Abstract

We introduce a simple scattered field (SF) technique that enables finite difference time domain (FDTD) modeling of light scattering from dispersive objects residing in stratified dispersive media. The introduced SF technique is verified against the total field scattered field (TFSF) technique. As an application example, we study surface plasmon polariton enhanced light transmission through a 100nm wide slit in a silver film.

© 2010 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media,” IEEE Trans. Antenn. Propag. 14(3), 302–307 (1966).
    [CrossRef]
  2. A. Taflove, and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Second Edition, Artech House, INC., 2000).
  3. K. S. Kunz, and R. J. Luebbers, The Finite Difference Time Domain Method for Electromagnetics (CRC Press, London, 1993).
  4. S. Winton, P. Kosmas, and C. M. Rappaport, “FDTD simulation of TE and TM plane waves at nonzero incidence in arbitrary layered medium,” IEEE Trans. Antenn. Propag. 53(5), 1721–1728 (2005).
    [CrossRef]
  5. Y.-N. Jiang, D.-B. Ge, and S. J. Ding, “Analysis of TF-SF boundary for 2D-FDTD with plane p-wave propagation in layered dispersive and lossy media,” Prog. In Electromagnetic Res PIER 83, 157–172 (2008).
    [CrossRef]
  6. J. B. Schneider and K. Abdijalilov, “Analytic field propagation TFSF boundary for FDTD problems involving planar interfaces: PECs, TE, and TM,” IEEE Trans. Antenn. Propag. 54(9), 2531–2542 (2006).
    [CrossRef]
  7. K. Abdijalilov and J. B. Schneider, “Analytic field propagation TFSF boundary for FDTD problems involving planar interfaces: lossy material and evanescent fields,” IEEE Antennas Wirel. Propag. Lett. 5(1), 454–458 (2006).
    [CrossRef]
  8. K. Demarest, R. Plump, and Z. Huan, “FDTD modeling of scatterers in stratified medium,” IEEE Trans. Antenn. Propag. 43(10), 1164–1168 (1995).
    [CrossRef]
  9. S.-C. Kong, J. J. Simpson, and V. Backman, “ADE-FDTD scattered field formulation for dispersive materials,” IEEE Microwave Wireless Comp. Letters 18(1), 4–6 (2008).
    [CrossRef]
  10. M. Okoniewski, M. Mrozowski, and M. A. Stuchly, “Simple treatment of multi-term dispersion in FDTD,” IEEE Microwave Guided Wave Lett. 7(5), 121–123 (1997).
    [CrossRef]
  11. D. F. Kelley and R. J. Luebbers, “Piecewise linear recursive convolution for dispersive media using FDTD,” IEEE Trans. Antenn. Propag. 44(6), 792–797 (1996).
    [CrossRef]
  12. M. G. Moharam, D. A. Pommet, E. B. Grann, and T. K. Gaylord, “Stable implementation of the rigorous coupled-wave analysis for surface relief gratings: enhanced transmittance matrix approach,” J. Opt. Soc. Am. A 12, 1077–1086 (1995).
    [CrossRef]
  13. C.-T. Tai, Dyadic green functions in electromagnetic theory (Second Edition, IEEE Press, 1993).
  14. S. D. Gedney, “An anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices,” IEEE Trans. Antenn. Propag. 44(12), 1630–1639 (1996).
    [CrossRef]
  15. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev., B, Solid State 6(12), 4370–4379 (1972).

