Abstract

We present a numerical model that describes the propagation of a single femtosecond laser pulse in a medium of which the optical properties dynamically change within the duration of the pulse. We use a finite-difference time-domain method to solve the Maxwell’s equations coupled to equations describing the changes in the material properties. We use the model to simulate the self-reflectivity of strongly focused femtosecond laser pulses on silicon and gold under laser ablation conditions. We compare the simulations to experimental results and find excellent agreement.

© 2015 Optical Society of America

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References

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    [Crossref]
  4. M. Li, K. Mori, M. Ishizuka, X. Liu, Y. Sugimoto, N. Ikeda, and K. Asakawa, “Photonic bandpass filter for 1550  nm fabricated by femtosecond direct laser ablation,” Appl. Phys. Lett. 83, 216–218 (2003).
    [Crossref]
  5. B. Rethfeld, K. Sokolowski-Tinten, D. Von Der Linde, and S. I. Anisimov, “Timescales in the response of materials to femtosecond laser excitation,” Appl. Phys. A 79, 767–773 (2004).
    [Crossref]
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2014 (2)

C. Fourment, F. Deneuville, D. Descamps, F. Dorchies, S. Petit, O. Peyrusse, B. Holst, and V. Recoules, “Experimental determination of temperature-dependent electron-electron collision frequency in isochorically heated warm dense gold,” Phys. Rev. B 89, 161110 (2014).

E. Bevillon, J. P. Colombier, V. Recoules, and R. Stoian, “Free-electron properties of metals under ultrafast laser-induced electron-phonon nonequilibrium: a first-principles study,” Phys. Rev. B 89, 115117 (2014).

2013 (3)

2012 (1)

2011 (2)

I. B. Bogatyrev, D. Grojo, P. Delaporte, S. Leyder, M. Sentis, W. Marine, and T. E. Itina, “Non-linear absorption of 1.3-μm wavelength femtosecond laser pulses focused inside semiconductors: finite difference time domain-two temperature model combined computational study,” J. Appl. Phys. 110, 103106 (2011).
[Crossref]

H. Zhang, D. van Oosten, D. M. Krol, and J. I. Dijkhuis, “Saturation effects in femtosecond laser ablation of silicon-on-insulator,” Appl. Phys. Lett. 99, 231108 (2011).
[Crossref]

2010 (1)

N. Medvedev and B. Rethfeld, “A comprehensive model for the ultrashort visible light irradiation of semiconductors,” J. Appl. Phys. 108, 103112 (2010).
[Crossref]

2008 (2)

Z. Lin, L. V. Zhigilei, and V. Celli, “Electron-phonon coupling and electron heat capacity of metals under conditions of strong electron-phonon nonequilibrium,” Phys. Rev. B 77, 075133 (2008). Updated calculations at http://www.faculty.virginia.edu/CompMat/electron-phonon-coupling/ .

C. Mézel, L. Hallo, A. Bourgeade, D. Hébert, V. T. Tikhonchuk, B. Chimier, B. Nkonga, G. Schurtz, and G. Travaillé, “Formation of nanocavities in dielectrics: a self-consistent modeling,” Phys. Plasmas 15, 093504 (2008).
[Crossref]

2007 (3)

A. D. Bristow, N. Rotenberg, and H. M. Van Driel, “Two-photon absorption and Kerr coefficients of silicon for 850–2200 nm,” Appl. Phys. Lett. 90, 191104 (2007).
[Crossref]

S. J. Youn, T. H. Rho, B. I. Min, and K. S. Kim, “Extended Drude model analysis of noble metals,” Phys. Status Solidi B 244, 1354–1362 (2007).
[Crossref]

L. Hallo, A. Bourgeade, V. T. Tikhonchuk, C. Mezel, and J. Breil, “Model and numerical simulations of the propagation and absorption of a short laser pulse in a transparent dielectric material: Blast-wave launch and cavity formation,” Phys. Rev. B 76, 024101 (2007).

2006 (2)

K. Vestentoft and P. Balling, “Formation of an extended nanostructured metal surface by ultra-short laser pulses: single-pulse ablation in the high-fluence limit,” Appl. Phys. A 84, 207–213 (2006).
[Crossref]

E. G. Gamaly, S. Juodkazis, K. Nishimura, H. Misawa, B. Luther-Davies, L. Hallo, Ph. Nicolai, and V. T. Tikhonchuk, “Laser-matter interaction in the bulk of a transparent solid: Confined microexplosion and void formation,” Phys. Rev. B 73, 214101 (2006).

2004 (1)

B. Rethfeld, K. Sokolowski-Tinten, D. Von Der Linde, and S. I. Anisimov, “Timescales in the response of materials to femtosecond laser excitation,” Appl. Phys. A 79, 767–773 (2004).
[Crossref]

2003 (1)

M. Li, K. Mori, M. Ishizuka, X. Liu, Y. Sugimoto, N. Ikeda, and K. Asakawa, “Photonic bandpass filter for 1550  nm fabricated by femtosecond direct laser ablation,” Appl. Phys. Lett. 83, 216–218 (2003).
[Crossref]

2002 (2)

T. Y. Choi and C. P. Grigoropoulos, “Plasma and ablation dynamics in ultrafast laser processing of crystalline silicon,” J. Appl. Phys. 92, 4918–4925 (2002).
[Crossref]

D. M. Riffe, “Temperature dependence of silicon carrier effective masses with application to femtosecond reflectivity measurements,” J. Opt. Soc. Am. B 19, 1092–1100 (2002).
[Crossref]

2000 (2)

K. Eidmann, J. Meyer-ter-Vehn, T. Schlegel, and S. Huller, “Hydrodynamic simulation of subpicosecond laser interaction with solid-density matter,” Phys. Rev. E 62, 1202–1214 (2000).
[Crossref]

K. Sokolowski-Tinten and D. von der Linde, “Generation of dense electron-hole plasmas in silicon,” Phys. Rev. B 61, 2643–2650 (2000).

1998 (1)

P. P. Pronko, P. A. VanRompay, C. Horvath, F. Loesel, T. Juhasz, X. Liu, and G. Mourou, “Avalanche ionization and dielectric breakdown in silicon with ultrafast laser pulses,” Phys. Rev. B 58, 2387–2390 (1998).

1997 (1)

Th. Brabec and F. Krausz, “Nonlinear optical pulse propagation in the single-cycle regime,” Phys. Rev. Lett. 78, 3282–3285 (1997).
[Crossref]

1996 (1)

B. C. Stuart, M. D. Feit, S. Herman, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Nanosecond-to-femtosecond laser-induced breakdown in dielectrics,” Phys. Rev. B 53, 1749–1761 (1996).

1995 (1)

K. Sokolowski-Tinten, J. Bialkowski, and D. von der Linde, “Ultrafast laser-induced order-disorder transitions in semiconductors,” Phys. Rev. B 51, 14186–14198 (1995).

1987 (1)

H. M. van Driel, “Kinetics of high-density plasmas generated in Si by 1.06- and 0.53-μm picosecond laser pulses,” Phys. Rev. B 35, 8166–8176 (1987).

