a 2 * P s b 2 * ] = G ( ln ( V n ) , P s ) .
ln ( V n ) = ln ( π b a ) = ln ( π b 2 R n ) = ln ( π b 2 F ˜ ( R b , P s ) ) = G ˜ ( ln ( V b ) , P s ) ,
F ˜ ( R b , P s ) = F 1 ( R n , P s ) | P s , fixed = [ ( a 1 P s + b 1 R b A ) 1 / 2 + a 2 P s + b 2 ] = R n
G ˜ ( ln ( V b ) , P s ) = G 1 ( ln ( V n ) , P s ) | P s , fixed = [ B * A * ln ( V b ) + a 2 * P s + b 2 * ] = ln ( V n ) .
b = [ exp ( G ˜ ( ln ( V b ) , P s ) ) π F ˜ ( R b , P s ) ] 1 / 2 and a = [ F ˜ ( R b , P s ) ) exp ( G ˜ ( ln ( V b ) , P s ) ) π ] 1 / 2 .
R b = A + a 1 T 0 + b 1 ( R n a 2 T 0 b 2 ) 2 = F * ( R n , T 0 )
ln ( V b ) = A * B * ln ( V n ) a 2 * T 0 b 2 * = G * ( ln ( V n ) , T 0 ) .
b = [ exp ( G ˜ * ( ( ln ( V b ) , T 0 ) ) π F ˜ * ( R b , T 0 ) ] 1 / 2 and a = [ F ˜ * ( R b , T 0 ) ) exp ( G ˜ * ( ln ( V b ) , T 0 ) ) π ] 1 / 2 ,
F ˜ * ( R b , T 0 ) = [ ( a 1 T 0 + b 1 R b A ) 1 / 2 + a 2 T 0 + b 2 ] = R n
G ˜ * ( ln ( V b ) , T 0 ) = [ B * A * ln ( V b ) + a 2 * T 0 + b 2 * ] = ln ( V n ) .

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