Abstract

We present, for the first time, an adjoint variable method (AVM) for wideband sensitivity analysis of dispersive materials. The time domain transmission line modeling technique is exploited to calculate the response and its sensitivities with respect to all the designable parameters using at most one extra simulation. A z-domain representation of dispersive materials is utilized in the derivation of this technique. Our approach is illustrated through sensitivity analysis of a two-dimensional teeth-shaped plasmonic resonator. The AVM sensitivities are compared with the accurate and expensive finite difference approach and good agreement is achieved. This theory can be extended to other dispersive materials and dispersive metamaterials as well.

© 2012 Optical Society of America

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  1. E. Ozbay, Science 311, 189 (2006).
    [CrossRef]
  2. M. E. Stewart, C. R. Anderton, L. B. Thompson, J. Maria, S. K. Gray, J. A. Rogers, and R. G. Nuzzo, Chem. Rev. 108, 494 (2008).
    [CrossRef]
  3. W. L. Barnes, A. Dereux, and T. W. Ebbesen, Nature 424, 824 (2003).
    [CrossRef]
  4. V. E. Ferry, L. A. Sweatlock, D. Pacifici, and H. A. Atwater, Nano Lett. 8, 4391 (2008).
    [CrossRef]
  5. L. de Menezes and W. J. R. Hoefer, IEEE Trans. Microw. Theory Technol. 44, 854 (1996).
    [CrossRef]
  6. M. H. Bakr and N. K. Nikolova, IEEE Trans. Microw. Theory Technol. 52, 554 (2004).
    [CrossRef]
  7. S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).
  8. X.-S. Lin and X.-G. Huang, Opt. Lett. 33, 2874 (2008).
    [CrossRef]
  9. O. S. Ahmed, M. A. Swillam, M. H. Bakr, and X. Li, Opt. Express 18, 21784 (2010).
    [CrossRef]
  10. J. Paul, C. Christopoulos, and D. W. P. Thomas, IEEE Trans. Antennas Propag. 47, 1528 (1999).
    [CrossRef]

2010

2008

M. E. Stewart, C. R. Anderton, L. B. Thompson, J. Maria, S. K. Gray, J. A. Rogers, and R. G. Nuzzo, Chem. Rev. 108, 494 (2008).
[CrossRef]

V. E. Ferry, L. A. Sweatlock, D. Pacifici, and H. A. Atwater, Nano Lett. 8, 4391 (2008).
[CrossRef]

X.-S. Lin and X.-G. Huang, Opt. Lett. 33, 2874 (2008).
[CrossRef]

2006

E. Ozbay, Science 311, 189 (2006).
[CrossRef]

2004

M. H. Bakr and N. K. Nikolova, IEEE Trans. Microw. Theory Technol. 52, 554 (2004).
[CrossRef]

2003

W. L. Barnes, A. Dereux, and T. W. Ebbesen, Nature 424, 824 (2003).
[CrossRef]

1999

J. Paul, C. Christopoulos, and D. W. P. Thomas, IEEE Trans. Antennas Propag. 47, 1528 (1999).
[CrossRef]

1996

L. de Menezes and W. J. R. Hoefer, IEEE Trans. Microw. Theory Technol. 44, 854 (1996).
[CrossRef]

Ahmed, O. S.

Anderton, C. R.

M. E. Stewart, C. R. Anderton, L. B. Thompson, J. Maria, S. K. Gray, J. A. Rogers, and R. G. Nuzzo, Chem. Rev. 108, 494 (2008).
[CrossRef]

Atwater, H. A.

V. E. Ferry, L. A. Sweatlock, D. Pacifici, and H. A. Atwater, Nano Lett. 8, 4391 (2008).
[CrossRef]

Bakr, M. H.

O. S. Ahmed, M. A. Swillam, M. H. Bakr, and X. Li, Opt. Express 18, 21784 (2010).
[CrossRef]

M. H. Bakr and N. K. Nikolova, IEEE Trans. Microw. Theory Technol. 52, 554 (2004).
[CrossRef]

Barnes, W. L.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, Nature 424, 824 (2003).
[CrossRef]

Christopoulos, C.

J. Paul, C. Christopoulos, and D. W. P. Thomas, IEEE Trans. Antennas Propag. 47, 1528 (1999).
[CrossRef]

de Menezes, L.

L. de Menezes and W. J. R. Hoefer, IEEE Trans. Microw. Theory Technol. 44, 854 (1996).
[CrossRef]

Dereux, A.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, Nature 424, 824 (2003).
[CrossRef]

Ebbesen, T. W.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, Nature 424, 824 (2003).
[CrossRef]

Ferry, V. E.

V. E. Ferry, L. A. Sweatlock, D. Pacifici, and H. A. Atwater, Nano Lett. 8, 4391 (2008).
[CrossRef]

Gray, S. K.

