Journal of the European Optical Society - Rapid publications, Vol 6 (2011)

Tridimensional multiphysics model for the study of photo-induced thermal effects in arbitrary nano-structures

G. Demésy, L. Gallais, M. Commandré


In the present paper, we detail the implementation of a numerical scheme based on the Finite Element Method (FEM) dedicated to a tri-dimensional investigation of photo-induced thermal effects in arbitrary nano-structures. The distribution of Joule losses resulting from the scattering of an incident wave by an arbitrary object embedded in a multilayered media is used as source of a conductive thermal transient problem. It is shown that an appropriate and rigorous formulation of the FEM consists in reducing the electromagnetic scattering problem to a radiative one whose sources are localized inside the scatterer. This approach makes the calculation very tractable. Its advantage compared to other existing methods lies in its complete independence towards the geometric, optical and thermal properties of both the scatterer and the medium in which it lies. Among the wide range of domain of application of this numerical scheme, we illustrate its relevance when applied to two typical cases of laser damage of optical components in high power applications.

© The Authors. All rights reserved. [DOI: 10.2971/jeos.2011.11037]

Full Text: PDF

Citation Details

Cite this article


A. K. Oyelere, P. C. Chen, X. Huang, I. H. El-Sayed, and M. A. El-Sayed, "Peptide-conjugated gold nanorods for nuclear targeting", Bioconjugate Chem. 18, 1490-1497 (2007).

C. Loo, A. Lowery, N. J. Halas, J. L. West, and R. Drezek, "Immunotargeted nanoshells for integrated cancer imaging and therapy", Nano Lett. 5, 709-711 (2005).

D. Pissuwan, S.M. Valenzuela, C.M. Miller, and M.B. Cortie, "A golden bullet? Selective targeting of Toxoplasma gondii tachyzoites using antibody-functionalized gold nanorods", Nano Lett. 7 3808-3812 (2007).

S. R. Sershen, S. L. Westcott, N. S. Halas, and J. L. West, "Temperature-sensitive polymer-nanoshell composites for photothermally modulated drug delivery", J. Biomed. Mater. Res. 51, 293-298 (2000).

D. A. Boyd, L. Greengard, L. Brongersma, M. Y. El-Naggar, and D. G. Goodwin, "Plasmon-assisted chemical vapor deposition", Nano Lett. 6, 2592-2597 (2006).

X. Miao, B. K. Wilson, and L. Y. Lin, "Localized surface plasmon assisted microfluidic mixing", Appl. Phys. Lett. 92, 124108-1-124108-3 (2008).

G. L. Liu, J. Kim, Y. Lu and L. Lee, "Optofluidic control using photothermal nanoparticles", Nat. Mater. 5, 27-32 (2005).

R. Q. G. Baffou and C. Girard, "Heat generation in plasmonic nanostructures: Influence of morphology", Appl. Phys. Lett. 94, 153109 (2009).

D. Milam, R. Bradbury, and M. Bass, "Laser damage threshold for dielectric coatings as determined by inclusions", Appl. Phys. Lett. 23, 654-657 (1973).

N. Zaitseva, L. Carman, I. Smolsky, R. Torres, and M. Yan, "The effect of impurities and supersaturation on the rapid growth of KDP crystals", J. Cryst. Growth 204, 512_U-524 (1999).

F. Kahnert, "Numerical methods in electromagnetic scattering theory", J. Quant. Spectrosc. Ra. 79, 775-824 (2003).

K. Yee, "Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media", IEEE Trans. Ant. Prop. AP-14, 302-307 (1966).

K. S. Yee and J. S. Chen, "The finite-difference time-domain (FDTD) and the finite-volume time-domain (FVTD) methods in solving Maxwell's equations", IEEE Trans. Ant. Prop. 45, 354-363 (1997).

J. L. Volakis, A. Chatterjee and L. C. Kempel, "Review of the finiteelement method for three-dimensional electromagnetic scattering", J. Opt. Soc. Am. A 11, 1422-1422 (1994).

X. Wei, A. J. Wachters and H. P.Urbach, "Finite-element model for three-dimensional optical scattering problems", J. Opt. Soc. Am. A 24, 866-881 (2007).

G. Demésy, F. Zolla, A. Nicolet and M. Commandré, "All-purpose finite element formulation for arbitrarily shaped crossed-gratings embedded in a multilayered stack", J. Opt. Soc. Am. A 27, 878-889 (2008).

