Abstract

We carry out a theoretical study on optical bistability of near field intensity and transmittance in two-dimensional nonlinear composite slab. This kind of 2D composite is composed of nonlocal metal/Kerr-type dielectric core-shell inclusions randomly embedded in the host medium, and we derivate the nonlinear relation between the field intensity in the shell of inclusions and the incident field intensity with self-consistent mean field approximation. Numerical demonstration has been performed to show the viable parameter space for the bistable near field. We show that nonlocality can provide broader region in geometric parameter space for bistable near field as well as bistable transmittance of the nonlocal composite slab compared to local case. Furthermore, we investigate the bistable transmittance in wavelength spectrum, and find that besides the input intensity, the wavelength operation could as well make the transmittance jump from a high value to a low one. This kind of self-tunable nano-composite slab might have potential application in optical switching devices.

© 2017 Optical Society of America

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References

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  32. R. Rojas, F. Claro, and R. Fuchs, “Nonlocal Response of a Small Coated Sphere,” Phys. Rev. B Condens. Matter 37(12), 6799–6807 (1988).
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    [Crossref] [PubMed]
  34. L. Gao, L. P. Gu, and Y. Y. Huang, “Effective medium approximation for optical bistability in nonlinear metal-dielectric composites,” Solid State Commun. 129(9), 593–598 (2004).
    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
  42. T. V. Teperik, P. Nordlander, J. Aizpurua, and A. G. Borisov, “Robust Subnanometric Plasmon Ruler by Rescaling of the Nonlocal Optical Response,” Phys. Rev. Lett. 110(26), 263901 (2013).
    [Crossref] [PubMed]
  43. L. Gao, “Effective nonlinear response in random mixture of coated granular cylinders,” Phys. Status Solidi 236(1), 182–190 (2003).
    [Crossref]
  44. S. Raza, G. Toscano, A. P. Jauho, M. Wubs, and N. A. Mortensen, “Unusual resonances in nanoplasmonic structures due to nonlocal response,” Phys. Rev. B 84(12), 121412 (2011).
    [Crossref]
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    [Crossref]

2016 (6)

A. V. Krasavin, P. Ginzburg, G. A. Wurtz, and A. V. Zayats, “Nonlocality-driven supercontinuum white light generation in plasmonic nanostructures,” Nat. Commun. 7, 11497 (2016).
[Crossref] [PubMed]

Y. Huang and L. Gao, “Tunable Fano resonances and enhanced optical bistability in composites of coated cylinders due to nonlocality,” Phys. Rev. B 93(23), 235439 (2016).
[Crossref]

H. J. Zhao, Z. H. Li, D. R. Yuan, and W. J. Li, “Optical bistability with low intensity threshold (1.83 MW/cm(2)) in SPPs resonator multilayer nanostructure,” Optik (Stuttg.) 127(7), 3509–3512 (2016).
[Crossref]

Y. Huang, A. E. Miroshnichenko, and L. Gao, “Low-threshold optical bistability of graphene-wrapped dielectric composite,” Sci. Rep. 6, 23354 (2016).
[Crossref] [PubMed]

H. Yuan, X. Jiang, F. Huang, and X. Sun, “Ultralow threshold optical bistability in metal/randomly layered media structure,” Opt. Lett. 41(4), 661–664 (2016).
[Crossref] [PubMed]

H. L. Chen, D. L. Gao, and L. Gao, “Effective nonlinear optical properties and optical bistability in composite media containing spherical particles with different sizes,” Opt. Express 24(5), 5334–5345 (2016).
[Crossref]

2015 (4)

C. Ciracì, M. Scalora, and D. R. Smith, “Third-harmonic generation in the presence of classical nonlocal effects in gap-plasmon nanostructures,” Phys. Rev. B 91(20), 205403 (2015).
[Crossref]

S. Raza, S. Kadkhodazadeh, T. Christensen, M. Di Vece, M. Wubs, N. A. Mortensen, and N. Stenger, “Multipole plasmons and their disappearance in few-nanometre silver nanoparticles,” Nat. Commun. 6, 8788 (2015).
[Crossref] [PubMed]

S. Raza, S. I. Bozhevolnyi, M. Wubs, and N. Asger Mortensen, “Nonlocal optical response in metallic nanostructures,” J. Phys. Condens. Matter 27(18), 183204 (2015).
[Crossref] [PubMed]

W. Yan, “Hydrodynamic theory for quantum plasmonics: Linear-response dynamics of the inhomogeneous electron gas,” Phys. Rev. B 91(11), 115416 (2015).
[Crossref]

2014 (3)

G. Hajisalem, M. S. Nezami, and R. Gordon, “Probing the Quantum Tunneling Limit of Plasmonic Enhancement by Third Harmonic Generation,” Nano Lett. 14(11), 6651–6654 (2014).
[Crossref] [PubMed]

