Abstract

We present a new method for sensitivity analysis of photonic crystal devices. The algorithm is based on a finite-difference frequency-domain model and uses the adjoint variable method and perturbation theory techniques. We show that our method is highly efficient and accurate and can be applied to calculation of the sensitivity of transmission parameters of resonant nanophotonic devices.

© 2004 Optical Society of America

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  1. K.-C. Kwan, X. Zhang, Z.-Q. Zhang, and C. T. Chan, Appl. Phys. Lett. 82, 4414 (2003).
    [CrossRef]
  2. A. Chutinan and S. Noda, J. Opt. Soc. Am. B 16, 240 (1999).
    [CrossRef]
  3. Z.-Y. Li and Z.-Q. Zhang, Phys. Rev. B 62, 1516 (2000).
    [CrossRef]
  4. A. A. Asatryan, P. A. Robinson, L. C. Botten, R. C. McPhedran, N. A. Nicorovici, and C. M. de Sterke, Phys. Rev. E 62, 5711 (2000).
    [CrossRef]
  5. S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, J. Appl. Phys. 78, 1415 (1995).
    [CrossRef]
  6. N. K. Georgieva, S. Glavic, M. H. Bakr, and J. W. Bandler, IEEE Trans. Microwave Theory Tech. 50, 2751 (2002).
    [CrossRef]
  7. S. D. Wu and E. N. Glytsis, J. Opt. Soc. Am. A 19, 2018 (2002).
    [CrossRef]
  8. J. Jin, The Finite Element Method in Electromagnetics (Wiley, New York, 2002).
  9. S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, Phys. Rev. E 65, 066611 (2002).
    [CrossRef]
  10. S. G. Johnson, S. Fan, A. Mekis, and J. D. Joannopoulos, Appl. Phys. Lett. 78, 3388 (2001).
    [CrossRef]

2003 (1)

K.-C. Kwan, X. Zhang, Z.-Q. Zhang, and C. T. Chan, Appl. Phys. Lett. 82, 4414 (2003).
[CrossRef]

2002 (3)

N. K. Georgieva, S. Glavic, M. H. Bakr, and J. W. Bandler, IEEE Trans. Microwave Theory Tech. 50, 2751 (2002).
[CrossRef]

S. D. Wu and E. N. Glytsis, J. Opt. Soc. Am. A 19, 2018 (2002).
[CrossRef]

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, Phys. Rev. E 65, 066611 (2002).
[CrossRef]

2001 (1)

S. G. Johnson, S. Fan, A. Mekis, and J. D. Joannopoulos, Appl. Phys. Lett. 78, 3388 (2001).
[CrossRef]

2000 (2)

Z.-Y. Li and Z.-Q. Zhang, Phys. Rev. B 62, 1516 (2000).
[CrossRef]

A. A. Asatryan, P. A. Robinson, L. C. Botten, R. C. McPhedran, N. A. Nicorovici, and C. M. de Sterke, Phys. Rev. E 62, 5711 (2000).
[CrossRef]

1999 (1)

1995 (1)

S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, J. Appl. Phys. 78, 1415 (1995).
[CrossRef]

Asatryan, A. A.

A. A. Asatryan, P. A. Robinson, L. C. Botten, R. C. McPhedran, N. A. Nicorovici, and C. M. de Sterke, Phys. Rev. E 62, 5711 (2000).
[CrossRef]

Bakr, M. H.

N. K. Georgieva, S. Glavic, M. H. Bakr, and J. W. Bandler, IEEE Trans. Microwave Theory Tech. 50, 2751 (2002).
[CrossRef]

Bandler, J. W.

N. K. Georgieva, S. Glavic, M. H. Bakr, and J. W. Bandler, IEEE Trans. Microwave Theory Tech. 50, 2751 (2002).
[CrossRef]

Botten, L. C.