1984 (1)

D. Hulin, M. Combescot, J. Bok, A. Migus, J. Y. Vinet, and A. Antonetti, “Energy transfer during silicon irradiation by femtosecond laser pulse,” Phys. Rev. Lett. 52, 1998–2001 (1984).
[Crossref]

1972 (1)

E. Yablonovitch and N. Bloembergen, “Avalanche ionization and the limiting diameter of filaments induced by light pulses in transparent media,” Phys. Rev. Lett. 29, 907–910 (1972).
[Crossref]

Anisimov, S. I.

B. Rethfeld, K. Sokolowski-Tinten, D. Von Der Linde, and S. I. Anisimov, “Timescales in the response of materials to femtosecond laser excitation,” Appl. Phys. A 79, 767–773 (2004).
[Crossref]

Antonetti, A.

D. Hulin, M. Combescot, J. Bok, A. Migus, J. Y. Vinet, and A. Antonetti, “Energy transfer during silicon irradiation by femtosecond laser pulse,” Phys. Rev. Lett. 52, 1998–2001 (1984).
[Crossref]

Asakawa, K.

M. Li, K. Mori, M. Ishizuka, X. Liu, Y. Sugimoto, N. Ikeda, and K. Asakawa, “Photonic bandpass filter for 1550  nm fabricated by femtosecond direct laser ablation,” Appl. Phys. Lett. 83, 216–218 (2003).
[Crossref]

Ashcroft, N. W.

N. W. Ashcroft and N. D. Mermin, Solid State Physics (Brooks/Cole, 1976).

Balling, P.

K. Vestentoft and P. Balling, “Formation of an extended nanostructured metal surface by ultra-short laser pulses: single-pulse ablation in the high-fluence limit,” Appl. Phys. A 84, 207–213 (2006).
[Crossref]

Bevillon, E.

E. Bevillon, J. P. Colombier, V. Recoules, and R. Stoian, “Free-electron properties of metals under ultrafast laser-induced electron-phonon nonequilibrium: a first-principles study,” Phys. Rev. B 89, 115117 (2014).

Bialkowski, J.

K. Sokolowski-Tinten, J. Bialkowski, and D. von der Linde, “Ultrafast laser-induced order-disorder transitions in semiconductors,” Phys. Rev. B 51, 14186–14198 (1995).

Bloembergen, N.

E. Yablonovitch and N. Bloembergen, “Avalanche ionization and the limiting diameter of filaments induced by light pulses in transparent media,” Phys. Rev. Lett. 29, 907–910 (1972).
[Crossref]

Bogatyrev, I. B.

I. B. Bogatyrev, D. Grojo, P. Delaporte, S. Leyder, M. Sentis, W. Marine, and T. E. Itina, “Non-linear absorption of 1.3-μm wavelength femtosecond laser pulses focused inside semiconductors: finite difference time domain-two temperature model combined computational study,” J. Appl. Phys. 110, 103106 (2011).
[Crossref]

Bok, J.

D. Hulin, M. Combescot, J. Bok, A. Migus, J. Y. Vinet, and A. Antonetti, “Energy transfer during silicon irradiation by femtosecond laser pulse,” Phys. Rev. Lett. 52, 1998–2001 (1984).
[Crossref]

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).

Bourgeade, A.

C. Mézel, L. Hallo, A. Bourgeade, D. Hébert, V. T. Tikhonchuk, B. Chimier, B. Nkonga, G. Schurtz, and G. Travaillé, “Formation of nanocavities in dielectrics: a self-consistent modeling,” Phys. Plasmas 15, 093504 (2008).
[Crossref]

L. Hallo, A. Bourgeade, V. T. Tikhonchuk, C. Mezel, and J. Breil, “Model and numerical simulations of the propagation and absorption of a short laser pulse in a transparent dielectric material: Blast-wave launch and cavity formation,” Phys. Rev. B 76, 024101 (2007).

Boyd, R. W.

R. W. Boyd, Nonlinear Optics3rd ed. (Academic, 2008).

Brabec, Th.

Th. Brabec and F. Krausz, “Nonlinear optical pulse propagation in the single-cycle regime,” Phys. Rev. Lett. 78, 3282–3285 (1997).
[Crossref]

Breil, J.

L. Hallo, A. Bourgeade, V. T. Tikhonchuk, C. Mezel, and J. Breil, “Model and numerical simulations of the propagation and absorption of a short laser pulse in a transparent dielectric material: Blast-wave launch and cavity formation,” Phys. Rev. B 76, 024101 (2007).

Bristow, A. D.

A. D. Bristow, N. Rotenberg, and H. M. Van Driel, “Two-photon absorption and Kerr coefficients of silicon for 850–2200 nm,” Appl. Phys. Lett. 90, 191104 (2007).
[Crossref]

Celli, V.

Z. Lin, L. V. Zhigilei, and V. Celli, “Electron-phonon coupling and electron heat capacity of metals under conditions of strong electron-phonon nonequilibrium,” Phys. Rev. B 77, 075133 (2008). Updated calculations at http://www.faculty.virginia.edu/CompMat/electron-phonon-coupling/ .

Chen, D.

Cheng, Y.

Chimier, B.

C. Mézel, L. Hallo, A. Bourgeade, D. Hébert, V. T. Tikhonchuk, B. Chimier, B. Nkonga, G. Schurtz, and G. Travaillé, “Formation of nanocavities in dielectrics: a self-consistent modeling,” Phys. Plasmas 15, 093504 (2008).
[Crossref]

Choi, T. Y.

T. Y. Choi and C. P. Grigoropoulos, “Plasma and ablation dynamics in ultrafast laser processing of crystalline silicon,” J. Appl. Phys. 92, 4918–4925 (2002).
[Crossref]

Colombier, J. P.

E. Bevillon, J. P. Colombier, V. Recoules, and R. Stoian, “Free-electron properties of metals under ultrafast laser-induced electron-phonon nonequilibrium: a first-principles study,” Phys. Rev. B 89, 115117 (2014).

Combescot, M.

D. Hulin, M. Combescot, J. Bok, A. Migus, J. Y. Vinet, and A. Antonetti, “Energy transfer during silicon irradiation by femtosecond laser pulse,” Phys. Rev. Lett. 52, 1998–2001 (1984).
[Crossref]

Delaporte, P.

I. B. Bogatyrev, D. Grojo, P. Delaporte, S. Leyder, M. Sentis, W. Marine, and T. E. Itina, “Non-linear absorption of 1.3-μm wavelength femtosecond laser pulses focused inside semiconductors: finite difference time domain-two temperature model combined computational study,” J. Appl. Phys. 110, 103106 (2011).
[Crossref]

Deneuville, F.

C. Fourment, F. Deneuville, D. Descamps, F. Dorchies, S. Petit, O. Peyrusse, B. Holst, and V. Recoules, “Experimental determination of temperature-dependent electron-electron collision frequency in isochorically heated warm dense gold,” Phys. Rev. B 89, 161110 (2014).

Descamps, D.

C. Fourment, F. Deneuville, D. Descamps, F. Dorchies, S. Petit, O. Peyrusse, B. Holst, and V. Recoules, “Experimental determination of temperature-dependent electron-electron collision frequency in isochorically heated warm dense gold,” Phys. Rev. B 89, 161110 (2014).

