Abstract

We present a simple and robust structure for realizing asymmetric Fano transmission characteristics in photonic crystal waveguide-cavity structures. The use of Fano resonances for optical switching is analyzed using temporal coupled mode theory in combination with three-dimensional finite difference time domain simulations taking into account the signal bandwidth. The results suggest a significant energy reduction by employing Fano resonances compared to more well established Lorentzian resonance structures. A specific example of a Kerr nonlinearity shows an order of magnitude energy reduction.

© 2013 Optical Society of America

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  1. U. Fano, Phys. Rev. 124, 1866 (1961).
    [CrossRef]
  2. A. E. Miroschnichenko, S. Flach, and Y. Kivshar, Rev. Mod. Phys. 82, 2257 (2010).
    [CrossRef]
  3. B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, Nat. Phys. 9, 707 (2010).
    [CrossRef]
  4. S. F. Mingaleev, A. E. Miroschnichenko, and Y. Kivshar, Opt. Express 16, 11647 (2008).
    [CrossRef]
  5. S. Fan, App. Phys. Lett. 80, 908 (2002).
    [CrossRef]
  6. A. R. Cowan and J. F. Young, Phys. Rev. E 68, 046606 (2003).
    [CrossRef]
  7. A. E. Miroschnichenko and Y. Kivshar, Phys. Rev. E 72, 056611 (2005).
    [CrossRef]
  8. K. Nozaki, A. Shinya, S. Matsuo, T. Sato, E. Kuramochi, and M. Notomi, Opt. Express 21, 11877 (2013).
    [CrossRef]
  9. X. Yang, C. Husko, C. W. Wong, M. Yu, and D. Kwong, App. Phys. Lett. 91, 051113 (2007).
    [CrossRef]
  10. K. K. Mehta, J. S. Orcutt, and R. J. Ram, Appl. Phys. Lett. 102, 081109 (2013).
    [CrossRef]
  11. S. Fan, W. Suh, and J. D. Joannopoulos, J. Opt. Soc. Am. A 20, 569 (2003).
    [CrossRef]
  12. M. Heuck, P. T. Kristensen, and J. Mørk, Opt. Express 19, 18410 (2011).
    [CrossRef]
  13. C. Husko, A. de Rossi, S. Combrié, Q. V. Tran, F. Raineri, and C. W. Wong, Appl. Phys. Lett. 94, 021111 (2009).
    [CrossRef]
  14. K. Nozaki, T. Tanabe, A. Shinya, S. Matsuo, T. Sato, H. Taniyama, and M. Notomi, Nat. Photonics 4, 477 (2010).
    [CrossRef]
  15. A. Taflove and S. C. Hagnes, Computational Electrodynamics–The Finite-Difference Time-Domain Method, 3rd ed. (Artech House, 2005).
  16. Y. Elesin, B. S. Lazarov, J. S. Jensen, and O. Sigmund, “Time domain topology optimization of 3D nanotonic devices,” Photon. Nanostructures, submitted for publication.
  17. Y. Yu, M. Heuck, S. Ek, N. Kuznetsova, K. Yvind, and J. Mørk, Appl. Phys. Lett. 101, 25 (2012).

2013

K. Nozaki, A. Shinya, S. Matsuo, T. Sato, E. Kuramochi, and M. Notomi, Opt. Express 21, 11877 (2013).
[CrossRef]

K. K. Mehta, J. S. Orcutt, and R. J. Ram, Appl. Phys. Lett. 102, 081109 (2013).
[CrossRef]

2012

Y. Yu, M. Heuck, S. Ek, N. Kuznetsova, K. Yvind, and J. Mørk, Appl. Phys. Lett. 101, 25 (2012).

2011

2010

K. Nozaki, T. Tanabe, A. Shinya, S. Matsuo, T. Sato, H. Taniyama, and M. Notomi, Nat. Photonics 4, 477 (2010).
[CrossRef]

A. E. Miroschnichenko, S. Flach, and Y. Kivshar, Rev. Mod. Phys. 82, 2257 (2010).
[CrossRef]

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, Nat. Phys. 9, 707 (2010).
[CrossRef]

2009

C. Husko, A. de Rossi, S. Combrié, Q. V. Tran, F. Raineri, and C. W. Wong, Appl. Phys. Lett. 94, 021111 (2009).
[CrossRef]

2008

2007

X. Yang, C. Husko, C. W. Wong, M. Yu, and D. Kwong, App. Phys. Lett. 91, 051113 (2007).
[CrossRef]

2005

A. E. Miroschnichenko and Y. Kivshar, Phys. Rev. E 72, 056611 (2005).
[CrossRef]

2003

2002

S. Fan, App. Phys. Lett. 80, 908 (2002).
[CrossRef]

1961

U. Fano, Phys. Rev. 124, 1866 (1961).
[CrossRef]

Chong, C. T.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, Nat. Phys. 9, 707 (2010).
[CrossRef]

Combrié, S.

