Abstract

Optical bistability typically occurs only when the optical thickness in the device or the input light power is unfavorably large. Here we show that, for a class of plasmonic metamaterials consisting of ultrathin holey metallic plates filled with nonlinear materials, the optical bistability can occur with an ultralow excitation power. We present a realistic design working at 0.2 THz and perform full-wave simulations to quantitatively study its optical bistability properties. An analytical model is developed to explain the inherent physics and provides a general design guideline for future development.

© 2014 Optical Society of America

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  1. D. A. Mazurenko, R. Kerst, and J. I. Dijkhuis, Phys. Rev. Lett. 91, 213903 (2003).
    [Crossref]
  2. H. Nihei and A. Okamoto, Jpn. J. Appl. Phys. 40, 6835 (2001).
    [Crossref]
  3. G. Assanto, Z. Wang, D. J. Hagan, and E. W. Van Stryland, Appl. Phys. Lett. 67, 2120 (1995).
    [Crossref]
  4. M. D. Tocci, M. J. Bloemer, M. Scalora, J. P. Dowling, and C. M. Bowden, Appl. Phys. Lett. 66, 2324 (1995).
    [Crossref]
  5. I. S. Nefedov, V. N. Gusyatnikov, and P. K. Kashkarov, Laser Phys. 10, 640 (2000).
  6. M. Born and E. Wolf, Principles of Optics, 4th ed. (Pergamon, 1970).
  7. F. S. Felber and J. H. Marburger, Appl. Phys. Lett. 28, 731 (1976).
    [Crossref]
  8. J. H. Marburger and F. S. Felber, Phys. Rev. A 17, 335 (1978).
    [Crossref]
  9. W. Chen and D. L. Mills, Phys. Rev. B 35, 524 (1987).
    [Crossref]
  10. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, Nature 391, 667 (1998).
    [Crossref]
  11. W. L. Barnes, A. Dereux, and T. W. Ebbesen, Nature 424, 824 (2003).
    [Crossref]
  12. The transmittance is less than 100% when metallic losses are taken into account.
  13. F. J. Garcia-Vidal, L. Martín-Moreno, and J. B. Pendry, J. Opt. A Pure Appl. Opt. 7, S97 (2005).
    [Crossref]
  14. A. B. Khanikaev, S. H. Mousavi, G. Shvets, and Y. S. Kivshar, Phys. Rev. Lett. 105, 1 (2010).
    [Crossref]
  15. N. F. Yu, Q. J. Wang, M. A. Kats, J. A. Fan, S. P. Khanna, L. Li, A. G. Davies, E. H. Linfield, and F. Capasso, Nat. Mater. 9, 730 (2010).
    [Crossref]
  16. Y. Ueba, J. Takahara, and T. Nagatsuma, Opt. Lett. 36, 909 (2011).
    [Crossref]
  17. D. Martin-Cano, O. Quevedo-Teruel, E. Moreno, L. Martin-Moreno, and F. J. Garcia-Vidal, Opt. Lett. 36, 4635 (2011).
    [Crossref]
  18. EastFDTD V4.0, DONGJUN Science and Technology Co., China.
  19. Calculations show that the working bandwidth of the device is about 19 GHz.
  20. A. Mayer and F. Keilmann, Phys. Rev. B 33, 6962 (1986).
    [Crossref]
  21. R. Brazis, R. Raguotis, and M. R. Siegrist, J. Appl. Phys. 84, 3474 (1998).
    [Crossref]
  22. S. Y. Xiao, Q. He, X. Q. Huang, and L. Zhou, Metamaterials 5, 112 (2011).
    [Crossref]
  23. J. Jung, F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, Phys. Rev. B 79, 153407 (2009).
    [Crossref]
  24. Such a relation can also be rigorously derived from the mode-expansion theory under the single-mode approximation.
  25. G. P. Agrawal and N. A. Olsson, IEEE JQE 25, 2297 (1989).