Dijkhuis, J. I.

H. Zhang, D. M. Krol, J. I. Dijkhuis, and D. van Oosten, “Self-scattering effects in femtosecond laser nanoablation,” Opt. Lett. 38, 5032–5035 (2013).
[Crossref]

H. Zhang, D. van Oosten, D. M. Krol, and J. I. Dijkhuis, “Saturation effects in femtosecond laser ablation of silicon-on-insulator,” Appl. Phys. Lett. 99, 231108 (2011).
[Crossref]

Dorchies, F.

C. Fourment, F. Deneuville, D. Descamps, F. Dorchies, S. Petit, O. Peyrusse, B. Holst, and V. Recoules, “Experimental determination of temperature-dependent electron-electron collision frequency in isochorically heated warm dense gold,” Phys. Rev. B 89, 161110 (2014).

Eidmann, K.

K. Eidmann, J. Meyer-ter-Vehn, T. Schlegel, and S. Huller, “Hydrodynamic simulation of subpicosecond laser interaction with solid-density matter,” Phys. Rev. E 62, 1202–1214 (2000).
[Crossref]

Feit, M. D.

B. C. Stuart, M. D. Feit, S. Herman, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Nanosecond-to-femtosecond laser-induced breakdown in dielectrics,” Phys. Rev. B 53, 1749–1761 (1996).

Fourment, C.

C. Fourment, F. Deneuville, D. Descamps, F. Dorchies, S. Petit, O. Peyrusse, B. Holst, and V. Recoules, “Experimental determination of temperature-dependent electron-electron collision frequency in isochorically heated warm dense gold,” Phys. Rev. B 89, 161110 (2014).

Gamaly, E. G.

E. G. Gamaly, S. Juodkazis, K. Nishimura, H. Misawa, B. Luther-Davies, L. Hallo, Ph. Nicolai, and V. T. Tikhonchuk, “Laser-matter interaction in the bulk of a transparent solid: Confined microexplosion and void formation,” Phys. Rev. B 73, 214101 (2006).

Grigoropoulos, C. P.

T. Y. Choi and C. P. Grigoropoulos, “Plasma and ablation dynamics in ultrafast laser processing of crystalline silicon,” J. Appl. Phys. 92, 4918–4925 (2002).
[Crossref]

Grojo, D.

I. B. Bogatyrev, D. Grojo, P. Delaporte, S. Leyder, M. Sentis, W. Marine, and T. E. Itina, “Non-linear absorption of 1.3-μm wavelength femtosecond laser pulses focused inside semiconductors: finite difference time domain-two temperature model combined computational study,” J. Appl. Phys. 110, 103106 (2011).
[Crossref]

Hallo, L.

C. Mézel, L. Hallo, A. Bourgeade, D. Hébert, V. T. Tikhonchuk, B. Chimier, B. Nkonga, G. Schurtz, and G. Travaillé, “Formation of nanocavities in dielectrics: a self-consistent modeling,” Phys. Plasmas 15, 093504 (2008).
[Crossref]

L. Hallo, A. Bourgeade, V. T. Tikhonchuk, C. Mezel, and J. Breil, “Model and numerical simulations of the propagation and absorption of a short laser pulse in a transparent dielectric material: Blast-wave launch and cavity formation,” Phys. Rev. B 76, 024101 (2007).

E. G. Gamaly, S. Juodkazis, K. Nishimura, H. Misawa, B. Luther-Davies, L. Hallo, Ph. Nicolai, and V. T. Tikhonchuk, “Laser-matter interaction in the bulk of a transparent solid: Confined microexplosion and void formation,” Phys. Rev. B 73, 214101 (2006).

Hébert, D.

C. Mézel, L. Hallo, A. Bourgeade, D. Hébert, V. T. Tikhonchuk, B. Chimier, B. Nkonga, G. Schurtz, and G. Travaillé, “Formation of nanocavities in dielectrics: a self-consistent modeling,” Phys. Plasmas 15, 093504 (2008).
[Crossref]

Hecht, B.

L. Novotny and B. Hecht, Nano Optics (Cambridge University, 2006).

Herman, S.

B. C. Stuart, M. D. Feit, S. Herman, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Nanosecond-to-femtosecond laser-induced breakdown in dielectrics,” Phys. Rev. B 53, 1749–1761 (1996).

Holst, B.

C. Fourment, F. Deneuville, D. Descamps, F. Dorchies, S. Petit, O. Peyrusse, B. Holst, and V. Recoules, “Experimental determination of temperature-dependent electron-electron collision frequency in isochorically heated warm dense gold,” Phys. Rev. B 89, 161110 (2014).

Horvath, C.

P. P. Pronko, P. A. VanRompay, C. Horvath, F. Loesel, T. Juhasz, X. Liu, and G. Mourou, “Avalanche ionization and dielectric breakdown in silicon with ultrafast laser pulses,” Phys. Rev. B 58, 2387–2390 (1998).

Hulin, D.

D. Hulin, M. Combescot, J. Bok, A. Migus, J. Y. Vinet, and A. Antonetti, “Energy transfer during silicon irradiation by femtosecond laser pulse,” Phys. Rev. Lett. 52, 1998–2001 (1984).
[Crossref]

Huller, S.

K. Eidmann, J. Meyer-ter-Vehn, T. Schlegel, and S. Huller, “Hydrodynamic simulation of subpicosecond laser interaction with solid-density matter,” Phys. Rev. E 62, 1202–1214 (2000).
[Crossref]

Ikeda, N.

M. Li, K. Mori, M. Ishizuka, X. Liu, Y. Sugimoto, N. Ikeda, and K. Asakawa, “Photonic bandpass filter for 1550  nm fabricated by femtosecond direct laser ablation,” Appl. Phys. Lett. 83, 216–218 (2003).
[Crossref]

Ishizuka, M.

M. Li, K. Mori, M. Ishizuka, X. Liu, Y. Sugimoto, N. Ikeda, and K. Asakawa, “Photonic bandpass filter for 1550  nm fabricated by femtosecond direct laser ablation,” Appl. Phys. Lett. 83, 216–218 (2003).
[Crossref]

Itina, T. E.

I. B. Bogatyrev, D. Grojo, P. Delaporte, S. Leyder, M. Sentis, W. Marine, and T. E. Itina, “Non-linear absorption of 1.3-μm wavelength femtosecond laser pulses focused inside semiconductors: finite difference time domain-two temperature model combined computational study,” J. Appl. Phys. 110, 103106 (2011).
[Crossref]

Juhasz, T.

P. P. Pronko, P. A. VanRompay, C. Horvath, F. Loesel, T. Juhasz, X. Liu, and G. Mourou, “Avalanche ionization and dielectric breakdown in silicon with ultrafast laser pulses,” Phys. Rev. B 58, 2387–2390 (1998).

Juodkazis, S.

E. G. Gamaly, S. Juodkazis, K. Nishimura, H. Misawa, B. Luther-Davies, L. Hallo, Ph. Nicolai, and V. T. Tikhonchuk, “Laser-matter interaction in the bulk of a transparent solid: Confined microexplosion and void formation,” Phys. Rev. B 73, 214101 (2006).