2008

Y.-N. Jiang, D.-B. Ge, and S. J. Ding, “Analysis of TF-SF boundary for 2D-FDTD with plane p-wave propagation in layered dispersive and lossy media,” Prog. In Electromagnetic Res PIER 83, 157–172 (2008).
[CrossRef]

S.-C. Kong, J. J. Simpson, and V. Backman, “ADE-FDTD scattered field formulation for dispersive materials,” IEEE Microwave Wireless Comp. Letters 18(1), 4–6 (2008).
[CrossRef]

2006

J. B. Schneider and K. Abdijalilov, “Analytic field propagation TFSF boundary for FDTD problems involving planar interfaces: PECs, TE, and TM,” IEEE Trans. Antenn. Propag. 54(9), 2531–2542 (2006).
[CrossRef]

K. Abdijalilov and J. B. Schneider, “Analytic field propagation TFSF boundary for FDTD problems involving planar interfaces: lossy material and evanescent fields,” IEEE Antennas Wirel. Propag. Lett. 5(1), 454–458 (2006).
[CrossRef]

2005

S. Winton, P. Kosmas, and C. M. Rappaport, “FDTD simulation of TE and TM plane waves at nonzero incidence in arbitrary layered medium,” IEEE Trans. Antenn. Propag. 53(5), 1721–1728 (2005).
[CrossRef]

1997

M. Okoniewski, M. Mrozowski, and M. A. Stuchly, “Simple treatment of multi-term dispersion in FDTD,” IEEE Microwave Guided Wave Lett. 7(5), 121–123 (1997).
[CrossRef]

1996

D. F. Kelley and R. J. Luebbers, “Piecewise linear recursive convolution for dispersive media using FDTD,” IEEE Trans. Antenn. Propag. 44(6), 792–797 (1996).
[CrossRef]

S. D. Gedney, “An anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices,” IEEE Trans. Antenn. Propag. 44(12), 1630–1639 (1996).
[CrossRef]

1995

1972

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev., B, Solid State 6(12), 4370–4379 (1972).

1966

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

Abdijalilov, K.

J. B. Schneider and K. Abdijalilov, “Analytic field propagation TFSF boundary for FDTD problems involving planar interfaces: PECs, TE, and TM,” IEEE Trans. Antenn. Propag. 54(9), 2531–2542 (2006).
[CrossRef]

K. Abdijalilov and J. B. Schneider, “Analytic field propagation TFSF boundary for FDTD problems involving planar interfaces: lossy material and evanescent fields,” IEEE Antennas Wirel. Propag. Lett. 5(1), 454–458 (2006).
[CrossRef]

Backman, V.

S.-C. Kong, J. J. Simpson, and V. Backman, “ADE-FDTD scattered field formulation for dispersive materials,” IEEE Microwave Wireless Comp. Letters 18(1), 4–6 (2008).
[CrossRef]

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev., B, Solid State 6(12), 4370–4379 (1972).

Demarest, K.

K. Demarest, R. Plump, and Z. Huan, “FDTD modeling of scatterers in stratified medium,” IEEE Trans. Antenn. Propag. 43(10), 1164–1168 (1995).
[CrossRef]

Ding, S. J.

Y.-N. Jiang, D.-B. Ge, and S. J. Ding, “Analysis of TF-SF boundary for 2D-FDTD with plane p-wave propagation in layered dispersive and lossy media,” Prog. In Electromagnetic Res PIER 83, 157–172 (2008).
[CrossRef]

Gaylord, T. K.

Ge, D.-B.

Y.-N. Jiang, D.-B. Ge, and S. J. Ding, “Analysis of TF-SF boundary for 2D-FDTD with plane p-wave propagation in layered dispersive and lossy media,” Prog. In Electromagnetic Res PIER 83, 157–172 (2008).
[CrossRef]

Gedney, S. D.

S. D. Gedney, “An anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices,” IEEE Trans. Antenn. Propag. 44(12), 1630–1639 (1996).
[CrossRef]

Grann, E. B.

Huan, Z.

K. Demarest, R. Plump, and Z. Huan, “FDTD modeling of scatterers in stratified medium,” IEEE Trans. Antenn. Propag. 43(10), 1164–1168 (1995).
[CrossRef]

Jiang, Y.-N.