2011 (3)

2010 (2)

A. B. Khanikaev, S. H. Mousavi, G. Shvets, and Y. S. Kivshar, Phys. Rev. Lett. 105, 1 (2010).
[Crossref]

N. F. Yu, Q. J. Wang, M. A. Kats, J. A. Fan, S. P. Khanna, L. Li, A. G. Davies, E. H. Linfield, and F. Capasso, Nat. Mater. 9, 730 (2010).
[Crossref]

2009 (1)

J. Jung, F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, Phys. Rev. B 79, 153407 (2009).
[Crossref]

2005 (1)

F. J. Garcia-Vidal, L. Martín-Moreno, and J. B. Pendry, J. Opt. A Pure Appl. Opt. 7, S97 (2005).
[Crossref]

2003 (2)

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

D. A. Mazurenko, R. Kerst, and J. I. Dijkhuis, Phys. Rev. Lett. 91, 213903 (2003).
[Crossref]

2001 (1)

H. Nihei and A. Okamoto, Jpn. J. Appl. Phys. 40, 6835 (2001).
[Crossref]

2000 (1)

I. S. Nefedov, V. N. Gusyatnikov, and P. K. Kashkarov, Laser Phys. 10, 640 (2000).

1998 (2)

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, Nature 391, 667 (1998).
[Crossref]

R. Brazis, R. Raguotis, and M. R. Siegrist, J. Appl. Phys. 84, 3474 (1998).
[Crossref]

1995 (2)

G. Assanto, Z. Wang, D. J. Hagan, and E. W. Van Stryland, Appl. Phys. Lett. 67, 2120 (1995).
[Crossref]

M. D. Tocci, M. J. Bloemer, M. Scalora, J. P. Dowling, and C. M. Bowden, Appl. Phys. Lett. 66, 2324 (1995).
[Crossref]

1989 (1)

G. P. Agrawal and N. A. Olsson, IEEE JQE 25, 2297 (1989).

1987 (1)

W. Chen and D. L. Mills, Phys. Rev. B 35, 524 (1987).
[Crossref]

1986 (1)

A. Mayer and F. Keilmann, Phys. Rev. B 33, 6962 (1986).
[Crossref]

1978 (1)

J. H. Marburger and F. S. Felber, Phys. Rev. A 17, 335 (1978).
[Crossref]

1976 (1)

F. S. Felber and J. H. Marburger, Appl. Phys. Lett. 28, 731 (1976).
[Crossref]

Agrawal, G. P.

G. P. Agrawal and N. A. Olsson, IEEE JQE 25, 2297 (1989).

Assanto, G.

G. Assanto, Z. Wang, D. J. Hagan, and E. W. Van Stryland, Appl. Phys. Lett. 67, 2120 (1995).
[Crossref]

Barnes, W. L.

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

Bloemer, M. J.

M. D. Tocci, M. J. Bloemer, M. Scalora, J. P. Dowling, and C. M. Bowden, Appl. Phys. Lett. 66, 2324 (1995).
[Crossref]

Born, M.

M. Born and E. Wolf, Principles of Optics, 4th ed. (Pergamon, 1970).

Bowden, C. M.

M. D. Tocci, M. J. Bloemer, M. Scalora, J. P. Dowling, and C. M. Bowden, Appl. Phys. Lett. 66, 2324 (1995).
[Crossref]

Brazis, R.

R. Brazis, R. Raguotis, and M. R. Siegrist, J. Appl. Phys. 84, 3474 (1998).
[Crossref]

Capasso, F.

N. F. Yu, Q. J. Wang, M. A. Kats, J. A. Fan, S. P. Khanna, L. Li, A. G. Davies, E. H. Linfield, and F. Capasso, Nat. Mater. 9, 730 (2010).
[Crossref]

Chen, W.

W. Chen and D. L. Mills, Phys. Rev. B 35, 524 (1987).
[Crossref]

Davies, A. G.

N. F. Yu, Q. J. Wang, M. A. Kats, J. A. Fan, S. P. Khanna, L. Li, A. G. Davies, E. H. Linfield, and F. Capasso, Nat. Mater. 9, 730 (2010).
[Crossref]

Dereux, A.

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

Dijkhuis, J. I.

D. A. Mazurenko, R. Kerst, and J. I. Dijkhuis, Phys. Rev. Lett. 91, 213903 (2003).
[Crossref]

Dowling, J. P.

M. D. Tocci, M. J. Bloemer, M. Scalora, J. P. Dowling, and C. M. Bowden, Appl. Phys. Lett. 66, 2324 (1995).
[Crossref]

Ebbesen, T. W.

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

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, Nature 391, 667 (1998).
[Crossref]

Fan, J. A.

N. F. Yu, Q. J. Wang, M. A. Kats, J. A. Fan, S. P. Khanna, L. Li, A. G. Davies, E. H. Linfield, and F. Capasso, Nat. Mater. 9, 730 (2010).
[Crossref]

Felber, F. S.

J. H. Marburger and F. S. Felber, Phys. Rev. A 17, 335 (1978).
[Crossref]

F. S. Felber and J. H. Marburger, Appl. Phys. Lett. 28, 731 (1976).
[Crossref]

Garcia-Vidal, F. J.