Kim, K. S.

S. J. Youn, T. H. Rho, B. I. Min, and K. S. Kim, “Extended Drude model analysis of noble metals,” Phys. Status Solidi B 244, 1354–1362 (2007).
[Crossref]

Krausz, F.

Th. Brabec and F. Krausz, “Nonlinear optical pulse propagation in the single-cycle regime,” Phys. Rev. Lett. 78, 3282–3285 (1997).
[Crossref]

Krol, D. M.

H. Zhang, D. M. Krol, J. I. Dijkhuis, and D. van Oosten, “Self-scattering effects in femtosecond laser nanoablation,” Opt. Lett. 38, 5032–5035 (2013).
[Crossref]

H. Zhang, D. van Oosten, D. M. Krol, and J. I. Dijkhuis, “Saturation effects in femtosecond laser ablation of silicon-on-insulator,” Appl. Phys. Lett. 99, 231108 (2011).
[Crossref]

Leyder, S.

I. B. Bogatyrev, D. Grojo, P. Delaporte, S. Leyder, M. Sentis, W. Marine, and T. E. Itina, “Non-linear absorption of 1.3-μm wavelength femtosecond laser pulses focused inside semiconductors: finite difference time domain-two temperature model combined computational study,” J. Appl. Phys. 110, 103106 (2011).
[Crossref]

Li, M.

M. Li, K. Mori, M. Ishizuka, X. Liu, Y. Sugimoto, N. Ikeda, and K. Asakawa, “Photonic bandpass filter for 1550  nm fabricated by femtosecond direct laser ablation,” Appl. Phys. Lett. 83, 216–218 (2003).
[Crossref]

Liao, Y.

Lin, Z.

Z. Lin, L. V. Zhigilei, and V. Celli, “Electron-phonon coupling and electron heat capacity of metals under conditions of strong electron-phonon nonequilibrium,” Phys. Rev. B 77, 075133 (2008). Updated calculations at http://www.faculty.virginia.edu/CompMat/electron-phonon-coupling/ .

Liu, X.

M. Li, K. Mori, M. Ishizuka, X. Liu, Y. Sugimoto, N. Ikeda, and K. Asakawa, “Photonic bandpass filter for 1550  nm fabricated by femtosecond direct laser ablation,” Appl. Phys. Lett. 83, 216–218 (2003).
[Crossref]

P. P. Pronko, P. A. VanRompay, C. Horvath, F. Loesel, T. Juhasz, X. Liu, and G. Mourou, “Avalanche ionization and dielectric breakdown in silicon with ultrafast laser pulses,” Phys. Rev. B 58, 2387–2390 (1998).

Loesel, F.

P. P. Pronko, P. A. VanRompay, C. Horvath, F. Loesel, T. Juhasz, X. Liu, and G. Mourou, “Avalanche ionization and dielectric breakdown in silicon with ultrafast laser pulses,” Phys. Rev. B 58, 2387–2390 (1998).

Luther-Davies, B.

E. G. Gamaly, S. Juodkazis, K. Nishimura, H. Misawa, B. Luther-Davies, L. Hallo, Ph. Nicolai, and V. T. Tikhonchuk, “Laser-matter interaction in the bulk of a transparent solid: Confined microexplosion and void formation,” Phys. Rev. B 73, 214101 (2006).

Marine, W.

I. B. Bogatyrev, D. Grojo, P. Delaporte, S. Leyder, M. Sentis, W. Marine, and T. E. Itina, “Non-linear absorption of 1.3-μm wavelength femtosecond laser pulses focused inside semiconductors: finite difference time domain-two temperature model combined computational study,” J. Appl. Phys. 110, 103106 (2011).
[Crossref]

Medvedev, N.

N. Medvedev and B. Rethfeld, “A comprehensive model for the ultrashort visible light irradiation of semiconductors,” J. Appl. Phys. 108, 103112 (2010).
[Crossref]

Mermin, N. D.

N. W. Ashcroft and N. D. Mermin, Solid State Physics (Brooks/Cole, 1976).

Meyer-ter-Vehn, J.

K. Eidmann, J. Meyer-ter-Vehn, T. Schlegel, and S. Huller, “Hydrodynamic simulation of subpicosecond laser interaction with solid-density matter,” Phys. Rev. E 62, 1202–1214 (2000).
[Crossref]

Mezel, C.

L. Hallo, A. Bourgeade, V. T. Tikhonchuk, C. Mezel, and J. Breil, “Model and numerical simulations of the propagation and absorption of a short laser pulse in a transparent dielectric material: Blast-wave launch and cavity formation,” Phys. Rev. B 76, 024101 (2007).

Mézel, C.

C. Mézel, L. Hallo, A. Bourgeade, D. Hébert, V. T. Tikhonchuk, B. Chimier, B. Nkonga, G. Schurtz, and G. Travaillé, “Formation of nanocavities in dielectrics: a self-consistent modeling,” Phys. Plasmas 15, 093504 (2008).
[Crossref]

Mezentsev, V.

Midorikawa, K.

Migus, A.

D. Hulin, M. Combescot, J. Bok, A. Migus, J. Y. Vinet, and A. Antonetti, “Energy transfer during silicon irradiation by femtosecond laser pulse,” Phys. Rev. Lett. 52, 1998–2001 (1984).
[Crossref]

Min, B. I.

S. J. Youn, T. H. Rho, B. I. Min, and K. S. Kim, “Extended Drude model analysis of noble metals,” Phys. Status Solidi B 244, 1354–1362 (2007).
[Crossref]

Misawa, H.

E. G. Gamaly, S. Juodkazis, K. Nishimura, H. Misawa, B. Luther-Davies, L. Hallo, Ph. Nicolai, and V. T. Tikhonchuk, “Laser-matter interaction in the bulk of a transparent solid: Confined microexplosion and void formation,” Phys. Rev. B 73, 214101 (2006).

Mori, K.

M. Li, K. Mori, M. Ishizuka, X. Liu, Y. Sugimoto, N. Ikeda, and K. Asakawa, “Photonic bandpass filter for 1550  nm fabricated by femtosecond direct laser ablation,” Appl. Phys. Lett. 83, 216–218 (2003).
[Crossref]

Mourou, G.

P. P. Pronko, P. A. VanRompay, C. Horvath, F. Loesel, T. Juhasz, X. Liu, and G. Mourou, “Avalanche ionization and dielectric breakdown in silicon with ultrafast laser pulses,” Phys. Rev. B 58, 2387–2390 (1998).

Mueller, B. Y.

B. Y. Mueller and B. Rethfeld, “Relaxation dynamics in laser-excited metals under nonequilibrium conditions,” Phys. Rev. B 87, 035139 (2013).

Nicolai, Ph.

E. G. Gamaly, S. Juodkazis, K. Nishimura, H. Misawa, B. Luther-Davies, L. Hallo, Ph. Nicolai, and V. T. Tikhonchuk, “Laser-matter interaction in the bulk of a transparent solid: Confined microexplosion and void formation,” Phys. Rev. B 73, 214101 (2006).

Nishimura, K.

