Abstract

The FDTD method has been successfully used for many electromagnetic problems, but its application to laser material processing has been limited because even a several-millimeter domain requires a prohibitively large number of grids. In this article, we present a novel FDTD method for simulating large-scale laser beam absorption problems, especially for metals, by enlarging laser wavelength while maintaining the material’s reflection characteristics. For validation purposes, the proposed method has been tested with in-house FDTD codes to simulate p-, s-, and circularly polarized 1.06 μm irradiation on Fe and Sn targets, and the simulation results are in good agreement with theoretical predictions.

© 2013 Optical Society of America

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References

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  1. K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwells equations in isotropic media,” IEEE Trans. Antenn. Propag.14(3), 302–307 (1966).
    [CrossRef]
  2. C. M. Dissanayake, M. Premaratne, I. D. Rukhlenko, and G. P. Agrawal, “FDTD modeling of anisotropic nonlinear optical phenomena in silicon waveguides,” Opt. Express18(20), 21427–21448 (2010).
    [CrossRef] [PubMed]
  3. K. Kitamura, K. Sakai, and S. Noda, “Finite-difference time-domain (FDTD) analysis on the interaction between a metal block and a radially polarized focused beam,” Opt. Express19(15), 13750–13756 (2011).
    [CrossRef] [PubMed]
  4. S. Buil, J. Laverdant, B. Berini, P. Maso, J. P. Hermier, and X. Quélin, “FDTD simulations of localization and enhancements on fractal plasmonics nanostructures,” Opt. Express20(11), 11968–11975 (2012).
    [CrossRef] [PubMed]
  5. C. Lundgren, R. Lopez, J. Redwing, and K. Melde, “FDTD modeling of solar energy absorption in silicon branched nanowires,” Opt. Express21(S3), A392–A400 (2013).
    [CrossRef]
  6. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. (Artech House, 2005).
  7. H. Ki and J. Mazumder, “Numerical simulation of femtosecond laser interaction with silicon,” J. Laser Appl.17(2), 110–117 (2005).
    [CrossRef]
  8. H. Li and H. Ki, “Effect of ionization on femtosecond laser pulse interaction with silicon,” J. Appl. Phys.100(10), 104907 (2006).
    [CrossRef]
  9. W. M. Steen and J. Mazumder, Laser Material Processing, 4th ed. (Springer-Verlag, 2010).
  10. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 1999).

2013 (1)

2012 (1)

2011 (1)

2010 (1)

2006 (1)

H. Li and H. Ki, “Effect of ionization on femtosecond laser pulse interaction with silicon,” J. Appl. Phys.100(10), 104907 (2006).
[CrossRef]

2005 (1)

H. Ki and J. Mazumder, “Numerical simulation of femtosecond laser interaction with silicon,” J. Laser Appl.17(2), 110–117 (2005).
[CrossRef]

1966 (1)

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwells equations in isotropic media,” IEEE Trans. Antenn. Propag.14(3), 302–307 (1966).
[CrossRef]

Agrawal, G. P.

Berini, B.

Buil, S.

Dissanayake, C. M.

Hermier, J. P.

Ki, H.

H. Li and H. Ki, “Effect of ionization on femtosecond laser pulse interaction with silicon,” J. Appl. Phys.100(10), 104907 (2006).
[CrossRef]

H. Ki and J. Mazumder, “Numerical simulation of femtosecond laser interaction with silicon,” J. Laser Appl.17(2), 110–117 (2005).
[CrossRef]

Kitamura, K.

Laverdant, J.

Li, H.

H. Li and H. Ki, “Effect of ionization on femtosecond laser pulse interaction with silicon,” J. Appl. Phys.100(10), 104907 (2006).
[CrossRef]

Lopez, R.

Lundgren, C.

Maso, P.

Mazumder, J.

H. Ki and J. Mazumder, “Numerical simulation of femtosecond laser interaction with silicon,” J. Laser Appl.17(2), 110–117 (2005).
[CrossRef]

Melde, K.

Noda, S.

Premaratne, M.

Quélin, X.

Redwing, J.

Rukhlenko, I. D.

Sakai, K.

Yee, K. S.