D. Martin-Cano, O. Quevedo-Teruel, E. Moreno, L. Martin-Moreno, and F. J. Garcia-Vidal, Opt. Lett. 36, 4635 (2011).
[Crossref]

J. Jung, F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, Phys. Rev. B 79, 153407 (2009).
[Crossref]

F. J. Garcia-Vidal, L. Martín-Moreno, and J. B. Pendry, J. Opt. A Pure Appl. Opt. 7, S97 (2005).
[Crossref]

Ghaemi, H. F.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, Nature 391, 667 (1998).
[Crossref]

Gusyatnikov, V. N.

I. S. Nefedov, V. N. Gusyatnikov, and P. K. Kashkarov, Laser Phys. 10, 640 (2000).

Hagan, D. J.

G. Assanto, Z. Wang, D. J. Hagan, and E. W. Van Stryland, Appl. Phys. Lett. 67, 2120 (1995).
[Crossref]

He, Q.

S. Y. Xiao, Q. He, X. Q. Huang, and L. Zhou, Metamaterials 5, 112 (2011).
[Crossref]

Huang, X. Q.

S. Y. Xiao, Q. He, X. Q. Huang, and L. Zhou, Metamaterials 5, 112 (2011).
[Crossref]

Jung, J.

J. Jung, F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, Phys. Rev. B 79, 153407 (2009).
[Crossref]

Kashkarov, P. K.

I. S. Nefedov, V. N. Gusyatnikov, and P. K. Kashkarov, Laser Phys. 10, 640 (2000).

Kats, M. A.

N. F. Yu, Q. J. Wang, M. A. Kats, J. A. Fan, S. P. Khanna, L. Li, A. G. Davies, E. H. Linfield, and F. Capasso, Nat. Mater. 9, 730 (2010).
[Crossref]

Keilmann, F.

A. Mayer and F. Keilmann, Phys. Rev. B 33, 6962 (1986).
[Crossref]

Kerst, R.

D. A. Mazurenko, R. Kerst, and J. I. Dijkhuis, Phys. Rev. Lett. 91, 213903 (2003).
[Crossref]

Khanikaev, A. B.

A. B. Khanikaev, S. H. Mousavi, G. Shvets, and Y. S. Kivshar, Phys. Rev. Lett. 105, 1 (2010).
[Crossref]

Khanna, S. P.

N. F. Yu, Q. J. Wang, M. A. Kats, J. A. Fan, S. P. Khanna, L. Li, A. G. Davies, E. H. Linfield, and F. Capasso, Nat. Mater. 9, 730 (2010).
[Crossref]

Kivshar, Y. S.

A. B. Khanikaev, S. H. Mousavi, G. Shvets, and Y. S. Kivshar, Phys. Rev. Lett. 105, 1 (2010).
[Crossref]

Lezec, H. J.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, Nature 391, 667 (1998).
[Crossref]

Li, L.

N. F. Yu, Q. J. Wang, M. A. Kats, J. A. Fan, S. P. Khanna, L. Li, A. G. Davies, E. H. Linfield, and F. Capasso, Nat. Mater. 9, 730 (2010).
[Crossref]

Linfield, E. H.

N. F. Yu, Q. J. Wang, M. A. Kats, J. A. Fan, S. P. Khanna, L. Li, A. G. Davies, E. H. Linfield, and F. Capasso, Nat. Mater. 9, 730 (2010).
[Crossref]

Marburger, J. H.

J. H. Marburger and F. S. Felber, Phys. Rev. A 17, 335 (1978).
[Crossref]

F. S. Felber and J. H. Marburger, Appl. Phys. Lett. 28, 731 (1976).
[Crossref]

Martin-Cano, D.

Martin-Moreno, L.

D. Martin-Cano, O. Quevedo-Teruel, E. Moreno, L. Martin-Moreno, and F. J. Garcia-Vidal, Opt. Lett. 36, 4635 (2011).
[Crossref]

J. Jung, F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, Phys. Rev. B 79, 153407 (2009).
[Crossref]

Martín-Moreno, L.

F. J. Garcia-Vidal, L. Martín-Moreno, and J. B. Pendry, J. Opt. A Pure Appl. Opt. 7, S97 (2005).
[Crossref]

Mayer, A.

A. Mayer and F. Keilmann, Phys. Rev. B 33, 6962 (1986).
[Crossref]

Mazurenko, D. A.

