Abstract

We present an adjoint variable method for estimating the sensitivities of arbitrary responses with respect to the parameters of dispersive discontinuities in nanoplasmonic devices. Our theory is formulated in terms of the electric field components at the vicinity of perturbed discontinuities. The adjoint sensitivities are computed using at most one extra finite-difference time-domain (FDTD) simulation regardless of the number of parameters. Our approach is illustrated through the sensitivity analysis of an add–drop coupler consisting of a square ring resonator between two parallel waveguides. The computed adjoint sensitivities of the scattering parameters are compared with those obtained using the accurate but computationally expensive central finite difference approach.

© 2014 Optical Society of America

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    [CrossRef]
  6. C. Delacour, S. Blaize, P. Grosse, J. M. Fedeli, A. Bruyant, R. S. Montiel, G. Lerondel, and A. Chelnokov, Nano Lett. 10, 2922 (2010).
  7. N. K. Nikolova, H. W. Tam, and M. H. Bakr, IEEE Trans. Microwave Theor. Tech. 52, 1207 (2004).
    [CrossRef]
  8. M. A. Swillam, M. H. Bakr, N. K. Nikolova, and X. Li, Electromagnetics 27, 123 (2007).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  11. N. K. Nikolova, Y. Li, Y. Li, and M. H. Bakr, IEEE Trans. Microwave Theor. Tech. 54, 1598 (2006).
    [CrossRef]

2012 (1)

2010 (2)

J. Liu, G. Fang, H. Zhao, Y. Zhang, and S. Liu, J. Phys. D 43, 055103 (2010).
[CrossRef]

C. Delacour, S. Blaize, P. Grosse, J. M. Fedeli, A. Bruyant, R. S. Montiel, G. Lerondel, and A. Chelnokov, Nano Lett. 10, 2922 (2010).

2009 (2)

M. A. Alsunaidi and A. A. Al-Jabr, IEEE Photon. Technol. Lett. 21, 817 (2009).
[CrossRef]

C. Min and G. Veronis, Opt. Express 17, 10757 (2009).
[CrossRef]

2008 (1)

2007 (2)

G. Veronis and S. Fan, Opt. Express 15, 1211 (2007).
[CrossRef]

M. A. Swillam, M. H. Bakr, N. K. Nikolova, and X. Li, Electromagnetics 27, 123 (2007).
[CrossRef]

2006 (2)

M. G. Silveirinha and N. Engheta, Phys. Rev. Lett. 97, 157403 (2006).
[CrossRef]

N. K. Nikolova, Y. Li, Y. Li, and M. H. Bakr, IEEE Trans. Microwave Theor. Tech. 54, 1598 (2006).
[CrossRef]

2004 (1)

N. K. Nikolova, H. W. Tam, and M. H. Bakr, IEEE Trans. Microwave Theor. Tech. 52, 1207 (2004).
[CrossRef]

Ahmed, O. S.

Al-Jabr, A. A.

M. A. Alsunaidi and A. A. Al-Jabr, IEEE Photon. Technol. Lett. 21, 817 (2009).
[CrossRef]

Alsunaidi, M. A.

M. A. Alsunaidi and A. A. Al-Jabr, IEEE Photon. Technol. Lett. 21, 817 (2009).
[CrossRef]

Bakr, M. H.

O. S. Ahmed, M. H. Bakr, X. Li, and T. Nomura, Opt. Lett. 37, 3453 (2012).
[CrossRef]

M. A. Swillam, M. H. Bakr, N. K. Nikolova, and X. Li, Electromagnetics 27, 123 (2007).
[CrossRef]

N. K. Nikolova, Y. Li, Y. Li, and M. H. Bakr, IEEE Trans. Microwave Theor. Tech. 54, 1598 (2006).
[CrossRef]

N. K. Nikolova, H. W. Tam, and M. H. Bakr, IEEE Trans. Microwave Theor. Tech. 52, 1207 (2004).
[CrossRef]

Blaize, S.

C. Delacour, S. Blaize, P. Grosse, J. M. Fedeli, A. Bruyant, R. S. Montiel, G. Lerondel, and A. Chelnokov, Nano Lett. 10, 2922 (2010).

