Abstract

We theoretically discuss all-optical switching at the Fano resonances of subwavelength gratings made of a chalcogenide glass (As2S3). Particular attention is devoted to the case in which the grating possesses extremely narrow slits (channels ranging from a10nm to a40nm). The remarkable local field enhancement available in these situations conspires to yield low-threshold switching intensities (~50MW/cm2) at telecommunication wavelengths for extremely thin (d200nm) gratings when a realistic value of the As2S3 cubic nonlinearity is used.

© 2011 Optical Society of America

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2011 (2)

2010 (4)

P. Ne˘mec, S. Zhang, V. Nazabal, K. Fedus, G. Boudebs, A. Moreac, M. Cathelinaud, and X.-H. Zhang, Opt. Express 18, 22944 (2010).
[CrossRef]

H. Duan, D. Winston, J. K. W. Yang, B. M. Cord, V. R. Manfrinato, and K. K. Berggren, J. Vac. Sci. Technol. B 28, C6 (2010) and references therein.
[CrossRef]

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

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

2007 (2)

2006 (1)

2003 (2)

M. Soljacic, M. Ibanescu, C. Luo, S. G. Johnson, S. Fan, Y. Fink, and J. D. Joannopoulos, Proc. SPIE 5000200 (2003).
[CrossRef]

N. Hô, J. M. Laniel, R. Valée, and A. Villeneuve, Opt. Lett. 28, 965 (2003).
[CrossRef] [PubMed]

1996 (1)

1989 (1)

1985 (1)

1961 (1)

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

Alù, A.

Baker, N. J.

Berggren, K. K.

H. Duan, D. Winston, J. K. W. Yang, B. M. Cord, V. R. Manfrinato, and K. K. Berggren, J. Vac. Sci. Technol. B 28, C6 (2010) and references therein.
[CrossRef]

Bloemer, M. J.

Boudebs, G.

Cathelinaud, M.

Choi, D. Y.

Chong, C. T.

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

Cord, B. M.

H. Duan, D. Winston, J. K. W. Yang, B. M. Cord, V. R. Manfrinato, and K. K. Berggren, J. Vac. Sci. Technol. B 28, C6 (2010) and references therein.
[CrossRef]

D’Aguanno, G.

de Ceglia, D.

DeLong, K. W.

Duan, H.

H. Duan, D. Winston, J. K. W. Yang, B. M. Cord, V. R. Manfrinato, and K. K. Berggren, J. Vac. Sci. Technol. B 28, C6 (2010) and references therein.
[CrossRef]

Eggleton, B. J.

Fan, S.

M. Soljacic, M. Ibanescu, C. Luo, S. G. Johnson, S. Fan, Y. Fink, and J. D. Joannopoulos, Proc. SPIE 5000200 (2003).
[CrossRef]

Fano, U.

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

Fedus, K.

Fejer, M. M.

Fink, Y.

M. Soljacic, M. Ibanescu, C. Luo, S. G. Johnson, S. Fan, Y. Fink, and J. D. Joannopoulos, Proc. SPIE 5000200 (2003).
[CrossRef]

Finsterbusch, K.

Flach, S.

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

Freeman, D.

Fu, L.

Gibbs, H. M.

H. M. Gibbs, Optical Bistability: Controlling Light with Light (Academic, 1985).

Giessen, H.

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

Grillet, C.

Halas, N. J.

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

Hô, N.

Hurlbut, W. C.

Ibanescu, M.

M. Soljacic, M. Ibanescu, C. Luo, S. G. Johnson, S. Fan, Y. Fink, and J. D. Joannopoulos, Proc. SPIE 5000200 (2003).
[CrossRef]

Joannopoulos, J. D.

M. Soljacic, M. Ibanescu, C. Luo, S. G. Johnson, S. Fan, Y. Fink, and J. D. Joannopoulos, Proc. SPIE 5000200 (2003).
[CrossRef]

Johnson, S. G.

M. Soljacic, M. Ibanescu, C. Luo, S. G. Johnson, S. Fan, Y. Fink, and J. D. Joannopoulos, Proc. SPIE 5000200 (2003).
[CrossRef]

Kivshar, Y. S.

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

Klocek, P.

P. Klocek, Handbook of Infrared Optical Materials (Marcel Dekker, 1991)

Koster, A.

Kuo, P. S.

Lamont, M. R. E.

Laniel, J. M.

Lee, Yun-Shik

Li, L.

Luk’yanchuck, B.

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

Luo, C.

M. Soljacic, M. Ibanescu, C. Luo, S. G. Johnson, S. Fan, Y. Fink, and J. D. Joannopoulos, Proc. SPIE 5000200 (2003).
[CrossRef]

Luther-Davis, B.

Madden, S.

Maier, S. A.

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

Manfrinato, V. R.