E. G. Gamaly, S. Juodkazis, K. Nishimura, H. Misawa, B. Luther-Davies, L. Hallo, Ph. Nicolai, and V. T. Tikhonchuk, “Laser-matter interaction in the bulk of a transparent solid: Confined microexplosion and void formation,” Phys. Rev. B 73, 214101 (2006).

Nkonga, B.

C. Mézel, L. Hallo, A. Bourgeade, D. Hébert, V. T. Tikhonchuk, B. Chimier, B. Nkonga, G. Schurtz, and G. Travaillé, “Formation of nanocavities in dielectrics: a self-consistent modeling,” Phys. Plasmas 15, 093504 (2008).
[Crossref]

Novotny, L.

L. Novotny and B. Hecht, Nano Optics (Cambridge University, 2006).

Perry, M. D.

B. C. Stuart, M. D. Feit, S. Herman, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Nanosecond-to-femtosecond laser-induced breakdown in dielectrics,” Phys. Rev. B 53, 1749–1761 (1996).

Petit, S.

C. Fourment, F. Deneuville, D. Descamps, F. Dorchies, S. Petit, O. Peyrusse, B. Holst, and V. Recoules, “Experimental determination of temperature-dependent electron-electron collision frequency in isochorically heated warm dense gold,” Phys. Rev. B 89, 161110 (2014).

Peyrusse, O.

C. Fourment, F. Deneuville, D. Descamps, F. Dorchies, S. Petit, O. Peyrusse, B. Holst, and V. Recoules, “Experimental determination of temperature-dependent electron-electron collision frequency in isochorically heated warm dense gold,” Phys. Rev. B 89, 161110 (2014).

Pronko, P. P.

P. P. Pronko, P. A. VanRompay, C. Horvath, F. Loesel, T. Juhasz, X. Liu, and G. Mourou, “Avalanche ionization and dielectric breakdown in silicon with ultrafast laser pulses,” Phys. Rev. B 58, 2387–2390 (1998).

Qiao, L.

Recoules, V.

E. Bevillon, J. P. Colombier, V. Recoules, and R. Stoian, “Free-electron properties of metals under ultrafast laser-induced electron-phonon nonequilibrium: a first-principles study,” Phys. Rev. B 89, 115117 (2014).

C. Fourment, F. Deneuville, D. Descamps, F. Dorchies, S. Petit, O. Peyrusse, B. Holst, and V. Recoules, “Experimental determination of temperature-dependent electron-electron collision frequency in isochorically heated warm dense gold,” Phys. Rev. B 89, 161110 (2014).

Rethfeld, B.

B. Y. Mueller and B. Rethfeld, “Relaxation dynamics in laser-excited metals under nonequilibrium conditions,” Phys. Rev. B 87, 035139 (2013).

N. Medvedev and B. Rethfeld, “A comprehensive model for the ultrashort visible light irradiation of semiconductors,” J. Appl. Phys. 108, 103112 (2010).
[Crossref]

B. Rethfeld, K. Sokolowski-Tinten, D. Von Der Linde, and S. I. Anisimov, “Timescales in the response of materials to femtosecond laser excitation,” Appl. Phys. A 79, 767–773 (2004).
[Crossref]

Rho, T. H.

S. J. Youn, T. H. Rho, B. I. Min, and K. S. Kim, “Extended Drude model analysis of noble metals,” Phys. Status Solidi B 244, 1354–1362 (2007).
[Crossref]

Riffe, D. M.

Rotenberg, N.

A. D. Bristow, N. Rotenberg, and H. M. Van Driel, “Two-photon absorption and Kerr coefficients of silicon for 850–2200 nm,” Appl. Phys. Lett. 90, 191104 (2007).
[Crossref]

Rubenchik, A. M.

B. C. Stuart, M. D. Feit, S. Herman, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Nanosecond-to-femtosecond laser-induced breakdown in dielectrics,” Phys. Rev. B 53, 1749–1761 (1996).

Schlegel, T.

K. Eidmann, J. Meyer-ter-Vehn, T. Schlegel, and S. Huller, “Hydrodynamic simulation of subpicosecond laser interaction with solid-density matter,” Phys. Rev. E 62, 1202–1214 (2000).
[Crossref]

Schmitz, H.

Schurtz, G.

C. Mézel, L. Hallo, A. Bourgeade, D. Hébert, V. T. Tikhonchuk, B. Chimier, B. Nkonga, G. Schurtz, and G. Travaillé, “Formation of nanocavities in dielectrics: a self-consistent modeling,” Phys. Plasmas 15, 093504 (2008).
[Crossref]

Sentis, M.

I. B. Bogatyrev, D. Grojo, P. Delaporte, S. Leyder, M. Sentis, W. Marine, and T. E. Itina, “Non-linear absorption of 1.3-μm wavelength femtosecond laser pulses focused inside semiconductors: finite difference time domain-two temperature model combined computational study,” J. Appl. Phys. 110, 103106 (2011).
[Crossref]

Shen, Y.

Shore, B. W.

B. C. Stuart, M. D. Feit, S. Herman, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Nanosecond-to-femtosecond laser-induced breakdown in dielectrics,” Phys. Rev. B 53, 1749–1761 (1996).

Sokolowski-Tinten, K.

B. Rethfeld, K. Sokolowski-Tinten, D. Von Der Linde, and S. I. Anisimov, “Timescales in the response of materials to femtosecond laser excitation,” Appl. Phys. A 79, 767–773 (2004).
[Crossref]

K. Sokolowski-Tinten and D. von der Linde, “Generation of dense electron-hole plasmas in silicon,” Phys. Rev. B 61, 2643–2650 (2000).

K. Sokolowski-Tinten, J. Bialkowski, and D. von der Linde, “Ultrafast laser-induced order-disorder transitions in semiconductors,” Phys. Rev. B 51, 14186–14198 (1995).

Stoian, R.

E. Bevillon, J. P. Colombier, V. Recoules, and R. Stoian, “Free-electron properties of metals under ultrafast laser-induced electron-phonon nonequilibrium: a first-principles study,” Phys. Rev. B 89, 115117 (2014).

Stuart, B. C.

B. C. Stuart, M. D. Feit, S. Herman, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Nanosecond-to-femtosecond laser-induced breakdown in dielectrics,” Phys. Rev. B 53, 1749–1761 (1996).

Sugimoto, Y.

M. Li, K. Mori, M. Ishizuka, X. Liu, Y. Sugimoto, N. Ikeda, and K. Asakawa, “Photonic bandpass filter for 1550  nm fabricated by femtosecond direct laser ablation,” Appl. Phys. Lett. 83, 216–218 (2003).
[Crossref]

Sugioka, K.

Sullivan, D. M.

D. M. Sullivan, “Electromagnetic simulation using the FDTD method,” IEEE, 2000.

Tikhonchuk, V. T.

C. Mézel, L. Hallo, A. Bourgeade, D. Hébert, V. T. Tikhonchuk, B. Chimier, B. Nkonga, G. Schurtz, and G. Travaillé, “Formation of nanocavities in dielectrics: a self-consistent modeling,” Phys. Plasmas 15, 093504 (2008).
[Crossref]

L. Hallo, A. Bourgeade, V. T. Tikhonchuk, C. Mezel, and J. Breil, “Model and numerical simulations of the propagation and absorption of a short laser pulse in a transparent dielectric material: Blast-wave launch and cavity formation,” Phys. Rev. B 76, 024101 (2007).