G. Demésy, F. Zolla, A. Nicolet, M. Commandré and C. Fossati, "The finite element method as applied to the diffraction by an anisotropic grating", Opt. Express 15, 18089-18102 (2007).

G. Demésy, F. Zolla, A. Nicolet, and M. Commandré, "Versatile full-vectorial finite element model for crossed gratings", Opt. Lett. 34, 2216-2218 (2009).

M. Perry, B. Stuart, P. Banks, M. Feit, V. Yanovsky, and A. Rubenchik, "Ultrashort-pulse laser machining of dielectric materials", J. Appl. Phys. 85, 6803 (1999).

C. Mätzler, "MATLAB Functions for Mie scattering and absorption", IAP Res. Rep (2002).

R. W. Hopper and D. P. Uhlmann, "Mechanism of Inclusion Damage in Laser Glass", J. Appl. Phys. 41, 4023 (1970).

J. Néauport, E. Lavastre, G. Razé, G. Dupuy, N. Bonod, M. Balas, G. de Villele, J. Flamand, S. Kaladgew, and F. Desserouer, "Effect of electric field on laser induced damage threshold of multilayer dielectric gratings", Opt. Express 15, 12508-12522 (2007).

X. Jing, J. Shao, J. Zhang, Y. Jin, H. He, and Z. Fan, "Calculation of femtosecond pulse laser induced damage threshold for broadband antireflective microstructure arrays", Opt. Express 17, 24137-24152 (2009).

F. Zolla and R. Petit, "Method of fictitious sources as applied to the electromagnetic diffraction of a plane wave by a grating in conical diffraction mounts", J. Opt. Soc. Am. A 13, 796-802 (1996).

Y. Ould Agha, F. Zolla, A. Nicolet, and S. Guenneau, "On the use of PML for the computation of leaky modes : an application to gradient index MOF", COMPEL 27-1, 95-109 (2008).

A. Bossavit and I. Mayergoyz, "Edge-elements for scattering problems", IEEE T. Magn. 25, 2816-2821 (1989).

P. Dular, A. Nicolet, A. Genon, and W. Legros, "A discrete sequence associated with mixed finite elements and its gauge condition for vector potentials", IEEE T. Magn. 31, 1356-1359 (1995).

G. Bao, Z. Chen and H. Wu, "Adaptive finite-element method for diffraction gratings", J. Opt. Soc. Am. A 22, 1106-1114 (2005).

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

M. Vujicic, "Finite element solution of transient heat conduction using iterative solvers", Eng. Computation 23, 408-431 (2006).

P. N. Brown, A. C. Hindmarsh, and L. R. Petzold, "Using Krylov methods in the solution of large-scale differential-algebraic systems", SIAM J. Sci. Comput. 15, 1467_U-1488 (1994).

A. C. Hindmarsh, P. N. Brown, K. E. Grant, S. L. Lee, R. Serban, D. E. Shumaker, and C. S. Woodward, "SUNDIALS: Suite of nonlinear and differential/algebraic equation solvers", ACM T. Math. Software (TOMS) 31, 363-396 (2005).

H. Bercegol, A. Boscheron, J. M. Di-Nicola, E. Journot, L. Lamaignère, J. Néauport and G. Razé, "Laser damage phenomena relevant to the design and operation of an ICF laser driver", J. Phys. Conf. Ser. 112, 032013 (2008).

P. Allenspacher, W. Riede, and D. Wernham, "Laser qualification testing of space optics", P. SPIE. IS&T Elect. Im. 6403, 64030T (2006).

C.W. Carr, H.B. Radousky, A.M. Rubenchik, M.D. Feit, and S.G. Demos, "Localized dynamics during laser-induced damage in optical materials", Phys. Rev. Lett. 92, 087401 (2004).

J. Néauport, P. Cormont, P. Legros, C. Ambard, and J. Destribats, "Imaging subsurface damage of grinded fused silica optics by confocal fluorescence microscopy", Opt. Express 17, 3543-3554 (2009).

N. Bloembergen, "Role of cracks, pores, and absorbing inclusions on laser induced damage threshold at surface of transparent dielectrics", Appl. Opt. 12, 661-664 (1973).