Bruyant, A.

C. Delacour, S. Blaize, P. Grosse, J. M. Fedeli, A. Bruyant, R. S. Montiel, G. Lerondel, and A. Chelnokov, Nano Lett. 10, 2922 (2010).

Chelnokov, A.

C. Delacour, S. Blaize, P. Grosse, J. M. Fedeli, A. Bruyant, R. S. Montiel, G. Lerondel, and A. Chelnokov, Nano Lett. 10, 2922 (2010).

Delacour, C.

C. Delacour, S. Blaize, P. Grosse, J. M. Fedeli, A. Bruyant, R. S. Montiel, G. Lerondel, and A. Chelnokov, Nano Lett. 10, 2922 (2010).

Engheta, N.

M. G. Silveirinha and N. Engheta, Phys. Rev. Lett. 97, 157403 (2006).
[CrossRef]

Fan, S.

Fang, G.

J. Liu, G. Fang, H. Zhao, Y. Zhang, and S. Liu, J. Phys. D 43, 055103 (2010).
[CrossRef]

Fedeli, J. M.

C. Delacour, S. Blaize, P. Grosse, J. M. Fedeli, A. Bruyant, R. S. Montiel, G. Lerondel, and A. Chelnokov, Nano Lett. 10, 2922 (2010).

Grosse, P.

C. Delacour, S. Blaize, P. Grosse, J. M. Fedeli, A. Bruyant, R. S. Montiel, G. Lerondel, and A. Chelnokov, Nano Lett. 10, 2922 (2010).

Lerondel, G.

C. Delacour, S. Blaize, P. Grosse, J. M. Fedeli, A. Bruyant, R. S. Montiel, G. Lerondel, and A. Chelnokov, Nano Lett. 10, 2922 (2010).

Li, X.

O. S. Ahmed, M. H. Bakr, X. Li, and T. Nomura, Opt. Lett. 37, 3453 (2012).
[CrossRef]

M. A. Swillam, M. H. Bakr, N. K. Nikolova, and X. Li, Electromagnetics 27, 123 (2007).
[CrossRef]

Li, Y.

N. K. Nikolova, Y. Li, Y. Li, and M. H. Bakr, IEEE Trans. Microwave Theor. Tech. 54, 1598 (2006).
[CrossRef]

N. K. Nikolova, Y. Li, Y. Li, and M. H. Bakr, IEEE Trans. Microwave Theor. Tech. 54, 1598 (2006).
[CrossRef]

Liu, J.

J. Liu, G. Fang, H. Zhao, Y. Zhang, and S. Liu, J. Phys. D 43, 055103 (2010).
[CrossRef]

Liu, S.

J. Liu, G. Fang, H. Zhao, Y. Zhang, and S. Liu, J. Phys. D 43, 055103 (2010).
[CrossRef]

Masanobu, H.

Masatoshi, N.

Min, C.

Montiel, R. S.

C. Delacour, S. Blaize, P. Grosse, J. M. Fedeli, A. Bruyant, R. S. Montiel, G. Lerondel, and A. Chelnokov, Nano Lett. 10, 2922 (2010).

Nikolova, N. K.

M. A. Swillam, M. H. Bakr, N. K. Nikolova, and X. Li, Electromagnetics 27, 123 (2007).
[CrossRef]

N. K. Nikolova, Y. Li, Y. Li, and M. H. Bakr, IEEE Trans. Microwave Theor. Tech. 54, 1598 (2006).
[CrossRef]

N. K. Nikolova, H. W. Tam, and M. H. Bakr, IEEE Trans. Microwave Theor. Tech. 52, 1207 (2004).
[CrossRef]

Nomura, T.

Silveirinha, M. G.

M. G. Silveirinha and N. Engheta, Phys. Rev. Lett. 97, 157403 (2006).
[CrossRef]

Swillam, M. A.

M. A. Swillam, M. H. Bakr, N. K. Nikolova, and X. Li, Electromagnetics 27, 123 (2007).
[CrossRef]

Tam, H. W.

N. K. Nikolova, H. W. Tam, and M. H. Bakr, IEEE Trans. Microwave Theor. Tech. 52, 1207 (2004).
[CrossRef]

Toshihiro, O.