E. G. Gamaly, S. Juodkazis, K. Nishimura, H. Misawa, B. Luther-Davies, L. Hallo, Ph. Nicolai, and V. T. Tikhonchuk, “Laser-matter interaction in the bulk of a transparent solid: Confined microexplosion and void formation,” Phys. Rev. B 73, 214101 (2006).

Travaillé, G.

C. Mézel, L. Hallo, A. Bourgeade, D. Hébert, V. T. Tikhonchuk, B. Chimier, B. Nkonga, G. Schurtz, and G. Travaillé, “Formation of nanocavities in dielectrics: a self-consistent modeling,” Phys. Plasmas 15, 093504 (2008).
[Crossref]

Van Driel, H. M.

A. D. Bristow, N. Rotenberg, and H. M. Van Driel, “Two-photon absorption and Kerr coefficients of silicon for 850–2200 nm,” Appl. Phys. Lett. 90, 191104 (2007).
[Crossref]

H. M. van Driel, “Kinetics of high-density plasmas generated in Si by 1.06- and 0.53-μm picosecond laser pulses,” Phys. Rev. B 35, 8166–8176 (1987).

van Oosten, D.

H. Zhang, D. M. Krol, J. I. Dijkhuis, and D. van Oosten, “Self-scattering effects in femtosecond laser nanoablation,” Opt. Lett. 38, 5032–5035 (2013).
[Crossref]

H. Zhang, D. van Oosten, D. M. Krol, and J. I. Dijkhuis, “Saturation effects in femtosecond laser ablation of silicon-on-insulator,” Appl. Phys. Lett. 99, 231108 (2011).
[Crossref]

VanRompay, P. A.

P. P. Pronko, P. A. VanRompay, C. Horvath, F. Loesel, T. Juhasz, X. Liu, and G. Mourou, “Avalanche ionization and dielectric breakdown in silicon with ultrafast laser pulses,” Phys. Rev. B 58, 2387–2390 (1998).

Vestentoft, K.

K. Vestentoft and P. Balling, “Formation of an extended nanostructured metal surface by ultra-short laser pulses: single-pulse ablation in the high-fluence limit,” Appl. Phys. A 84, 207–213 (2006).
[Crossref]

Vinet, J. Y.

D. Hulin, M. Combescot, J. Bok, A. Migus, J. Y. Vinet, and A. Antonetti, “Energy transfer during silicon irradiation by femtosecond laser pulse,” Phys. Rev. Lett. 52, 1998–2001 (1984).
[Crossref]

Von Der Linde, D.

B. Rethfeld, K. Sokolowski-Tinten, D. Von Der Linde, and S. I. Anisimov, “Timescales in the response of materials to femtosecond laser excitation,” Appl. Phys. A 79, 767–773 (2004).
[Crossref]

K. Sokolowski-Tinten and D. von der Linde, “Generation of dense electron-hole plasmas in silicon,” Phys. Rev. B 61, 2643–2650 (2000).

K. Sokolowski-Tinten, J. Bialkowski, and D. von der Linde, “Ultrafast laser-induced order-disorder transitions in semiconductors,” Phys. Rev. B 51, 14186–14198 (1995).

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).

Yablonovitch, E.

E. Yablonovitch and N. Bloembergen, “Avalanche ionization and the limiting diameter of filaments induced by light pulses in transparent media,” Phys. Rev. Lett. 29, 907–910 (1972).
[Crossref]

Youn, S. J.

S. J. Youn, T. H. Rho, B. I. Min, and K. S. Kim, “Extended Drude model analysis of noble metals,” Phys. Status Solidi B 244, 1354–1362 (2007).
[Crossref]

Zhang, H.

H. Zhang, D. M. Krol, J. I. Dijkhuis, and D. van Oosten, “Self-scattering effects in femtosecond laser nanoablation,” Opt. Lett. 38, 5032–5035 (2013).
[Crossref]

H. Zhang, D. van Oosten, D. M. Krol, and J. I. Dijkhuis, “Saturation effects in femtosecond laser ablation of silicon-on-insulator,” Appl. Phys. Lett. 99, 231108 (2011).
[Crossref]

Zhigilei, L. V.

Z. Lin, L. V. Zhigilei, and V. Celli, “Electron-phonon coupling and electron heat capacity of metals under conditions of strong electron-phonon nonequilibrium,” Phys. Rev. B 77, 075133 (2008). Updated calculations at http://www.faculty.virginia.edu/CompMat/electron-phonon-coupling/ .

Appl. Phys. A (2)

B. Rethfeld, K. Sokolowski-Tinten, D. Von Der Linde, and S. I. Anisimov, “Timescales in the response of materials to femtosecond laser excitation,” Appl. Phys. A 79, 767–773 (2004).
[Crossref]

K. Vestentoft and P. Balling, “Formation of an extended nanostructured metal surface by ultra-short laser pulses: single-pulse ablation in the high-fluence limit,” Appl. Phys. A 84, 207–213 (2006).
[Crossref]

Appl. Phys. Lett. (3)

A. D. Bristow, N. Rotenberg, and H. M. Van Driel, “Two-photon absorption and Kerr coefficients of silicon for 850–2200 nm,” Appl. Phys. Lett. 90, 191104 (2007).
[Crossref]

H. Zhang, D. van Oosten, D. M. Krol, and J. I. Dijkhuis, “Saturation effects in femtosecond laser ablation of silicon-on-insulator,” Appl. Phys. Lett. 99, 231108 (2011).
[Crossref]

M. Li, K. Mori, M. Ishizuka, X. Liu, Y. Sugimoto, N. Ikeda, and K. Asakawa, “Photonic bandpass filter for 1550  nm fabricated by femtosecond direct laser ablation,” Appl. Phys. Lett. 83, 216–218 (2003).
[Crossref]

J. Appl. Phys. (3)

T. Y. Choi and C. P. Grigoropoulos, “Plasma and ablation dynamics in ultrafast laser processing of crystalline silicon,” J. Appl. Phys. 92, 4918–4925 (2002).
[Crossref]

N. Medvedev and B. Rethfeld, “A comprehensive model for the ultrashort visible light irradiation of semiconductors,” J. Appl. Phys. 108, 103112 (2010).
[Crossref]

I. B. Bogatyrev, D. Grojo, P. Delaporte, S. Leyder, M. Sentis, W. Marine, and T. E. Itina, “Non-linear absorption of 1.3-μm wavelength femtosecond laser pulses focused inside semiconductors: finite difference time domain-two temperature model combined computational study,” J. Appl. Phys. 110, 103106 (2011).
[Crossref]

J. Opt. Soc. Am. B (2)

Opt. Lett. (2)

Phys. Plasmas (1)

C. Mézel, L. Hallo, A. Bourgeade, D. Hébert, V. T. Tikhonchuk, B. Chimier, B. Nkonga, G. Schurtz, and G. Travaillé, “Formation of nanocavities in dielectrics: a self-consistent modeling,” Phys. Plasmas 15, 093504 (2008).
[Crossref]

Phys. Rev. B (11)

E. G. Gamaly, S. Juodkazis, K. Nishimura, H. Misawa, B. Luther-Davies, L. Hallo, Ph. Nicolai, and V. T. Tikhonchuk, “Laser-matter interaction in the bulk of a transparent solid: Confined microexplosion and void formation,” Phys. Rev. B 73, 214101 (2006).