C. Husko, A. de Rossi, S. Combrié, Q. V. Tran, F. Raineri, and C. W. Wong, Appl. Phys. Lett. 94, 021111 (2009).
[CrossRef]

Cowan, A. R.

A. R. Cowan and J. F. Young, Phys. Rev. E 68, 046606 (2003).
[CrossRef]

de Rossi, A.

C. Husko, A. de Rossi, S. Combrié, Q. V. Tran, F. Raineri, and C. W. Wong, Appl. Phys. Lett. 94, 021111 (2009).
[CrossRef]

Ek, S.

Y. Yu, M. Heuck, S. Ek, N. Kuznetsova, K. Yvind, and J. Mørk, Appl. Phys. Lett. 101, 25 (2012).

Elesin, Y.

Y. Elesin, B. S. Lazarov, J. S. Jensen, and O. Sigmund, “Time domain topology optimization of 3D nanotonic devices,” Photon. Nanostructures, submitted for publication.

Fan, S.

Fano, U.

U. Fano, Phys. Rev. 124, 1866 (1961).
[CrossRef]

Flach, S.

A. E. Miroschnichenko, S. Flach, and Y. Kivshar, Rev. Mod. Phys. 82, 2257 (2010).
[CrossRef]

Giessen, H.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, Nat. Phys. 9, 707 (2010).
[CrossRef]

Hagnes, S. C.

A. Taflove and S. C. Hagnes, Computational Electrodynamics–The Finite-Difference Time-Domain Method, 3rd ed. (Artech House, 2005).

Halas, N. J.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, Nat. Phys. 9, 707 (2010).
[CrossRef]

Heuck, M.

Y. Yu, M. Heuck, S. Ek, N. Kuznetsova, K. Yvind, and J. Mørk, Appl. Phys. Lett. 101, 25 (2012).

M. Heuck, P. T. Kristensen, and J. Mørk, Opt. Express 19, 18410 (2011).
[CrossRef]

Husko, C.

C. Husko, A. de Rossi, S. Combrié, Q. V. Tran, F. Raineri, and C. W. Wong, Appl. Phys. Lett. 94, 021111 (2009).
[CrossRef]

X. Yang, C. Husko, C. W. Wong, M. Yu, and D. Kwong, App. Phys. Lett. 91, 051113 (2007).
[CrossRef]

Jensen, J. S.

Y. Elesin, B. S. Lazarov, J. S. Jensen, and O. Sigmund, “Time domain topology optimization of 3D nanotonic devices,” Photon. Nanostructures, submitted for publication.

Joannopoulos, J. D.

Kivshar, Y.

A. E. Miroschnichenko, S. Flach, and Y. Kivshar, Rev. Mod. Phys. 82, 2257 (2010).
[CrossRef]

S. F. Mingaleev, A. E. Miroschnichenko, and Y. Kivshar, Opt. Express 16, 11647 (2008).
[CrossRef]

A. E. Miroschnichenko and Y. Kivshar, Phys. Rev. E 72, 056611 (2005).
[CrossRef]

Kristensen, P. T.

Kuramochi, E.

Kuznetsova, N.

Y. Yu, M. Heuck, S. Ek, N. Kuznetsova, K. Yvind, and J. Mørk, Appl. Phys. Lett. 101, 25 (2012).

Kwong, D.

X. Yang, C. Husko, C. W. Wong, M. Yu, and D. Kwong, App. Phys. Lett. 91, 051113 (2007).
[CrossRef]

Lazarov, B. S.

Y. Elesin, B. S. Lazarov, J. S. Jensen, and O. Sigmund, “Time domain topology optimization of 3D nanotonic devices,” Photon. Nanostructures, submitted for publication.

Luk’yanchuk, B.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, Nat. Phys. 9, 707 (2010).
[CrossRef]

Maier, S. A.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, Nat. Phys. 9, 707 (2010).
[CrossRef]

Matsuo, S.

K. Nozaki, A. Shinya, S. Matsuo, T. Sato, E. Kuramochi, and M. Notomi, Opt. Express 21, 11877 (2013).
[CrossRef]

K. Nozaki, T. Tanabe, A. Shinya, S. Matsuo, T. Sato, H. Taniyama, and M. Notomi, Nat. Photonics 4, 477 (2010).
[CrossRef]

Mehta, K. K.

K. K. Mehta, J. S. Orcutt, and R. J. Ram, Appl. Phys. Lett. 102, 081109 (2013).
[CrossRef]

Mingaleev, S. F.

Miroschnichenko, A. E.

