Abstract

The frequency dependent dielectric permittivity of dispersive materials is commonly modeled as a rational polynomial based on multiple Debye, Drude, or Lorentz terms in the finite-difference time-domain (FDTD) method. We identify a simple effective model in which dielectric polarization depends both on the electric field and its first time derivative. This enables nearly exact FDTD simulation of light propagation and absorption in silicon in the spectral range of 300–1000 nm. Numerical precision of our model is demonstrated for Mie scattering from a silicon sphere and solar absorption in a silicon nanowire photonic crystal.

© 2012 Optical Society of America

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References

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2011

A. Vial, T. Laroche, M. Dridi, and L. Le Cunff, Appl. Phys. A 103, 849 (2011).
[CrossRef]

L. J. Prokopeva, J. D. Borneman, and A. V. Kildishev, IEEE Trans. Magn. 47, 1150 (2011).
[CrossRef]

A. Deinega and I. Valuev, Comput. Phys. Commun. 182, 149 (2011).
[CrossRef]

A. Deinega, I. Valuev, B. Potapkin, and Yu. Lozovik, J. Opt. Soc. Am. A 28, 770 (2011).
[CrossRef]

2010

2009

2008

2007

A. Deinega and I. Valuev, Opt. Lett. 32, 3429 (2007).
[CrossRef]

L. Hu and G. Chen, Nano Lett. 7, 3249 (2007).
[CrossRef]

A. Vial, J. Opt. A 9, 745 (2007).
[CrossRef]

2006

P. G. Etchegoin, E. C. Le Ru, and M. Meyer, J. Chem. Phys. 125, 164705 (2006).
[CrossRef]

2003

S. Liu, N. Yuan, and J. Mo, IEEE Microw. Wireless Compon. Lett. 13, 187 (2003).
[CrossRef]

2002

J. A. Pereda, A. Vegas, and A. Prieto, IEEE Trans. Microwave Theory Tech. 50, 1689 (2002).
[CrossRef]

1998

J. Leng, J. Opsal, H. Chu, M. Senko, and D. E. Aspnes, Thin Solid Films 313–314, 132 (1998).
[CrossRef]

1997

1995

M. A. Green and M. Keevers, Progr. Photovol. 3, 189 (1995).
[CrossRef]

Aspnes, D. E.

J. Leng, J. Opsal, H. Chu, M. Senko, and D. E. Aspnes, Thin Solid Films 313–314, 132 (1998).
[CrossRef]

Belousov, S.

Borneman, J. D.

L. J. Prokopeva, J. D. Borneman, and A. V. Kildishev, IEEE Trans. Magn. 47, 1150 (2011).
[CrossRef]

Chang, Y.

J. Lu and Y. Chang, Superlattices Microstruct. 47, 60 (2010).
[CrossRef]

Chen, G.

L. Hu and G. Chen, Nano Lett. 7, 3249 (2007).
[CrossRef]

Chu, H.

J. Leng, J. Opsal, H. Chu, M. Senko, and D. E. Aspnes, Thin Solid Films 313–314, 132 (1998).
[CrossRef]

Commandre, M.

Deinega, A.

Demesy, G.

Dridi, M.

A. Vial, T. Laroche, M. Dridi, and L. Le Cunff, Appl. Phys. A 103, 849 (2011).
[CrossRef]

Etchegoin, P. G.

P. G. Etchegoin, E. C. Le Ru, and M. Meyer, J. Chem. Phys. 125, 164705 (2006).
[CrossRef]

Fichtner, W.

Green, M. A.

M. A. Green and M. Keevers, Progr. Photovol. 3, 189 (1995).
[CrossRef]

Hagness, S. H.

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

Hao, Y.

Y. Hao and R. Mittra, FDTD Modeling of Metamaterials: Theory and Applications (Artech House, 2009).

Hu, L.

L. Hu and G. Chen, Nano Lett. 7, 3249 (2007).
[CrossRef]

Keevers, M.

M. A. Green and M. Keevers, Progr. Photovol. 3, 189 (1995).
[CrossRef]

Kildishev, A. V.