B. Y. Mueller and B. Rethfeld, “Relaxation dynamics in laser-excited metals under nonequilibrium conditions,” Phys. Rev. B 87, 035139 (2013).

L. Hallo, A. Bourgeade, V. T. Tikhonchuk, C. Mezel, and J. Breil, “Model and numerical simulations of the propagation and absorption of a short laser pulse in a transparent dielectric material: Blast-wave launch and cavity formation,” Phys. Rev. B 76, 024101 (2007).

B. C. Stuart, M. D. Feit, S. Herman, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Nanosecond-to-femtosecond laser-induced breakdown in dielectrics,” Phys. Rev. B 53, 1749–1761 (1996).

H. M. van Driel, “Kinetics of high-density plasmas generated in Si by 1.06- and 0.53-μm picosecond laser pulses,” Phys. Rev. B 35, 8166–8176 (1987).

C. Fourment, F. Deneuville, D. Descamps, F. Dorchies, S. Petit, O. Peyrusse, B. Holst, and V. Recoules, “Experimental determination of temperature-dependent electron-electron collision frequency in isochorically heated warm dense gold,” Phys. Rev. B 89, 161110 (2014).

E. Bevillon, J. P. Colombier, V. Recoules, and R. Stoian, “Free-electron properties of metals under ultrafast laser-induced electron-phonon nonequilibrium: a first-principles study,” Phys. Rev. B 89, 115117 (2014).

Z. Lin, L. V. Zhigilei, and V. Celli, “Electron-phonon coupling and electron heat capacity of metals under conditions of strong electron-phonon nonequilibrium,” Phys. Rev. B 77, 075133 (2008). Updated calculations at http://www.faculty.virginia.edu/CompMat/electron-phonon-coupling/ .

P. P. Pronko, P. A. VanRompay, C. Horvath, F. Loesel, T. Juhasz, X. Liu, and G. Mourou, “Avalanche ionization and dielectric breakdown in silicon with ultrafast laser pulses,” Phys. Rev. B 58, 2387–2390 (1998).

K. Sokolowski-Tinten and D. von der Linde, “Generation of dense electron-hole plasmas in silicon,” Phys. Rev. B 61, 2643–2650 (2000).

K. Sokolowski-Tinten, J. Bialkowski, and D. von der Linde, “Ultrafast laser-induced order-disorder transitions in semiconductors,” Phys. Rev. B 51, 14186–14198 (1995).

Phys. Rev. E (1)

K. Eidmann, J. Meyer-ter-Vehn, T. Schlegel, and S. Huller, “Hydrodynamic simulation of subpicosecond laser interaction with solid-density matter,” Phys. Rev. E 62, 1202–1214 (2000).
[Crossref]

Phys. Rev. Lett. (3)

E. Yablonovitch and N. Bloembergen, “Avalanche ionization and the limiting diameter of filaments induced by light pulses in transparent media,” Phys. Rev. Lett. 29, 907–910 (1972).
[Crossref]

D. Hulin, M. Combescot, J. Bok, A. Migus, J. Y. Vinet, and A. Antonetti, “Energy transfer during silicon irradiation by femtosecond laser pulse,” Phys. Rev. Lett. 52, 1998–2001 (1984).
[Crossref]

Th. Brabec and F. Krausz, “Nonlinear optical pulse propagation in the single-cycle regime,” Phys. Rev. Lett. 78, 3282–3285 (1997).
[Crossref]

Phys. Status Solidi B (1)

S. J. Youn, T. H. Rho, B. I. Min, and K. S. Kim, “Extended Drude model analysis of noble metals,” Phys. Status Solidi B 244, 1354–1362 (2007).
[Crossref]

Other (6)

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).

Lumerical Solutions, Inc. http://www.lumerical.com/tcad-products/fdtd/ .

L. Novotny and B. Hecht, Nano Optics (Cambridge University, 2006).

R. W. Boyd, Nonlinear Optics3rd ed. (Academic, 2008).

N. W. Ashcroft and N. D. Mermin, Solid State Physics (Brooks/Cole, 1976).

D. M. Sullivan, “Electromagnetic simulation using the FDTD method,” IEEE, 2000.

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Figures (7)

Fig. 1.
Fig. 1. Diagrammatic view of the model. The iteration starts at Maxwell’s equations, which solve the propagation of the laser pulse in an initially unexcited material. Once every optical half-cycle, the optical intensity inside the material can be derived using the electric field obtained with Maxwell’s equations. This optical intensity is used as an input to the material equations that describe the response of the material to the intensity. By solving the material equations, parameters of the excited material, such as electron density and electron temperature, are obtained. Subsequently, a new susceptibility can be deduced from the parameters of the excited material. This new susceptibility and thus the dielectric function are further inserted into Maxwell’s equations to complete a single iteration. The iterations are conducted once every optical half-cycle until the end of the pulse.
Fig. 2.
Fig. 2. Layout of the 2D-FDTD simulation box. The FDTD grid is excited by a soft source that is located 200 nm above the silicon–air interface. Scattered E and H near-field values are recorded at the detector plane to extract the reflectivity.
Fig. 3.
Fig. 3. 2D-FDTD calculations and experimental measurements of self-reflectivity for bulk silicon and SOI samples. Open and closed symbols indicate results of two independent experimental runs for bulk silicon (circles), SOI 1 (squares), and SOI 2 (diamonds). The solid lines show the reflectivity calculated by 2D-FDTD simulations with the TM and TE modes combined for bulk (green), SOI 1 (blue), and SOI 2 (red). The dashed lines show the results obtained from a 1D-FDTD simulation. The blue dashed–dotted and dotted lines show the reflectivity calculated for SOI 1 using either the TE or the TM mode, respectively. The left inset shows the reflectivity calculated using a dynamically changing collision rate with a T dependence, and the right inset shows the reflectivity calculated using a collision rate with a T 2 dependence.
Fig. 4.
Fig. 4. FDTD calculations and experimental measurements of self-reflectivity on the SOI 1 , SOI 2 , and bulk samples. For the calculations, an impact ionization coefficient θ = 0 cm 2 / J is used. The lines and symbols have the same meaning as in Fig. 3.
Fig. 5.
Fig. 5. Calculated (a) carrier density, (b) carrier temperature, and (c) optical effective mass on the surface of the sample after the end of the pulse. In each plot, the green line shows the data for the bulk silicon sample, the blue line for the SOI 1 sample, and the red line for the SOI 2 sample.
Fig. 6.
Fig. 6. (a) FDTD calculation and experimental measurements of self-reflectivity on a 400 nm gold film on glass. Open and closed squares are the experimental data from two independent runs. The solid line shows the calculated self-reflectivity taking both the TM and the TE mode into account. The dotted and dashed–dotted lines show the self-reflectivity taking only the TE mode or only the TM mode into account, respectively. The dashed line shows the self-reflectivity calculated with the conduction electron density at room temperature. (b) Calculated electron temperature on the surface of the sample. (c) The corresponding Drude damping time.
Fig. 7.
Fig. 7. Error of the FDTD method. Results with a range of PML thicknesses are presented.