N. A. Mortensen, S. Raza, M. Wubs, T. Søndergaard, and S. I. Bozhevolnyi, “A generalized non-local optical response theory for plasmonic nanostructures,” Nat. Commun. 5, 3809 (2014).
[Crossref] [PubMed]

Y. Huang and L. Gao, “Superscattering of Light from Core-Shell Nonlocal Plasmonic Nanoparticles,” J. Phys. Chem. C 118(51), 30170–30178 (2014).
[Crossref]

2013 (3)

Y. Luo, A. I. Fernandez-Dominguez, A. Wiener, S. A. Maier, and J. B. Pendry, “Surface Plasmons and Nonlocality: A Simple Model,” Phys. Rev. Lett. 111(9), 093901 (2013).
[Crossref] [PubMed]

Y. Huang and L. Gao, “Equivalent Permittivity and Permeability and Multiple Fano Resonances for Nonlocal Metallic Nanowires,” J. Phys. Chem. C 117(37), 19203–19211 (2013).
[Crossref]

T. V. Teperik, P. Nordlander, J. Aizpurua, and A. G. Borisov, “Robust Subnanometric Plasmon Ruler by Rescaling of the Nonlocal Optical Response,” Phys. Rev. Lett. 110(26), 263901 (2013).
[Crossref] [PubMed]

2012 (8)

J. B. Pendry, A. Aubry, D. R. Smith, and S. A. Maier, “Transformation Optics and Subwavelength Control of Light,” Science 337(6094), 549–552 (2012).
[Crossref] [PubMed]

C. Ciracì, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernández-Domínguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the Ultimate Limits of Plasmonic Enhancement,” Science 337(6098), 1072–1074 (2012).
[Crossref] [PubMed]

A. I. Fernández-Domínguez, Y. Luo, A. Wiener, J. B. Pendry, and S. A. Maier, “Theory of Three-Dimensional Nanocrescent Light Harvesters,” Nano Lett. 12(11), 5946–5953 (2012).
[Crossref] [PubMed]

R. Esteban, A. G. Borisov, P. Nordlander, and J. Aizpurua, “Bridging quantum and classical plasmonics with a quantum-corrected model,” Nat. Commun. 3, 825 (2012).
[Crossref] [PubMed]

D. C. Marinica, A. K. Kazansky, P. Nordlander, J. Aizpurua, and A. G. Borisov, “Quantum Plasmonics: Nonlinear Effects in the Field Enhancement of a Plasmonic Nanoparticle Dimer,” Nano Lett. 12(3), 1333–1339 (2012).
[Crossref] [PubMed]

M. Kauranen and A. V. Zayats, “Nonlinear plasmonics,” Nat. Photonics 6(11), 737–748 (2012).
[Crossref]

J. A. Scholl, A. L. Koh, and J. A. Dionne, “Quantum plasmon resonances of individual metallic nanoparticles,” Nature 483(7390), 421–427 (2012).
[Crossref] [PubMed]

J. Sheng, U. Khadka, and M. Xiao, “Realization of all-optical multistate switching in an atomic coherent medium,” Phys. Rev. Lett. 109(22), 223906 (2012).
[Crossref] [PubMed]

2011 (5)

G. A. Wurtz, R. Pollard, W. Hendren, G. P. Wiederrecht, D. J. Gosztola, V. A. Podolskiy, and A. V. Zayats, “Designed ultrafast optical nonlinearity in a plasmonic nanorod metamaterial enhanced by nonlocality,” Nat. Nanotechnol. 6(2), 107–111 (2011).
[Crossref] [PubMed]

C. David and F. J. García de Abajo, “Spatial Nonlocality in the Optical Response of Metal Nanoparticles,” J. Phys. Chem. C 115(40), 19470–19475 (2011).
[Crossref]

L. Novotny and N. van Hulst, “Antennas for light,” Nat. Photonics 5(2), 83–90 (2011).
[Crossref]

S. Raza, G. Toscano, A. P. Jauho, M. Wubs, and N. A. Mortensen, “Unusual resonances in nanoplasmonic structures due to nonlocal response,” Phys. Rev. B 84(12), 121412 (2011).
[Crossref]

M. I. Stockman, “Nanoplasmonics: past, present, and glimpse into future,” Opt. Express 19(22), 22029–22106 (2011).
[Crossref] [PubMed]

2009 (1)

J. M. McMahon, S. K. Gray, and G. C. Schatz, “Nonlocal Optical Response of Metal Nanostructures with Arbitrary Shape,” Phys. Rev. Lett. 103(9), 097403 (2009).
[Crossref] [PubMed]