A. A. Asatryan, P. A. Robinson, L. C. Botten, R. C. McPhedran, N. A. Nicorovici, and C. M. de Sterke, Phys. Rev. E 62, 5711 (2000).
[CrossRef]

Chan, C. T.

K.-C. Kwan, X. Zhang, Z.-Q. Zhang, and C. T. Chan, Appl. Phys. Lett. 82, 4414 (2003).
[CrossRef]

Chutinan, A.

de Sterke, C. M.

A. A. Asatryan, P. A. Robinson, L. C. Botten, R. C. McPhedran, N. A. Nicorovici, and C. M. de Sterke, Phys. Rev. E 62, 5711 (2000).
[CrossRef]

Fan, S.

S. G. Johnson, S. Fan, A. Mekis, and J. D. Joannopoulos, Appl. Phys. Lett. 78, 3388 (2001).
[CrossRef]

S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, J. Appl. Phys. 78, 1415 (1995).
[CrossRef]

Fink, Y.

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, Phys. Rev. E 65, 066611 (2002).
[CrossRef]

Georgieva, N. K.

N. K. Georgieva, S. Glavic, M. H. Bakr, and J. W. Bandler, IEEE Trans. Microwave Theory Tech. 50, 2751 (2002).
[CrossRef]

Glavic, S.

N. K. Georgieva, S. Glavic, M. H. Bakr, and J. W. Bandler, IEEE Trans. Microwave Theory Tech. 50, 2751 (2002).
[CrossRef]

Glytsis, E. N.

Ibanescu, M.

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, Phys. Rev. E 65, 066611 (2002).
[CrossRef]

Jin, J.

J. Jin, The Finite Element Method in Electromagnetics (Wiley, New York, 2002).

Joannopoulos, J. D.

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, Phys. Rev. E 65, 066611 (2002).
[CrossRef]

S. G. Johnson, S. Fan, A. Mekis, and J. D. Joannopoulos, Appl. Phys. Lett. 78, 3388 (2001).
[CrossRef]

S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, J. Appl. Phys. 78, 1415 (1995).
[CrossRef]

Johnson, S. G.

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, Phys. Rev. E 65, 066611 (2002).
[CrossRef]

S. G. Johnson, S. Fan, A. Mekis, and J. D. Joannopoulos, Appl. Phys. Lett. 78, 3388 (2001).
[CrossRef]

Kwan, K.-C.

K.-C. Kwan, X. Zhang, Z.-Q. Zhang, and C. T. Chan, Appl. Phys. Lett. 82, 4414 (2003).
[CrossRef]

Li, Z.-Y.

Z.-Y. Li and Z.-Q. Zhang, Phys. Rev. B 62, 1516 (2000).
[CrossRef]

McPhedran, R. C.

A. A. Asatryan, P. A. Robinson, L. C. Botten, R. C. McPhedran, N. A. Nicorovici, and C. M. de Sterke, Phys. Rev. E 62, 5711 (2000).
[CrossRef]

Mekis, A.

S. G. Johnson, S. Fan, A. Mekis, and J. D. Joannopoulos, Appl. Phys. Lett. 78, 3388 (2001).
[CrossRef]

Nicorovici, N. A.

A. A. Asatryan, P. A. Robinson, L. C. Botten, R. C. McPhedran, N. A. Nicorovici, and C. M. de Sterke, Phys. Rev. E 62, 5711 (2000).
[CrossRef]

Noda, S.

Robinson, P. A.

A. A. Asatryan, P. A. Robinson, L. C. Botten, R. C. McPhedran, N. A. Nicorovici, and C. M. de Sterke, Phys. Rev. E 62, 5711 (2000).
[CrossRef]

Skorobogatiy, M. A.

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, Phys. Rev. E 65, 066611 (2002).
[CrossRef]

Villeneuve, P. R.

S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, J. Appl. Phys. 78, 1415 (1995).
[CrossRef]

Weisberg, O.