Tables (4)

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Table 1. Material Parameters Used in the Simulation as Obtained from Literature a

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Table 2. Sample Parameters a

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Table 3. Physical Parameters Used in the Simulation for Gold a

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Table 4. Comparison between the Results of Our 2D-FDTD Code with the Results from the Commercial Software FDTD Solutions a

Equations (61)

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× H = D t + j , × E = B t ,
D = ϵ 0 E + P , H = 1 μ 0 B M .
H ( r , t ) t = 1 μ 0 × E ( r , t ) ,
E ( r , t ) t = 1 ϵ 0 ϵ r ( r , t ) × H ( r , t ) ,
N ( r , t ) t + · [ D 0 ( r , t ) N ( r , t ) ] = S N ( E ( r , t ) ) ,
ϵ r ( r , t ) = 1 + χ ( r , N ( r , t ) , ) ,
N ( r , t ) t + · [ D 0 ( r , t ) N ( r , t ) ] = α 0 I ( r , t ) ω + β I 2 ( r , t ) 2 ω + θ I ( r , t ) N ( r , t ) ,
I ( r , t ) = 1 2 ϵ 0 c Re { n ex ( r , t ) } | E 0 ( r , t ) | 2 ,
ϵ ex ( r , t ) = ϵ Si + ϵ Drude + ϵ NL ,
ϵ Drude ( r , t ) = ( ω p / ω ) 2 1 + i / ω τ d ,
ϵ NL ( r , t ) = 3 4 χ 3 | E 0 ( r , t ) | 2 ,
ω p ( r , t ) = N ( r , t ) e 2 m * ( r , t ) ϵ 0 ,
n ex = ϵ ex ,
α ex = 4 π Im { n ex } λ 0 .
[ U c ( r , t ) ] t + · [ κ c T c ( r , t ) ] = α ex I ( r , t ) .
U c = C c T c + N E g ,
κ c = 1 3 C c v c 2 τ d ,
D 0 = k B T c τ d m * ,
m * m e = m 0 * m e + m k T c ,
C e [ T e ( r , t ) ] t + · [ κ e T e ( r , t ) ] = α ex I ( r , t ) ,
τ d = 1 ν ph + 0.301 ( 11 Z eff ) ( Z eff 1 ) ,
ϵ ex ( r , t ) = ϵ + ϵ Drude ( r , t ) ,
ϵ Drude ( r , t ) = ( ω p / ω ) 2 1 + i / ω τ d ( r , t ) ,
U refl , inc = 0 r max 2 π r d r ( F refl , inc TE ( r ) + F refl , inc TM ( r ) ) ,
R = U refl U inc .
1 τ e e ( T e ) = π 4 k B 2 3 256 ω p E F 2 T e 2 = B T e 2 ,
E ( t ) = E 0 cos ( ω 0 t + ϕ ) ,
0 T / 2 E 2 ( t ) d t = 0 T / 2 E 0 2 cos 2 ( ω 0 t + ϕ ) d t = 1 4 T E 0 2 ,
E 0 = 4 0 T / 2 E 2 ( t ) d t T .
0 T / 2 E 2 ( t ) d t n = n 1 n 1 + m E 2 ( n Δ t ) · Δ t ,
0 T / 2 E 0 cos ( ω 0 t + ϕ ) e i ω 0 t d t = E 0 π 2 ω 0 ( cos ϕ + i sin ϕ ) .
R = ( n 1 n + 1 ) 2 ,
D ˜ z t = 1 ϵ 0 μ 0 ( H y x H x y ) ,
D ˜ z ( ω ) = ϵ r * ( ω ) E ˜ z ( ω ) ,
H x t = 1 ϵ 0 μ 0 E ˜ z y ,
H y t = 1 ϵ 0 μ 0 E ˜ z x .
D ˜ x t = 1 ϵ 0 μ 0 H z y ,
D ˜ y t = 1 ϵ 0 μ 0 H z x ,
D ˜ x ( ω ) = ϵ r * ( ω ) E ˜ x ( ω ) ,
D ˜ y ( ω ) = ϵ r * ( ω ) E ˜ y ( ω ) ,
H z t = 1 ϵ 0 μ 0 ( E ˜ y x E ˜ x y ) .
E ˜ = ϵ 0 μ 0 E ,
D ˜ = ϵ 0 μ 0 D ,
ϵ r * ( ω ) = ϵ ex = ϵ Si ( ω p ω ) 2 1 1 + i 1 ω τ .
ϵ ex = ϵ Si + ω p 2 τ j ω ω p 2 τ 2 1 + j ω τ = ϵ Si + σ Drude j ω ϵ 0 + χ 1 + j ω τ ,
σ Drude = ϵ 0 ω p 2 τ ,
χ = ω p 2 τ 2 ,
D ( ω ) = ϵ ex ( ω ) E ( ω ) = ϵ Si E ( ω ) + σ Drude j ω ϵ 0 E ( ω ) + χ 1 + j ω τ E ( ω ) = D ( ω ) + S ( ω ) ,
D ( t ) = ϵ Si E ( t ) + σ Drude ϵ 0 0 t E ( t ) d t .
D n = ϵ S i E n + σ Drude Δ t ϵ 0 i = 0 n E i ,
D n = ϵ S i E n + σ Drude Δ t ϵ 0 E n + σ Drude Δ t ϵ 0 i = 0 n 1 E i ,
E n = D n σ Drude Δ t ϵ 0 i = 0 n 1 E i ϵ S i + σ Drude Δ t ϵ 0 .
S ( ω ) = χ 1 + j ω τ E ( ω )
S ( t ) = χ τ 0 t e t t τ E ( t ) d t .
S n = χ Δ t τ i = 0 n e Δ t ( n i ) τ E i = χ Δ t τ [ E n + i = 0 n 1 e Δ t ( n i ) τ E i ] .
D n = ϵ Si E n + σ Drude Δ t ϵ 0 E n + σ Drude Δ t ϵ 0 i = 0 n 1 E i + χ Δ t τ [ E n + i = 0 n 1 e Δ t ( n i ) τ E i ] ,
E n = D n σ Drude Δ t ϵ 0 i = 0 n 1 E i χ Δ t τ i = 0 n 1 e Δ t ( n i ) τ E i ϵ S i + σ Drude Δ t ϵ 0 + χ Δ t τ .
E n = D n σ Δ t ϵ 0 i = 0 n 1 E i χ Δ t τ i = 0 n 1 e Δ t ( n i ) τ E i R e [ ϵ Si ] + Δ ϵ + σ Δ t ϵ 0 + χ Δ t τ ,
k x = k 2 k y 2 ,
A ^ ( k y ) = 1 2 π A ( y ) e i k y y d y ,
A ( y ) = 1 2 π 0.8 k 0.8 k A ^ ( k y ) e i k y y d k y .

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