L. J. Prokopeva, J. D. Borneman, and A. V. Kildishev, IEEE Trans. Magn. 47, 1150 (2011).
[CrossRef]

Korner, T. O.

Laroche, T.

A. Vial, T. Laroche, M. Dridi, and L. Le Cunff, Appl. Phys. A 103, 849 (2011).
[CrossRef]

Le Cunff, L.

A. Vial, T. Laroche, M. Dridi, and L. Le Cunff, Appl. Phys. A 103, 849 (2011).
[CrossRef]

Le Ru, E. C.

P. G. Etchegoin, E. C. Le Ru, and M. Meyer, J. Chem. Phys. 125, 164705 (2006).
[CrossRef]

Leng, J.

J. Leng, J. Opsal, H. Chu, M. Senko, and D. E. Aspnes, Thin Solid Films 313–314, 132 (1998).
[CrossRef]

Liu, S.

S. Liu, N. Yuan, and J. Mo, IEEE Microw. Wireless Compon. Lett. 13, 187 (2003).
[CrossRef]

Lozovik, Yu.

Lu, J.

J. Lu and Y. Chang, Superlattices Microstruct. 47, 60 (2010).
[CrossRef]

Meyer, M.

P. G. Etchegoin, E. C. Le Ru, and M. Meyer, J. Chem. Phys. 125, 164705 (2006).
[CrossRef]

Mittra, R.

Y. Hao and R. Mittra, FDTD Modeling of Metamaterials: Theory and Applications (Artech House, 2009).

Mo, J.

S. Liu, N. Yuan, and J. Mo, IEEE Microw. Wireless Compon. Lett. 13, 187 (2003).
[CrossRef]

Nicolet, A.

Opsal, J.

J. Leng, J. Opsal, H. Chu, M. Senko, and D. E. Aspnes, Thin Solid Films 313–314, 132 (1998).
[CrossRef]

Pereda, J. A.

J. A. Pereda, A. Vegas, and A. Prieto, IEEE Trans. Microwave Theory Tech. 50, 1689 (2002).
[CrossRef]

Potapkin, B.

Prieto, A.

J. A. Pereda, A. Vegas, and A. Prieto, IEEE Trans. Microwave Theory Tech. 50, 1689 (2002).
[CrossRef]

Prokopeva, L. J.

L. J. Prokopeva, J. D. Borneman, and A. V. Kildishev, IEEE Trans. Magn. 47, 1150 (2011).
[CrossRef]

Senko, M.

J. Leng, J. Opsal, H. Chu, M. Senko, and D. E. Aspnes, Thin Solid Films 313–314, 132 (1998).
[CrossRef]

Taflove, A.

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

Valuev, I.

Vegas, A.

J. A. Pereda, A. Vegas, and A. Prieto, IEEE Trans. Microwave Theory Tech. 50, 1689 (2002).
[CrossRef]

Vial, A.

A. Vial, T. Laroche, M. Dridi, and L. Le Cunff, Appl. Phys. A 103, 849 (2011).
[CrossRef]

A. Vial, J. Opt. A 9, 745 (2007).
[CrossRef]

Yuan, N.

S. Liu, N. Yuan, and J. Mo, IEEE Microw. Wireless Compon. Lett. 13, 187 (2003).
[CrossRef]

Zolla, F.

Appl. Phys. A

A. Vial, T. Laroche, M. Dridi, and L. Le Cunff, Appl. Phys. A 103, 849 (2011).
[CrossRef]

Comput. Phys. Commun.

A. Deinega and I. Valuev, Comput. Phys. Commun. 182, 149 (2011).
[CrossRef]

IEEE Microw. Wireless Compon. Lett.

S. Liu, N. Yuan, and J. Mo, IEEE Microw. Wireless Compon. Lett. 13, 187 (2003).
[CrossRef]

IEEE Trans. Magn.

L. J. Prokopeva, J. D. Borneman, and A. V. Kildishev, IEEE Trans. Magn. 47, 1150 (2011).
[CrossRef]

IEEE Trans. Microwave Theory Tech.