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, Phys. Rev. E 65, 066611 (2002).
[CrossRef]

Wu, S. D.

Zhang, X.

K.-C. Kwan, X. Zhang, Z.-Q. Zhang, and C. T. Chan, Appl. Phys. Lett. 82, 4414 (2003).
[CrossRef]

Zhang, Z.-Q.

K.-C. Kwan, X. Zhang, Z.-Q. Zhang, and C. T. Chan, Appl. Phys. Lett. 82, 4414 (2003).
[CrossRef]

Z.-Y. Li and Z.-Q. Zhang, Phys. Rev. B 62, 1516 (2000).
[CrossRef]

Appl. Phys. Lett. (2)

K.-C. Kwan, X. Zhang, Z.-Q. Zhang, and C. T. Chan, Appl. Phys. Lett. 82, 4414 (2003).
[CrossRef]

S. G. Johnson, S. Fan, A. Mekis, and J. D. Joannopoulos, Appl. Phys. Lett. 78, 3388 (2001).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

N. K. Georgieva, S. Glavic, M. H. Bakr, and J. W. Bandler, IEEE Trans. Microwave Theory Tech. 50, 2751 (2002).
[CrossRef]

J. Appl. Phys. (1)

S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, J. Appl. Phys. 78, 1415 (1995).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (1)

Phys. Rev. B (1)

Z.-Y. Li and Z.-Q. Zhang, Phys. Rev. B 62, 1516 (2000).
[CrossRef]

Phys. Rev. E (2)

A. A. Asatryan, P. A. Robinson, L. C. Botten, R. C. McPhedran, N. A. Nicorovici, and C. M. de Sterke, Phys. Rev. E 62, 5711 (2000).
[CrossRef]

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, Phys. Rev. E 65, 066611 (2002).
[CrossRef]

Other (1)

J. Jin, The Finite Element Method in Electromagnetics (Wiley, New York, 2002).

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Figures (3)

Fig. 1
Fig. 1

(a) Comparison of the DA and AVM methods in high-resolution grids (160 points per a). We show the normalized sensitivity of the transmission defined as T/sT/s-1 (s is either the square size L or r1) as a function of frequency. The structure, a dielectric block, is shown in the inset, L=0.9375a, and r1=11.56. (b) Comparison of the DA and AVM methods in low-resolution grids (16 points per a) with the benchmark DA in the high-resolution grid (160 points per a) for s=L.

Fig. 2
Fig. 2

Transmission spectrum calculated by the finite-difference frequency-domain (FDFD) method and the corresponding Lorentzian fit for a photonic-crystal-based bandpass optical filter (the device geometry is shown in the inset). The distance between adjacent rods is a, and their radius is 0.2a. The radius of the central dielectric rod is rd=0.4a. The width of the dielectric waveguides is 0.35a, and their distance from the center of the closest rod is 0.4a.

Fig. 3
Fig. 3

(a) Ω0, (c) Ω1, Ω2 (dashed curve) as a function of the radius of the central dielectric rod rd. Normalized sensitivities (b) Ω0/rdΩ0/a-1, (d) Ω1/rdΩ1/a-1, Ω2/rdΩ2/a-1 (dashed curve) as a function of rd.

Equations (11)

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

-××+k02rE=×M+jωμ0J,
ZsI=V,
sT=-IˆTsZI,
ZTIˆ=ITT,
Tr1=-k02iIˆiIi,
Ts=-k02iΔli-1dhrsurfi,sds×Δ12EˆiEi-Δ12-1DˆiDi,
2x2+2y2+k02rEz=jωμ0Jz.
x1rx+y1ry+k02Hz=jω0Mz.
TsTs+Δs/2-Ts-Δs/2Δs.
Tω=Ω12ω-Ω02+Ω22,
Tωis=TωiΩ0Ω0s+TωiΩ1Ω1s+TωiΩ2Ω2s.

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