D. A. Mazurenko, R. Kerst, and J. I. Dijkhuis, Phys. Rev. Lett. 91, 213903 (2003).
[Crossref]

Mills, D. L.

W. Chen and D. L. Mills, Phys. Rev. B 35, 524 (1987).
[Crossref]

Moreno, E.

Mousavi, S. H.

A. B. Khanikaev, S. H. Mousavi, G. Shvets, and Y. S. Kivshar, Phys. Rev. Lett. 105, 1 (2010).
[Crossref]

Nagatsuma, T.

Nefedov, I. S.

I. S. Nefedov, V. N. Gusyatnikov, and P. K. Kashkarov, Laser Phys. 10, 640 (2000).

Nihei, H.

H. Nihei and A. Okamoto, Jpn. J. Appl. Phys. 40, 6835 (2001).
[Crossref]

Okamoto, A.

H. Nihei and A. Okamoto, Jpn. J. Appl. Phys. 40, 6835 (2001).
[Crossref]

Olsson, N. A.

G. P. Agrawal and N. A. Olsson, IEEE JQE 25, 2297 (1989).

Pendry, J. B.

J. Jung, F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, Phys. Rev. B 79, 153407 (2009).
[Crossref]

F. J. Garcia-Vidal, L. Martín-Moreno, and J. B. Pendry, J. Opt. A Pure Appl. Opt. 7, S97 (2005).
[Crossref]

Quevedo-Teruel, O.

Raguotis, R.

R. Brazis, R. Raguotis, and M. R. Siegrist, J. Appl. Phys. 84, 3474 (1998).
[Crossref]

Scalora, M.

M. D. Tocci, M. J. Bloemer, M. Scalora, J. P. Dowling, and C. M. Bowden, Appl. Phys. Lett. 66, 2324 (1995).
[Crossref]

Shvets, G.

A. B. Khanikaev, S. H. Mousavi, G. Shvets, and Y. S. Kivshar, Phys. Rev. Lett. 105, 1 (2010).
[Crossref]

Siegrist, M. R.

R. Brazis, R. Raguotis, and M. R. Siegrist, J. Appl. Phys. 84, 3474 (1998).
[Crossref]

Takahara, J.

Thio, T.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, Nature 391, 667 (1998).
[Crossref]

Tocci, M. D.

M. D. Tocci, M. J. Bloemer, M. Scalora, J. P. Dowling, and C. M. Bowden, Appl. Phys. Lett. 66, 2324 (1995).
[Crossref]

Ueba, Y.

Van Stryland, E. W.

G. Assanto, Z. Wang, D. J. Hagan, and E. W. Van Stryland, Appl. Phys. Lett. 67, 2120 (1995).
[Crossref]

Wang, Q. J.

N. F. Yu, Q. J. Wang, M. A. Kats, J. A. Fan, S. P. Khanna, L. Li, A. G. Davies, E. H. Linfield, and F. Capasso, Nat. Mater. 9, 730 (2010).
[Crossref]

Wang, Z.

G. Assanto, Z. Wang, D. J. Hagan, and E. W. Van Stryland, Appl. Phys. Lett. 67, 2120 (1995).
[Crossref]

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 4th ed. (Pergamon, 1970).

Wolff, P. A.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, Nature 391, 667 (1998).
[Crossref]

Xiao, S. Y.

S. Y. Xiao, Q. He, X. Q. Huang, and L. Zhou, Metamaterials 5, 112 (2011).
[Crossref]

Yu, N. F.

N. F. Yu, Q. J. Wang, M. A. Kats, J. A. Fan, S. P. Khanna, L. Li, A. G. Davies, E. H. Linfield, and F. Capasso, Nat. Mater. 9, 730 (2010).
[Crossref]

Zhou, L.

S. Y. Xiao, Q. He, X. Q. Huang, and L. Zhou, Metamaterials 5, 112 (2011).
[Crossref]

Appl. Phys. Lett. (3)

G. Assanto, Z. Wang, D. J. Hagan, and E. W. Van Stryland, Appl. Phys. Lett. 67, 2120 (1995).
[Crossref]

M. D. Tocci, M. J. Bloemer, M. Scalora, J. P. Dowling, and C. M. Bowden, Appl. Phys. Lett. 66, 2324 (1995).
[Crossref]

F. S. Felber and J. H. Marburger, Appl. Phys. Lett. 28, 731 (1976).
[Crossref]

IEEE JQE (1)