2008 (2)

F. J. García de Abajo, “Nonlocal Effects in the Plasmons of Strongly Interacting Nanoparticles, Dimers, and Waveguides,” J. Phys. Chem. C 112(46), 17983–17987 (2008).
[Crossref]

X. Hu, P. Jiang, C. Ding, H. Yang, and Q. Gong, “Picosecond and low-power all-optical switching based on an organic photonic-bandgap microcavity,” Nat. Photonics 2(3), 185–189 (2008).
[Crossref]

2006 (1)

G. A. Wurtz, R. Pollard, and A. V. Zayats, “Optical bistability in nonlinear surface-plasmon polaritonic crystals,” Phys. Rev. Lett. 97(5), 057402 (2006).
[Crossref] [PubMed]

2005 (1)

A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, “Nano-optics of surface plasmon polaritons,” Phys. Rep. 408(3–4), 131–314 (2005).
[Crossref]

2004 (1)

L. Gao, L. P. Gu, and Y. Y. Huang, “Effective medium approximation for optical bistability in nonlinear metal-dielectric composites,” Solid State Commun. 129(9), 593–598 (2004).
[Crossref]

2003 (2)

L. Gao, L. Gu, and Z. Li, “Optical bistability and tristability in nonlinear metal/dielectric composite media of nonspherical particles,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 68(6), 066601 (2003).
[Crossref] [PubMed]

L. Gao, “Effective nonlinear response in random mixture of coated granular cylinders,” Phys. Status Solidi 236(1), 182–190 (2003).
[Crossref]

1994 (1)

D. J. Bergman, O. Levy, and D. Stroud, “Theory of optical bistability in a weakly nonlinear composite medium,” Phys. Rev. B Condens. Matter 49(1), 129–134 (1994).
[Crossref] [PubMed]

1988 (1)

R. Rojas, F. Claro, and R. Fuchs, “Nonlocal Response of a Small Coated Sphere,” Phys. Rev. B Condens. Matter 37(12), 6799–6807 (1988).
[Crossref] [PubMed]

1982 (2)

E. Abraham and S. D. Smith, “Optical bistability and related devices,” Rep. Prog. Phys. 45(8), 815–885 (1982).
[Crossref]

Y. R. Shen, “Recent Advances in Optical Bistability,” Nature 299(5886), 779–780 (1982).
[Crossref]

1981 (1)

B. B. Dasgupta and R. Fuchs, “Polarizability of a Small Sphere Including Nonlocal Effects,” Phys. Rev. B 24(2), 554–561 (1981).
[Crossref]

1973 (1)

R. Ruppin, “Optical Properties of a Plasma Sphere,” Phys. Rev. Lett. 31(24), 1434–1437 (1973).
[Crossref]

Abraham, E.

E. Abraham and S. D. Smith, “Optical bistability and related devices,” Rep. Prog. Phys. 45(8), 815–885 (1982).
[Crossref]

Aizpurua, J.

T. V. Teperik, P. Nordlander, J. Aizpurua, and A. G. Borisov, “Robust Subnanometric Plasmon Ruler by Rescaling of the Nonlocal Optical Response,” Phys. Rev. Lett. 110(26), 263901 (2013).
[Crossref] [PubMed]

R. Esteban, A. G. Borisov, P. Nordlander, and J. Aizpurua, “Bridging quantum and classical plasmonics with a quantum-corrected model,” Nat. Commun. 3, 825 (2012).
[Crossref] [PubMed]

D. C. Marinica, A. K. Kazansky, P. Nordlander, J. Aizpurua, and A. G. Borisov, “Quantum Plasmonics: Nonlinear Effects in the Field Enhancement of a Plasmonic Nanoparticle Dimer,” Nano Lett. 12(3), 1333–1339 (2012).
[Crossref] [PubMed]

Asger Mortensen, N.

S. Raza, S. I. Bozhevolnyi, M. Wubs, and N. Asger Mortensen, “Nonlocal optical response in metallic nanostructures,” J. Phys. Condens. Matter 27(18), 183204 (2015).
[Crossref] [PubMed]

Aubry, A.

J. B. Pendry, A. Aubry, D. R. Smith, and S. A. Maier, “Transformation Optics and Subwavelength Control of Light,” Science 337(6094), 549–552 (2012).
[Crossref] [PubMed]

Bergman, D. J.

D. J. Bergman, O. Levy, and D. Stroud, “Theory of optical bistability in a weakly nonlinear composite medium,” Phys. Rev. B Condens. Matter 49(1), 129–134 (1994).
[Crossref] [PubMed]

Borisov, A. G.