Veronis, G.

Yosuku, M.

Zhang, Y.

J. Liu, G. Fang, H. Zhao, Y. Zhang, and S. Liu, J. Phys. D 43, 055103 (2010).
[CrossRef]

Zhao, H.

J. Liu, G. Fang, H. Zhao, Y. Zhang, and S. Liu, J. Phys. D 43, 055103 (2010).
[CrossRef]

Electromagnetics (1)

M. A. Swillam, M. H. Bakr, N. K. Nikolova, and X. Li, Electromagnetics 27, 123 (2007).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

M. A. Alsunaidi and A. A. Al-Jabr, IEEE Photon. Technol. Lett. 21, 817 (2009).
[CrossRef]

IEEE Trans. Microwave Theor. Tech. (2)

N. K. Nikolova, Y. Li, Y. Li, and M. H. Bakr, IEEE Trans. Microwave Theor. Tech. 54, 1598 (2006).
[CrossRef]

N. K. Nikolova, H. W. Tam, and M. H. Bakr, IEEE Trans. Microwave Theor. Tech. 52, 1207 (2004).
[CrossRef]

J. Phys. D (1)

J. Liu, G. Fang, H. Zhao, Y. Zhang, and S. Liu, J. Phys. D 43, 055103 (2010).
[CrossRef]

Nano Lett. (1)

C. Delacour, S. Blaize, P. Grosse, J. M. Fedeli, A. Bruyant, R. S. Montiel, G. Lerondel, and A. Chelnokov, Nano Lett. 10, 2922 (2010).

Opt. Express (3)

Opt. Lett. (1)

Phys. Rev. Lett. (1)

M. G. Silveirinha and N. Engheta, Phys. Rev. Lett. 97, 157403 (2006).
[CrossRef]

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Figures (7)

Fig. 1.
Fig. 1.

The add–drop coupler with a SRR. The colored region represents silver, while uncolored region is air.

Fig. 2.
Fig. 2.

Scattering parameters of the add–drop coupler.

Fig. 3.
Fig. 3.

Adjoint sensitivities of the scattering parameters with respect to the edge p1 as compared to central finite differences.

Fig. 4.
Fig. 4.

Adjoint sensitivities of the scattering parameters with respect to the edge p2 as compared to central finite differences.

Fig. 5.
Fig. 5.

Adjoint sensitivities of the scattering parameters with respect to the edge p3 as compared to central finite differences.

Fig. 6.
Fig. 6.

Adjoint sensitivities of the scattering parameters with respect to the edge p5 as compared to central finite differences.

Fig. 7.
Fig. 7.

Adjoint sensitivities of the scattering parameters with respect to the edge p8 as compared to central finite differences.

Equations (19)

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

F(e,p)=0TmaxΩψ(e,p)dΩdt,
Fpi=eFpi+0Tmaxψeepidt,
Ke+Me=q.
Mj(f)=c2f+c1f+c0f+g*f,
g*f=0tf(τ)g(tτ)dτ.
K(e+Δe)+(M+ΔM)(e+Δe)=q.
KΔe+MΔerwithr=ΔM·e.
rj=Δc2E+Δc1E+Δc0E+Δg*E.
0Tmaxe^T·(KΔe)dt+0Tmaxe^T·(MΔe)dt=0Tmaxe^T·rdt.
0Tmaxe^T·(MΔe)dt=0TmaxΔeT·(M^e^)dt,
M^j(f)=c2fc1f+c0f+g*¯f.
g*¯f=tTmaxf(τ)g(τt)dτ.
0Tmax(Ke^+M^e^)TΔedt=0Tmaxe^T·rdt.
Fpi=eFpi1pi0Tmaxe^T·rdt.
Ke^+M^e^=q^andq^=ψe.
D(s)=εE(s)+εpωp2s2vcsE(s),
D=εE+εpωp2E+εpωp2vcexp(vct)u(t)*E,
c2=εc0=εpωp2g=c0vcexp(vct)u(t).
ψ(t)=e(t)·emexp(jω0t)/ψ0(ω0),

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