G. P. Agrawal and N. A. Olsson, IEEE JQE 25, 2297 (1989).

J. Appl. Phys. (1)

R. Brazis, R. Raguotis, and M. R. Siegrist, J. Appl. Phys. 84, 3474 (1998).
[Crossref]

J. Opt. A Pure Appl. Opt. (1)

F. J. Garcia-Vidal, L. Martín-Moreno, and J. B. Pendry, J. Opt. A Pure Appl. Opt. 7, S97 (2005).
[Crossref]

Jpn. J. Appl. Phys. (1)

H. Nihei and A. Okamoto, Jpn. J. Appl. Phys. 40, 6835 (2001).
[Crossref]

Laser Phys. (1)

I. S. Nefedov, V. N. Gusyatnikov, and P. K. Kashkarov, Laser Phys. 10, 640 (2000).

Metamaterials (1)

S. Y. Xiao, Q. He, X. Q. Huang, and L. Zhou, Metamaterials 5, 112 (2011).
[Crossref]

Nat. Mater. (1)

N. F. Yu, Q. J. Wang, M. A. Kats, J. A. Fan, S. P. Khanna, L. Li, A. G. Davies, E. H. Linfield, and F. Capasso, Nat. Mater. 9, 730 (2010).
[Crossref]

Nature (2)

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, Nature 391, 667 (1998).
[Crossref]

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

Opt. Lett. (2)

Phys. Rev. A (1)

J. H. Marburger and F. S. Felber, Phys. Rev. A 17, 335 (1978).
[Crossref]

Phys. Rev. B (3)

W. Chen and D. L. Mills, Phys. Rev. B 35, 524 (1987).
[Crossref]

J. Jung, F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, Phys. Rev. B 79, 153407 (2009).
[Crossref]

A. Mayer and F. Keilmann, Phys. Rev. B 33, 6962 (1986).
[Crossref]

Phys. Rev. Lett. (2)

D. A. Mazurenko, R. Kerst, and J. I. Dijkhuis, Phys. Rev. Lett. 91, 213903 (2003).
[Crossref]

A. B. Khanikaev, S. H. Mousavi, G. Shvets, and Y. S. Kivshar, Phys. Rev. Lett. 105, 1 (2010).
[Crossref]

Other (5)

The transmittance is less than 100% when metallic losses are taken into account.

EastFDTD V4.0, DONGJUN Science and Technology Co., China.

Calculations show that the working bandwidth of the device is about 19 GHz.

M. Born and E. Wolf, Principles of Optics, 4th ed. (Pergamon, 1970).

Such a relation can also be rigorously derived from the mode-expansion theory under the single-mode approximation.

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Figures (5)

Fig. 1.
Fig. 1.

(a) Schematic of the device. Shown is a unit cell with d = 240 μm , l 1 = 100 μm , l 2 = l 3 = 40 μm , and l 4 = 60 μm . The yellow (blue) region denotes the metal (nonlinear material). (b) Transmission spectra of the device with varying ε d , calculated by FDTD simulations (circles) and the analytical model (solid lines) using Eq. (1), respectively.

Fig. 2.
Fig. 2.

Bistable hysteresis for a device with parameters (a)  w = 20 μm , h = 60 μm ; (b)  w = 20 μm , h = 80 μm ; and (c)  w = 15 μm , h = 60 μm , calculated by a nonlinear FDTD scheme [18] (circles) and the analytic model calculations using Eqs. (1) and (3) (lines). Red arrows indicate the direction of the input power change.

Fig. 3.
Fig. 3.

Film-thickness dependences of the threshold field (blue triangles) and saturation field (red circles) for (a) our design. (b) An FP slab with the same thickness, obtained by the nonlinear FDTD calculations. Lines denote the model results calculated with Eqs. (1) and (3). The operating frequency is f = 0.2 THz .

Fig. 4.
Fig. 4.

Graphical representation and determination of the optical bistability threshold and saturation fields for different thicknesses. Solid and dashed lines are calculated by Eqs. (1) and (3), respectively.

Fig. 5.
Fig. 5.

Optical bistability threshold as a function of S 0 and h .

Equations (3)

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

T = | 4 Y 0 Y hole e i q z h ( Y 0 + Y hole ) 2 ( Y 0 Y hole ) 2 e 2 i q z h | 2 ,
S 0 = hole ( E⃗ inc ) * · ( E⃗ wg ) d x d y unitcell | E⃗ inc | 2 d x d y · hole | E⃗ wg | 2 d x d y
ε d = 2.25 + χ ( 3 ) · A u.c. A hole · | E⃗ 0 | 2 · T | S 0 | 2 .

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