M. E. Stewart, C. R. Anderton, L. B. Thompson, J. Maria, S. K. Gray, J. A. Rogers, and R. G. Nuzzo, Chem. Rev. 108, 494 (2008).
[CrossRef]

Hoefer, W. J. R.

L. de Menezes and W. J. R. Hoefer, IEEE Trans. Microw. Theory Technol. 44, 854 (1996).
[CrossRef]

Huang, X.-G.

Li, X.

Lin, X.-S.

Maier, S. A.

S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).

Maria, J.

M. E. Stewart, C. R. Anderton, L. B. Thompson, J. Maria, S. K. Gray, J. A. Rogers, and R. G. Nuzzo, Chem. Rev. 108, 494 (2008).
[CrossRef]

Nikolova, N. K.

M. H. Bakr and N. K. Nikolova, IEEE Trans. Microw. Theory Technol. 52, 554 (2004).
[CrossRef]

Nuzzo, R. G.

M. E. Stewart, C. R. Anderton, L. B. Thompson, J. Maria, S. K. Gray, J. A. Rogers, and R. G. Nuzzo, Chem. Rev. 108, 494 (2008).
[CrossRef]

Ozbay, E.

E. Ozbay, Science 311, 189 (2006).
[CrossRef]

Pacifici, D.

V. E. Ferry, L. A. Sweatlock, D. Pacifici, and H. A. Atwater, Nano Lett. 8, 4391 (2008).
[CrossRef]

Paul, J.

J. Paul, C. Christopoulos, and D. W. P. Thomas, IEEE Trans. Antennas Propag. 47, 1528 (1999).
[CrossRef]

Rogers, J. A.

M. E. Stewart, C. R. Anderton, L. B. Thompson, J. Maria, S. K. Gray, J. A. Rogers, and R. G. Nuzzo, Chem. Rev. 108, 494 (2008).
[CrossRef]

Stewart, M. E.

M. E. Stewart, C. R. Anderton, L. B. Thompson, J. Maria, S. K. Gray, J. A. Rogers, and R. G. Nuzzo, Chem. Rev. 108, 494 (2008).
[CrossRef]

Sweatlock, L. A.

V. E. Ferry, L. A. Sweatlock, D. Pacifici, and H. A. Atwater, Nano Lett. 8, 4391 (2008).
[CrossRef]

Swillam, M. A.

Thomas, D. W. P.

J. Paul, C. Christopoulos, and D. W. P. Thomas, IEEE Trans. Antennas Propag. 47, 1528 (1999).
[CrossRef]

Thompson, L. B.

M. E. Stewart, C. R. Anderton, L. B. Thompson, J. Maria, S. K. Gray, J. A. Rogers, and R. G. Nuzzo, Chem. Rev. 108, 494 (2008).
[CrossRef]

Chem. Rev.

M. E. Stewart, C. R. Anderton, L. B. Thompson, J. Maria, S. K. Gray, J. A. Rogers, and R. G. Nuzzo, Chem. Rev. 108, 494 (2008).
[CrossRef]

IEEE Trans. Antennas Propag.

J. Paul, C. Christopoulos, and D. W. P. Thomas, IEEE Trans. Antennas Propag. 47, 1528 (1999).
[CrossRef]

IEEE Trans. Microw. Theory Technol.

L. de Menezes and W. J. R. Hoefer, IEEE Trans. Microw. Theory Technol. 44, 854 (1996).
[CrossRef]

M. H. Bakr and N. K. Nikolova, IEEE Trans. Microw. Theory Technol. 52, 554 (2004).
[CrossRef]

Nano Lett.

V. E. Ferry, L. A. Sweatlock, D. Pacifici, and H. A. Atwater, Nano Lett. 8, 4391 (2008).
[CrossRef]

Nature

W. L. Barnes, A. Dereux, and T. W. Ebbesen, Nature 424, 824 (2003).
[CrossRef]

Opt. Express

Opt. Lett.

Science

E. Ozbay, Science 311, 189 (2006).
[CrossRef]

Other

S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).

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Figures (3)

Fig. 1.
Fig. 1.

Teeth-shaped plasmonic resonator.

Fig. 2.
Fig. 2.

Sensitivity calculation of the scattering parameter |S11| to the teeth widths and thicknesses using AVM is compared to the expensive finite difference approach.

Fig. 3.
Fig. 3.

Sensitivity calculation of the scattering parameter |S11| to w1 using FFD, CFD, BFD, and AVM.

Equations (8)

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

Tj=[tex0tez0tmy]j,
Vx=texVxex=2Vxex[4+gex(z)+4(1z11+z1)χex(z)].
ge(z)=ge01z1βc,
[FSe]=Uj[Fexz1Se]=[U11(p)U12(p)U21(p)U22(p)][Fexz1Se],
Xk+1=Q(WUWexJ)Xk+Xks,
F=0Tmψ(p,X)dt.
Fpi=Δtjkλj,kTQjηj,ki,
λk1=(WUTWexJ)QTλkλks,λ(Tm)=0.

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