Y.-N. Jiang, D.-B. Ge, and S. J. Ding, “Analysis of TF-SF boundary for 2D-FDTD with plane p-wave propagation in layered dispersive and lossy media,” Prog. In Electromagnetic Res PIER 83, 157–172 (2008).
[CrossRef]

Johnson, P. B.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev., B, Solid State 6(12), 4370–4379 (1972).

Kelley, D. F.

D. F. Kelley and R. J. Luebbers, “Piecewise linear recursive convolution for dispersive media using FDTD,” IEEE Trans. Antenn. Propag. 44(6), 792–797 (1996).
[CrossRef]

Kong, S.-C.

S.-C. Kong, J. J. Simpson, and V. Backman, “ADE-FDTD scattered field formulation for dispersive materials,” IEEE Microwave Wireless Comp. Letters 18(1), 4–6 (2008).
[CrossRef]

Kosmas, P.

S. Winton, P. Kosmas, and C. M. Rappaport, “FDTD simulation of TE and TM plane waves at nonzero incidence in arbitrary layered medium,” IEEE Trans. Antenn. Propag. 53(5), 1721–1728 (2005).
[CrossRef]

Luebbers, R. J.

D. F. Kelley and R. J. Luebbers, “Piecewise linear recursive convolution for dispersive media using FDTD,” IEEE Trans. Antenn. Propag. 44(6), 792–797 (1996).
[CrossRef]

Moharam, M. G.

Mrozowski, M.

M. Okoniewski, M. Mrozowski, and M. A. Stuchly, “Simple treatment of multi-term dispersion in FDTD,” IEEE Microwave Guided Wave Lett. 7(5), 121–123 (1997).
[CrossRef]

Okoniewski, M.

M. Okoniewski, M. Mrozowski, and M. A. Stuchly, “Simple treatment of multi-term dispersion in FDTD,” IEEE Microwave Guided Wave Lett. 7(5), 121–123 (1997).
[CrossRef]

Plump, R.

K. Demarest, R. Plump, and Z. Huan, “FDTD modeling of scatterers in stratified medium,” IEEE Trans. Antenn. Propag. 43(10), 1164–1168 (1995).
[CrossRef]

Pommet, D. A.

Rappaport, C. M.

S. Winton, P. Kosmas, and C. M. Rappaport, “FDTD simulation of TE and TM plane waves at nonzero incidence in arbitrary layered medium,” IEEE Trans. Antenn. Propag. 53(5), 1721–1728 (2005).
[CrossRef]

Schneider, J. B.

J. B. Schneider and K. Abdijalilov, “Analytic field propagation TFSF boundary for FDTD problems involving planar interfaces: PECs, TE, and TM,” IEEE Trans. Antenn. Propag. 54(9), 2531–2542 (2006).
[CrossRef]

K. Abdijalilov and J. B. Schneider, “Analytic field propagation TFSF boundary for FDTD problems involving planar interfaces: lossy material and evanescent fields,” IEEE Antennas Wirel. Propag. Lett. 5(1), 454–458 (2006).
[CrossRef]

Simpson, J. J.

S.-C. Kong, J. J. Simpson, and V. Backman, “ADE-FDTD scattered field formulation for dispersive materials,” IEEE Microwave Wireless Comp. Letters 18(1), 4–6 (2008).
[CrossRef]

Stuchly, M. A.

M. Okoniewski, M. Mrozowski, and M. A. Stuchly, “Simple treatment of multi-term dispersion in FDTD,” IEEE Microwave Guided Wave Lett. 7(5), 121–123 (1997).
[CrossRef]

Winton, S.

S. Winton, P. Kosmas, and C. M. Rappaport, “FDTD simulation of TE and TM plane waves at nonzero incidence in arbitrary layered medium,” IEEE Trans. Antenn. Propag. 53(5), 1721–1728 (2005).
[CrossRef]

Yee, K. S.

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

IEEE Antennas Wirel. Propag. Lett.