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwells equations in isotropic media,” IEEE Trans. Antenn. Propag.14(3), 302–307 (1966).
[CrossRef]

IEEE Trans. Antenn. Propag. (1)

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwells equations in isotropic media,” IEEE Trans. Antenn. Propag.14(3), 302–307 (1966).
[CrossRef]

J. Appl. Phys. (1)

H. Li and H. Ki, “Effect of ionization on femtosecond laser pulse interaction with silicon,” J. Appl. Phys.100(10), 104907 (2006).
[CrossRef]

J. Laser Appl. (1)

H. Ki and J. Mazumder, “Numerical simulation of femtosecond laser interaction with silicon,” J. Laser Appl.17(2), 110–117 (2005).
[CrossRef]

Opt. Express (4)

Other (3)

W. M. Steen and J. Mazumder, Laser Material Processing, 4th ed. (Springer-Verlag, 2010).

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 1999).

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. (Artech House, 2005).

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Figures (10)

Fig. 1
Fig. 1

Reflectance contour lines obtained from Eqs. (1) and (2) assuming an incident angle of 0°. At this angle, p- and s-polarizations cannot be distinguished.

Fig. 2
Fig. 2

Reflectance versus incident angle for Fe under 1.06 μm irradiation. Red lines are analytical solutions of Fe for s- and p-polarized lights (n = 3.81 and κ = 4.44). Blues lines are generated from Eqs. (1) and (2) assuming θi* = 0° and R p = R s =0.644 .

Fig. 3
Fig. 3

Lines of constant reflectance (R = 0.644) for s- and p-polarized lights shown as blue dashed lines and red solid lines, respectively.

Fig. 4
Fig. 4

Reflectance versus incident angle for Fe under 1.06 μm irradiation. Red lines are analytical solutions of Fe for s- and p-polarized lights (n = 3.81 and κ = 4.44). Blues lines are generated from Eqs. (1) and (2) assuming θi* = 75.2° and R p = R s =0.644 .

Fig. 5
Fig. 5

Overall relative errors generated when a different n and κ values are used to approximate the material’s reflectance patterns. Errors are calculated for Fe under 1.06 μm irradiation.

Fig. 6
Fig. 6

Schematic diagram of the computational domain.

Fig. 7
Fig. 7

Electric fields in the computational domain showing the reflection patterns at different tilting angles. Simulations were performed for Fe with an enlarged wavelength using the dispersive FDTD code assuming the laser beam is s-polarized. The width of the computational domain is 200 μm.

Fig. 8
Fig. 8

Simulated reflection curves with analytical solutions.

Fig. 9
Fig. 9

Schematic diagram of the computational domain.

Fig. 10
Fig. 10

Simulation results showing a Gaussian beam irradiating on a cylinder made of Fe. Here, the dispersive FDTD with an enlarged wavelength of 21.2 μm was used instead of 1.06 μm. The width and height of the figures are both 240 μm.

Tables (6)

Tables Icon

Table 1 Several selected n and κ values that lead to the same reflectance at normal incidence (θi* = 0°) as the actual reflectance value of iron under 1.06 μm irradiation (n = 3.81, κ = 4.44). Bold faced cases are shown in Fig. 2 as blue lines.

Tables Icon

Table 2 Parameters used for the standard FDTD simulation of Sn

Tables Icon

Table 4 Parameters used for the standard FDTD simulation of Fe

Tables Icon

Table 3 Parameters used for the dispersive FDTD simulation of Sn

Tables Icon

Table 5 Parameters used for the dispersive FDTD simulation of Fe

Tables Icon

Table 6 Calculated reflectance values and errors for p-, s-, and circular polarized Gaussian beams irradiated on a half cylinder

Equations (12)

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R s = [ ncos θ i ] 2 + κ 2 [ n+cos θ i ] 2 + κ 2 ,
R p = [ n 1 cos θ i ] 2 + κ 2 [ n+ 1 cos θ i ] 2 + κ 2 ,
n ˜ =n+iκ,
n 2 = c 2 2 ( ( με ) 2 + ( μσλ 2πc ) 2 +με ),
κ 2 = c 2 2 ( ( με ) 2 + ( μσλ 2πc ) 2 με ),
με= a 1 and μσλ 2πc = a 2 .
n 2 = μ r ( ε 1 2 + ε 2 2 + ε 1 2 ),
κ 2 = μ r ( ε 1 2 + ε 2 2 ε 1 2 ),
ε ˜ r = ε 1 +i ε 2 =( ε ω p 2 ω 2 + γ p 2 )+i( ω p 2 γ p ω 3 +ω γ p 2 ),
ω= 2πc λ .
error= 0 π/2 [ R s,p * (θ) R s,p (θ) ] 2 dθ 0 π/2 [ R s,p (θ) ] 2 dθ .
R s,p * = 0 R s,p ( sin 1 ( r/ )) E 0 e (r/ r 0 ) 2 dr 0 E 0 e (r/ r 0 ) 2 dr ,

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