F. Y. Génin, A. Salleo, T. V. Pistor, and L. L. Chase, "Role of light intensification by cracks in optical breakdown on surfaces", J. Opt. Soc. Am. A 18, 2607-2616 (2001).

K. Bien-Aimé, C. Belin, L. Gallais, P. Grua, E. Fargin, J. Néauport and I. Tovena-Pecault, "Impact of storage induced outgassing organic contamination on laser induced damage of silica optics at 351 nm", Opt. Express 17, 18703-18713 (2009).

R. Chow, S.Falabella, G. E. Loomis, F. Rainer, C. J. Stolz, and M. R. Kozlowski, "Reactive evaporation of low-defect density hafnia", Appl. Opt. 23, 174 (1993).

M. Reichling, A. Bodemann, and N. Kaiser, "Defect induced laser damage in oxide multilayer coatings for 248 nm", Thin Solid Films 320, 264-279 (1998).

S. Papernov and A. Schmid, "Localized absorption effects during 351 nm, pulsed laser irradiation of dielectric multilayer thin films", J. Appl. Phys. 82, 5422 (1997).

D. Ristau, M. Jupé, and K. Starke, "Laser damage thresholds of optical coatings", Thin Solid Films 518, 1607-1613 (2009).

J. J. DeYoreo, Z. U. Rek, N. P. Zaitseva, and B. W. Woodsa, "Sources of optical distortion in rapidly grown crystals of KH2PO4", J. Cryst. Growth 166, 291_U-297 (1996).

N. Y. Garces, K. T. Stevens, L. E. Halliburton, S. G. Demos, H. B. Radousky, and N. P. Zaitseva, "Identification of electron and hole traps in KH2PO4 crystals", J. Appl. Phys. 89, 47-52 (2001).

A. Hildenbrand, F.R. Wagner, J.-Y. Natoli, and M. Commandré, "Nanosecond laser induced damage in RbTiOPO4: The missing influence of crystal quality", Opt. Express 17, 18273-18280 (2009).

L. Gallais, P. Voarino, and C. Amra, "Optical measurement of size and complex index of laser-damage precursors: the inverse problem", JOSA B 21, 1073-1080 (2004).

J. Trenholme, M. Feit, and A. Rubenchik, "Size-selection initiation model extended to include shape and random factors", Proc. of SPIE 5991, 59910X (2005).

F. Bonneau, P. Combis, J. Rullier, J. Vierne, B. Bertussi, M. Commandre, L. Gallais, J. Natoli, I. Bertron, F. Malaise, et al., "Numerical simulations for description of UV laser interaction with goldnanoparticles embedded in silica", Appl. Phys. B-Lasers O. 78, 447-452 (2004).

G. Duchateau, "Simple models for laser-induced damage and conditioningof potassium dihydrogen phosphate crystals by nanosecond pulses", Opt. Express 17, 10434-10456 (2009).

C. J. Stolz, M. D. Feit, and T. V. Pistor, "Laser intensification by spherical inclusions embedded within multilayer coatings", Appl. Optics 45, 1495-1601 (2006).

C. Dorrer, "High-damage-threshold beam shaping using binary phase plates", Opt. Lett. 34, 2330-2332 (2009).

L. Gallais, J. Capoulade, J.Y. Natoli and M. Commandré, "Investigation of nanodefect properties in optical coatings by coupling measured and simulated laser damage statistics", J. Appl. Phys. 104, 053120 (2008).

Y. S. Touloukian, Thermo-physical properties of matter (IFI/Plenum, 1970).

D. Lide, CRC handbook of chemistry and physics (CRC press, 1993).

G. Duchateau and A. Dyan, "Coupling statistics and heat transfer to study laser-induced crystal damage by nanosecond pulses", Appl. Opt. 23, 3796 (1984).

S. G. Demos, P. DeMange, R. A. Negres, and M. D. Feit, "Investigation of the electronic and physical properties of defect structures responsible for laser-induced damage in DKDP crystals", Opt. Express 18, 13788-13804 (2010).

S. Reyné, G. Duchateau, J. Natoli, and L. Lamaignère, "Laserinduced damage of KDP crystals by 1w nanosecond pulses: influence of crystal orientation", Opt. Express 17 21652-21665 (2009).

C. Carr, H. Radousky, A. Rubenchik, M. Feit, and S. Demos, "Localized dynamics during laser-induced damage in optical materials", Phys. Rev. Lett. 92, 87401 (2004).