K. Abdijalilov and J. B. Schneider, “Analytic field propagation TFSF boundary for FDTD problems involving planar interfaces: lossy material and evanescent fields,” IEEE Antennas Wirel. Propag. Lett. 5(1), 454–458 (2006).
[CrossRef]

IEEE Microwave Guided Wave Lett.

M. Okoniewski, M. Mrozowski, and M. A. Stuchly, “Simple treatment of multi-term dispersion in FDTD,” IEEE Microwave Guided Wave Lett. 7(5), 121–123 (1997).
[CrossRef]

IEEE Microwave Wireless Comp. Letters

S.-C. Kong, J. J. Simpson, and V. Backman, “ADE-FDTD scattered field formulation for dispersive materials,” IEEE Microwave Wireless Comp. Letters 18(1), 4–6 (2008).
[CrossRef]

IEEE Trans. Antenn. Propag.

J. B. Schneider and K. Abdijalilov, “Analytic field propagation TFSF boundary for FDTD problems involving planar interfaces: PECs, TE, and TM,” IEEE Trans. Antenn. Propag. 54(9), 2531–2542 (2006).
[CrossRef]

K. Demarest, R. Plump, and Z. Huan, “FDTD modeling of scatterers in stratified medium,” IEEE Trans. Antenn. Propag. 43(10), 1164–1168 (1995).
[CrossRef]

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

S. Winton, P. Kosmas, and C. M. Rappaport, “FDTD simulation of TE and TM plane waves at nonzero incidence in arbitrary layered medium,” IEEE Trans. Antenn. Propag. 53(5), 1721–1728 (2005).
[CrossRef]

D. F. Kelley and R. J. Luebbers, “Piecewise linear recursive convolution for dispersive media using FDTD,” IEEE Trans. Antenn. Propag. 44(6), 792–797 (1996).
[CrossRef]

S. D. Gedney, “An anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices,” IEEE Trans. Antenn. Propag. 44(12), 1630–1639 (1996).
[CrossRef]

J. Opt. Soc. Am. A

Phys. Rev., B, Solid State

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev., B, Solid State 6(12), 4370–4379 (1972).

Prog. In Electromagnetic Res

Y.-N. Jiang, D.-B. Ge, and S. J. Ding, “Analysis of TF-SF boundary for 2D-FDTD with plane p-wave propagation in layered dispersive and lossy media,” Prog. In Electromagnetic Res PIER 83, 157–172 (2008).
[CrossRef]

Other

A. Taflove, and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Second Edition, Artech House, INC., 2000).

K. S. Kunz, and R. J. Luebbers, The Finite Difference Time Domain Method for Electromagnetics (CRC Press, London, 1993).

C.-T. Tai, Dyadic green functions in electromagnetic theory (Second Edition, IEEE Press, 1993).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

(a) Normalized transmission efficiency of a normally incident plane having free space wavelength of λ0 through a 100 nm wide (w) slit in a 200 nm thick (t) silver film as calculated by the SF and the TFSF technique. In the case (1), the slit is empty, whereas in the case (2), the slit contains a 80 nm diameter gold cylinder in the slit entrance as illustrated in the inset (2). These results were obtained with a square Yee cell size (Δ) of 5 nm. (b) Relative percentage error between the SF and the TFSF techniques as function of the λ0 in the case (1) for square Yee cell sizes of 10, 5, 2.5 and 1 nm. (c) The same as (b), but now a 80 nm diameter gold cylinder is located in the slit entrance.

Fig. 2
Fig. 2

(a) Reflectance of a TM polarized plane wave from the multilayer structure shown in the inset (t1 = 480 nm, t2 = 200 nm, n1 = 2.0, n2 = 1.5, nair = 1.0) as a function of the angle of incidence (θ) and the free space wavelength λ0. The plane wave is incident in the n1-medium. When θ = 53.7° and λ0 = 615 nm, the reflectance of the structure is practically zero and nearly all incident light is coupled to SPPs. At the studied wavelength range, transmittance through the structure is always zero due to the opaque silver film. (b) Amplitude of the electric field components in the studied structure at the SPP resonance angle and the wavelength. Incident electric field amplitude is 1.0 V/m in the n1-medium. The dashed black lines show the locations of the material interfaces of the studied structure.