A. E. Miroschnichenko, S. Flach, and Y. Kivshar, Rev. Mod. Phys. 82, 2257 (2010).
[CrossRef]

S. F. Mingaleev, A. E. Miroschnichenko, and Y. Kivshar, Opt. Express 16, 11647 (2008).
[CrossRef]

A. E. Miroschnichenko and Y. Kivshar, Phys. Rev. E 72, 056611 (2005).
[CrossRef]

Mørk, J.

Y. Yu, M. Heuck, S. Ek, N. Kuznetsova, K. Yvind, and J. Mørk, Appl. Phys. Lett. 101, 25 (2012).

M. Heuck, P. T. Kristensen, and J. Mørk, Opt. Express 19, 18410 (2011).
[CrossRef]

Nordlander, P.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, Nat. Phys. 9, 707 (2010).
[CrossRef]

Notomi, M.

K. Nozaki, A. Shinya, S. Matsuo, T. Sato, E. Kuramochi, and M. Notomi, Opt. Express 21, 11877 (2013).
[CrossRef]

K. Nozaki, T. Tanabe, A. Shinya, S. Matsuo, T. Sato, H. Taniyama, and M. Notomi, Nat. Photonics 4, 477 (2010).
[CrossRef]

Nozaki, K.

K. Nozaki, A. Shinya, S. Matsuo, T. Sato, E. Kuramochi, and M. Notomi, Opt. Express 21, 11877 (2013).
[CrossRef]

K. Nozaki, T. Tanabe, A. Shinya, S. Matsuo, T. Sato, H. Taniyama, and M. Notomi, Nat. Photonics 4, 477 (2010).
[CrossRef]

Orcutt, J. S.

K. K. Mehta, J. S. Orcutt, and R. J. Ram, Appl. Phys. Lett. 102, 081109 (2013).
[CrossRef]

Raineri, F.

C. Husko, A. de Rossi, S. Combrié, Q. V. Tran, F. Raineri, and C. W. Wong, Appl. Phys. Lett. 94, 021111 (2009).
[CrossRef]

Ram, R. J.

K. K. Mehta, J. S. Orcutt, and R. J. Ram, Appl. Phys. Lett. 102, 081109 (2013).
[CrossRef]

Sato, T.

K. Nozaki, A. Shinya, S. Matsuo, T. Sato, E. Kuramochi, and M. Notomi, Opt. Express 21, 11877 (2013).
[CrossRef]

K. Nozaki, T. Tanabe, A. Shinya, S. Matsuo, T. Sato, H. Taniyama, and M. Notomi, Nat. Photonics 4, 477 (2010).
[CrossRef]

Shinya, A.

K. Nozaki, A. Shinya, S. Matsuo, T. Sato, E. Kuramochi, and M. Notomi, Opt. Express 21, 11877 (2013).
[CrossRef]

K. Nozaki, T. Tanabe, A. Shinya, S. Matsuo, T. Sato, H. Taniyama, and M. Notomi, Nat. Photonics 4, 477 (2010).
[CrossRef]

Sigmund, O.

Y. Elesin, B. S. Lazarov, J. S. Jensen, and O. Sigmund, “Time domain topology optimization of 3D nanotonic devices,” Photon. Nanostructures, submitted for publication.

Suh, W.

Taflove, A.

A. Taflove and S. C. Hagnes, Computational Electrodynamics–The Finite-Difference Time-Domain Method, 3rd ed. (Artech House, 2005).

Tanabe, T.

K. Nozaki, T. Tanabe, A. Shinya, S. Matsuo, T. Sato, H. Taniyama, and M. Notomi, Nat. Photonics 4, 477 (2010).
[CrossRef]

Taniyama, H.

K. Nozaki, T. Tanabe, A. Shinya, S. Matsuo, T. Sato, H. Taniyama, and M. Notomi, Nat. Photonics 4, 477 (2010).
[CrossRef]

Tran, Q. V.

C. Husko, A. de Rossi, S. Combrié, Q. V. Tran, F. Raineri, and C. W. Wong, Appl. Phys. Lett. 94, 021111 (2009).
[CrossRef]

Wong, C. W.

C. Husko, A. de Rossi, S. Combrié, Q. V. Tran, F. Raineri, and C. W. Wong, Appl. Phys. Lett. 94, 021111 (2009).
[CrossRef]

X. Yang, C. Husko, C. W. Wong, M. Yu, and D. Kwong, App. Phys. Lett. 91, 051113 (2007).
[CrossRef]

Yang, X.

X. Yang, C. Husko, C. W. Wong, M. Yu, and D. Kwong, App. Phys. Lett. 91, 051113 (2007).
[CrossRef]

Young, J. F.