H. Duan, D. Winston, J. K. W. Yang, B. M. Cord, V. R. Manfrinato, and K. K. Berggren, J. Vac. Sci. Technol. B 28, C6 (2010) and references therein.
[CrossRef]

Mattiucci, N.

McPhedran, R.

Miroshnichenko, A. E.

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

Mizrahi, V.

Moreac, A.

Moss, D. J.

Nazabal, V.

Ne?mec, P.

Neviere, M.

Nguyen, H. C.

Nordlander, P.

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

Paraire, N.

Reinisch, R.

Scalora, M.

Soljacic, M.

M. Soljacic, M. Ibanescu, C. Luo, S. G. Johnson, S. Fan, Y. Fink, and J. D. Joannopoulos, Proc. SPIE 5000200 (2003).
[CrossRef]

Steel, M. J.

Stegeman, G. I.

Sutherland, R. L.

Here we suppose to write the relative permittivity of the medium as ε=εL+χ(3)|E|2 and the intensity as I=(1/2)ε0cnL|E|2. Other conventions also exist where ε=εL+3χ(3)|E|2 and I=2ε0cnL|E|2, in this case we would have had that Re⁡[χ(3)]=4ε0cnL2n2/3 and Im⁡[χ(3)]=ε0cnL2λ3πβ. See, for example, R. L. Sutherland, Handbook of Nonlinear Optics (Marcel Dekker, 1996).

Ta’eed, V.

Valée, R.

Vicent, P.

Villeneuve, A.

Vincenti, M. A.

Vodopyanov, K. L.

Winston, D.

H. Duan, D. Winston, J. K. W. Yang, B. M. Cord, V. R. Manfrinato, and K. K. Berggren, J. Vac. Sci. Technol. B 28, C6 (2010) and references therein.
[CrossRef]

Yang, J. K. W.

H. Duan, D. Winston, J. K. W. Yang, B. M. Cord, V. R. Manfrinato, and K. K. Berggren, J. Vac. Sci. Technol. B 28, C6 (2010) and references therein.
[CrossRef]

Zhang, S.

Zhang, X.-H.

Zheludev, N. I.

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

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

J. Opt. Soc. Am. B (2)

J. Vac. Sci. Technol. B (1)

H. Duan, D. Winston, J. K. W. Yang, B. M. Cord, V. R. Manfrinato, and K. K. Berggren, J. Vac. Sci. Technol. B 28, C6 (2010) and references therein.
[CrossRef]

Nat. Mater. (1)

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

Opt. Express (3)

Opt. Lett. (4)

Phys. Rev. (1)

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

Proc. SPIE (1)

M. Soljacic, M. Ibanescu, C. Luo, S. G. Johnson, S. Fan, Y. Fink, and J. D. Joannopoulos, Proc. SPIE 5000200 (2003).
[CrossRef]

Rev. Mod. Phys. (1)

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

Other (3)

H. M. Gibbs, Optical Bistability: Controlling Light with Light (Academic, 1985).

Here we suppose to write the relative permittivity of the medium as ε=εL+χ(3)|E|2 and the intensity as I=(1/2)ε0cnL|E|2. Other conventions also exist where ε=εL+3χ(3)|E|2 and I=2ε0cnL|E|2, in this case we would have had that Re⁡[χ(3)]=4ε0cnL2n2/3 and Im⁡[χ(3)]=ε0cnL2λ3πβ. See, for example, R. L. Sutherland, Handbook of Nonlinear Optics (Marcel Dekker, 1996).

P. Klocek, Handbook of Infrared Optical Materials (Marcel Dekker, 1991)

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Figures (3)

Fig. 1
Fig. 1

(a)  As 2 S 3 grating, thickness d = 200 nm , period Λ = 864 nm , and slit aperture a, grown on a glass substrate with n s = 1.52 . We consider an electromagnetic wave, TE-polarized at normal incidence. (b) Fano resonances in reflection for various slits’ sizes. The Q factors of the resonances are, respectively, Q 7800 for a = 12 nm , Q 2200 for a = 24 nm , and Q 1000 for a = 36 nm .

Fig. 2
Fig. 2

Linear reflection ( R L ) and nonlinear reflection (R) with the onset of optical bistability at different values of the input intensity ( I in ) for the three Fano resonances already described in Fig. 1b.

Fig. 3
Fig. 3

Reflection versus input intensity ( I in ) at different incident wavelengths for the three cases. The dots indicated with S1 and S2 and the corresponding dashed arrows represent, respectively, the switching points of the transition from the stable branch 1 to stable branch 2 (S1) for increasing input intensity and from stable branch 2 to stable branch 1 (S2) for decreasing input intensity.

Equations (1)

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sin ( ϑ ) | ± n WG m λ Λ | , m = 0 , 1 , 2 , ,

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