Fig. 3
Fig. 3

The structure shown in the inset (n1 = 2.0, n2 = 1.5, t1 = 480nm, t2 = 200nm) is illuminated by a TM polarized (Hy, Ex, Ez) plane wave pulse at the SPP resonance angle (θ = 53.7°). The pulse shape of the illuminating magnetic field is given by Eq. (13) with τ = 1.6988 fs and f0 = c0/533.3nm. The green line shows the magnetic field amplitude of the illuminating field in the point P1, whereas the red line shows Hy in the point P2 at the surface of the silver film. Hy in the point P2 decays slowly to zero due to SPPs propagating along the silver film.

Fig. 4
Fig. 4

Normalized transmission efficiency of a TM polarized plane wave through a slit structure shown in the inset (n1 = 2.0, n2 = 1.5, t1 = 480nm, t2 = 200nm, w = 100nm) as a function of the free space wavelength λ0. The plane wave is incident in the n1-layer with the incidence angle of θ. When θ = 53.7° and λ0 = 615 nm, light transmission through the slit is enhanced due to the excitation of SPPs.

Equations (21)

Equations on this page are rendered with MathJax. Learn more.

E = E inc + E sca ,
H = H inc + H sca .
× E ( ω ) = j ω μ 0 H ( ω ) ,
× H ( ω ) = j ω ε ( ω ) E ( ω ) ,
× E inc ( ω ) = j ω μ 0 H inc ( ω ) ,
× H inc ( ω ) = j ω ε inc ( ω ) E inc ( ω ) ,
× E sca ( ω ) = j ω μ 0 H sca ( ω ) + ( j ω μ 0 H inc ( ω ) × E inc ( ω ) ) = 0 ,
× H sca ( ω ) = j ω ε ( ω ) E sca ( ω ) + S ( ω ) ,
S ( ω ) = j ω [ ε ( ω ) ε inc ( ω ) ] E inc ( ω ) .
× E sca ( t ) = μ 0 t H sca ( t ) ,
× H sca ( t ) = F 1 { j ω ε ( ω ) E sca ( ω ) } + S ( t ) ,
S ( t ) = F 1 { S ( ω ) } .
f ( t ) = exp [ ( t t 0 ) 2 / τ 2 ] sin ( 2 π f 0 ( t t 0 ) ) ,
S ( t k ) = Re { i = 0 N max S ( ω i ) exp [ j ω i t k ] } .
S ( t ) = F 1 { j ω ε ( ω ) E inc ( ω ) × H inc ( ω ) } .
( × H inc ( ω ) ) x | z = z 0 = ( H z , inc y = 0 H y , inc z ) | z = z 0 H y , inc ( z 0 + Δ z / 2 ) = 0 H y , inc ( z 0 Δ z / 2 ) Δ z = H y , inc ( z 0 Δ z / 2 ) Δ z ,
( × H inc ( ω ) ) y | z = z 0 = ( H x , inc z H z , i nc x = 0 ) | z = z 0 H x , inc ( z 0 + Δ z / 2 ) = 0 H x , inc ( z 0 Δ z / 2 ) Δ z = H x , inc ( z 0 Δ z / 2 ) Δ z ,
( × H inc ( ω ) ) z | z = z 0 = ( H y , inc x H x , inc y ) | z = z 0 ,
S x ( i , j + 1 / 2 , k 0 + 1 / 2 ) = H y , inc ( i , j + 1 / 2 , k 0 ) Δ z ,
S y ( i + 1 / 2 , j , k 0 + 1 / 2 ) = H x , inc ( i + 1 / 2 , j , k 0 ) Δ z .
ε r ( ω ) = ε + ( ε s ε ) ω 0 2 ω 0 2 + 2 j ω δ 0 ω 2 ,

Metrics