A. R. Cowan and J. F. Young, Phys. Rev. E 68, 046606 (2003).
[CrossRef]

Yu, M.

X. Yang, C. Husko, C. W. Wong, M. Yu, and D. Kwong, App. Phys. Lett. 91, 051113 (2007).
[CrossRef]

Yu, Y.

Y. Yu, M. Heuck, S. Ek, N. Kuznetsova, K. Yvind, and J. Mørk, Appl. Phys. Lett. 101, 25 (2012).

Yvind, K.

Y. Yu, M. Heuck, S. Ek, N. Kuznetsova, K. Yvind, and J. Mørk, Appl. Phys. Lett. 101, 25 (2012).

Zheludev, N. I.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, Nat. Phys. 9, 707 (2010).
[CrossRef]

App. Phys. Lett.

S. Fan, App. Phys. Lett. 80, 908 (2002).
[CrossRef]

X. Yang, C. Husko, C. W. Wong, M. Yu, and D. Kwong, App. Phys. Lett. 91, 051113 (2007).
[CrossRef]

Appl. Phys. Lett.

K. K. Mehta, J. S. Orcutt, and R. J. Ram, Appl. Phys. Lett. 102, 081109 (2013).
[CrossRef]

C. Husko, A. de Rossi, S. Combrié, Q. V. Tran, F. Raineri, and C. W. Wong, Appl. Phys. Lett. 94, 021111 (2009).
[CrossRef]

Y. Yu, M. Heuck, S. Ek, N. Kuznetsova, K. Yvind, and J. Mørk, Appl. Phys. Lett. 101, 25 (2012).

J. Opt. Soc. Am. A

Nat. Photonics

K. Nozaki, T. Tanabe, A. Shinya, S. Matsuo, T. Sato, H. Taniyama, and M. Notomi, Nat. Photonics 4, 477 (2010).
[CrossRef]

Nat. Phys.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, Nat. Phys. 9, 707 (2010).
[CrossRef]

Opt. Express

Phys. Rev.

U. Fano, Phys. Rev. 124, 1866 (1961).
[CrossRef]

Phys. Rev. E

A. R. Cowan and J. F. Young, Phys. Rev. E 68, 046606 (2003).
[CrossRef]

A. E. Miroschnichenko and Y. Kivshar, Phys. Rev. E 72, 056611 (2005).
[CrossRef]

Rev. Mod. Phys.

A. E. Miroschnichenko, S. Flach, and Y. Kivshar, Rev. Mod. Phys. 82, 2257 (2010).
[CrossRef]

Other

A. Taflove and S. C. Hagnes, Computational Electrodynamics–The Finite-Difference Time-Domain Method, 3rd ed. (Artech House, 2005).

Y. Elesin, B. S. Lazarov, J. S. Jensen, and O. Sigmund, “Time domain topology optimization of 3D nanotonic devices,” Photon. Nanostructures, submitted for publication.

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Figures (3)

Fig. 1.
Fig. 1.

(a) Photonic crystal waveguide-cavity structure with holes of radii rb in the waveguide (red and green) and r0 in the remaining lattice. The field profile |H|2 is overlaid. (b) Transmission spectra found from 3D FDTD calculations (circles) for the different blockade configurations in (a), where a is the lattice constant and c the speed of light. The blue curve corresponds to an unblocked waveguide, and the red and green curves match the colors in (a). The solid lines are fits using Eq. (3). The insets show |H|2 using CW excitation in the “on” and “off” states of the Fano structure as indicated by the red squares.

Fig. 2.
Fig. 2.

Left: Energy transmission as a function of detuning for three different values of |tB| with ΔωC/ΩS=5. The thick parts of the curves indicate the intervals [δSmin;δSmin+δNLmin]. Right: Minimum nonlinear shift δNLmin as a function of the cavity linewidth ΔωC and blockade transmittance |tB|. The frequency shift and cavity linewidth are normalized with the signal bandwidth ΩS. TUmax and TUmin are the maximum and minimum transmission for a given parameter set (|tB|,ΔωC).

Fig. 3.
Fig. 3.

Minimum switching energy UPimin as a function of the resonance linewidth ΔωC and blockade transmittance |tB|. The characteristic energy is given by U0=ΩS/FNL. The orange circle indicates the minimum for a Lorentzian line shape, the cross indicates the overall energy minimum, and their ratio of 11 dB quantifies the achievable energy reduction by using a Fano resonance.

Equations (4)

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

daS(t)dt=(i[δS+δNL(t)]γC)aS(t)+γsSi(t),
sSo(t)=tBsSi(t)γaS(t),
TCW=||tB|2+i|tB||rB|γiδS+γC|2,
TU(|tB|,δS,ΩS)=TCW(ω)PSi(ω,ΩS)dωPSi(ω,ΩS)dω,

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