J. A. Pereda, A. Vegas, and A. Prieto, IEEE Trans. Microwave Theory Tech. 50, 1689 (2002).
[CrossRef]

J. Chem. Phys.

P. G. Etchegoin, E. C. Le Ru, and M. Meyer, J. Chem. Phys. 125, 164705 (2006).
[CrossRef]

J. Opt. A

A. Vial, J. Opt. A 9, 745 (2007).
[CrossRef]

J. Opt. Soc. Am. A

Nano Lett.

L. Hu and G. Chen, Nano Lett. 7, 3249 (2007).
[CrossRef]

Opt. Lett.

Progr. Photovol.

M. A. Green and M. Keevers, Progr. Photovol. 3, 189 (1995).
[CrossRef]

Superlattices Microstruct.

J. Lu and Y. Chang, Superlattices Microstruct. 47, 60 (2010).
[CrossRef]

Thin Solid Films

J. Leng, J. Opsal, H. Chu, M. Senko, and D. E. Aspnes, Thin Solid Films 313–314, 132 (1998).
[CrossRef]

Other

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

Y. Hao and R. Mittra, FDTD Modeling of Metamaterials: Theory and Applications (Artech House, 2009).

Electromagnetic Template Library, http://kintechlab.com .

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Figures (3)

Fig. 1.
Fig. 1.

Real and imaginary components of the silicon dielectric permittivity: comparison of the experimental data (dots) with fitting by two terms of the type (3) (curve).

Fig. 2.
Fig. 2.

Comparison of scattering Qsca of a silicon sphere with radius R=150nm for FDTD and exact Mie solution. Inset: scheme of FDTD simulation geometry.

Fig. 3.
Fig. 3.

Comparison of absorption of silicon nanowires packed in square lattice (lattice period a=100nm. The nanowire’s diameter is d=50nm and length is L=2.33μm) for FDTD, the finite element method, and the transfer matrix method. Inset: scheme of the FDTD simulation geometry; 1—generating (TF/SF) border; 2, 2—detector arrays for reflected and transmitted signals; 3—periodic cell of nanowires array.

Equations (18)

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ε(ω)=ε+p=1Pεp(ω),
εp(ω)=ap,0+ap,1(iω)bp,0+bp,1(iω)bp,2ω2,
εp(ω)=Δε(ωp2iγpω)ωp22iωγpω2
×H⃗=εddtE⃗+σE⃗+pJ⃗p,
J⃗p=iωεp(ω)E⃗.
J⃗p(ω)=iωΔε(ωp2iγpω)ωp22iωγpω2E⃗(ω).
(ωp22iωγpω2)J⃗p(ω)=Δε(ωp2iγpω)·(iω)E⃗(ω)
ωp2J⃗p+2ddtγpJ⃗p+d2dt2J⃗p=Δεωp2ddtE⃗+Δεγpd2dt2E⃗.
ωp2J⃗pn+2γpJ⃗pn+1J⃗pn12Δt+J⃗pn+12J⃗pn+J⃗pn1(Δt)2=Δεpωp2E⃗n+1E⃗n12Δt+ΔεpγpE⃗n+12E⃗n+E⃗n1(Δt)2.
J⃗pn+1=αpJ⃗pn+ξpJ⃗pn1+ζp+E⃗n+1+ζpE⃗n1+ζpE⃗nΔt,
αp=2ωp2(Δt)2γpΔt+1,ξp=γpΔt1γpΔt+1,
ζp±=ΔεpΔt(±ωp2Δt/2+γp)γpΔt+1,ζp=2ΔεpγpΔtγpΔt+1.
×H⃗n+1/2=εE⃗n+1`E⃗nΔt+σE⃗n+1+E⃗n2+pJ⃗pn+1/2,
J⃗pn+1/2=12(J⃗pn+J⃗pn+1)=1+αp2J⃗pn+ξp2J⃗pn1+ζp+E⃗n+1+ζpE⃗n1+ζpE⃗n2Δt.
E⃗n+1=C1E⃗n1+C2E⃗n+C3{×H⃗n+1/212p[(1+αp)J⃗pn+ξpJ⃗pn1]},
C1=pζp2ε+σΔt+pζp+,
C2=2εσΔtpζp2ε+σΔt+pζp+,
C3=2Δt2ε+σΔt+pζp+.

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