T. V. Teperik, P. Nordlander, J. Aizpurua, and A. G. Borisov, “Robust Subnanometric Plasmon Ruler by Rescaling of the Nonlocal Optical Response,” Phys. Rev. Lett. 110(26), 263901 (2013).
[Crossref] [PubMed]

D. C. Marinica, A. K. Kazansky, P. Nordlander, J. Aizpurua, and A. G. Borisov, “Quantum Plasmonics: Nonlinear Effects in the Field Enhancement of a Plasmonic Nanoparticle Dimer,” Nano Lett. 12(3), 1333–1339 (2012).
[Crossref] [PubMed]

R. Esteban, A. G. Borisov, P. Nordlander, and J. Aizpurua, “Bridging quantum and classical plasmonics with a quantum-corrected model,” Nat. Commun. 3, 825 (2012).
[Crossref] [PubMed]

Bozhevolnyi, S. I.

S. Raza, S. I. Bozhevolnyi, M. Wubs, and N. Asger Mortensen, “Nonlocal optical response in metallic nanostructures,” J. Phys. Condens. Matter 27(18), 183204 (2015).
[Crossref] [PubMed]

N. A. Mortensen, S. Raza, M. Wubs, T. Søndergaard, and S. I. Bozhevolnyi, “A generalized non-local optical response theory for plasmonic nanostructures,” Nat. Commun. 5, 3809 (2014).
[Crossref] [PubMed]

Chen, H. L.

Chilkoti, A.

C. Ciracì, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernández-Domínguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the Ultimate Limits of Plasmonic Enhancement,” Science 337(6098), 1072–1074 (2012).
[Crossref] [PubMed]

Christensen, T.

S. Raza, S. Kadkhodazadeh, T. Christensen, M. Di Vece, M. Wubs, N. A. Mortensen, and N. Stenger, “Multipole plasmons and their disappearance in few-nanometre silver nanoparticles,” Nat. Commun. 6, 8788 (2015).
[Crossref] [PubMed]

Ciracì, C.

C. Ciracì, M. Scalora, and D. R. Smith, “Third-harmonic generation in the presence of classical nonlocal effects in gap-plasmon nanostructures,” Phys. Rev. B 91(20), 205403 (2015).
[Crossref]

C. Ciracì, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernández-Domínguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the Ultimate Limits of Plasmonic Enhancement,” Science 337(6098), 1072–1074 (2012).
[Crossref] [PubMed]

Claro, F.

R. Rojas, F. Claro, and R. Fuchs, “Nonlocal Response of a Small Coated Sphere,” Phys. Rev. B Condens. Matter 37(12), 6799–6807 (1988).
[Crossref] [PubMed]

Dasgupta, B. B.

B. B. Dasgupta and R. Fuchs, “Polarizability of a Small Sphere Including Nonlocal Effects,” Phys. Rev. B 24(2), 554–561 (1981).
[Crossref]

David, C.

C. David and F. J. García de Abajo, “Spatial Nonlocality in the Optical Response of Metal Nanoparticles,” J. Phys. Chem. C 115(40), 19470–19475 (2011).
[Crossref]

Di Vece, M.

S. Raza, S. Kadkhodazadeh, T. Christensen, M. Di Vece, M. Wubs, N. A. Mortensen, and N. Stenger, “Multipole plasmons and their disappearance in few-nanometre silver nanoparticles,” Nat. Commun. 6, 8788 (2015).
[Crossref] [PubMed]

Ding, C.

X. Hu, P. Jiang, C. Ding, H. Yang, and Q. Gong, “Picosecond and low-power all-optical switching based on an organic photonic-bandgap microcavity,” Nat. Photonics 2(3), 185–189 (2008).
[Crossref]

Dionne, J. A.

J. A. Scholl, A. L. Koh, and J. A. Dionne, “Quantum plasmon resonances of individual metallic nanoparticles,” Nature 483(7390), 421–427 (2012).
[Crossref] [PubMed]

Esteban, R.

R. Esteban, A. G. Borisov, P. Nordlander, and J. Aizpurua, “Bridging quantum and classical plasmonics with a quantum-corrected model,” Nat. Commun. 3, 825 (2012).
[Crossref] [PubMed]

Fernandez-Dominguez, A. I.

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Figures (6)

Fig. 1
Fig. 1 2D composite compose of core-shell inclusions embedded in the host medium.
Fig. 2
Fig. 2 The average local field E s as a function of the incident field E 0 for various aspect ratios of the core-shell inclusions: (a) η = 0.1 , (b) η = 0.5 and (c) η = 0.7 under nonlocal (red) and local (black) descriptions respectively. The incident wavelength is λ = 340 nm and the outer radius of the inclusion is b = 10 nm .
Fig. 3
Fig. 3 Numbers of real solutions of Eq. (18) in the functions of incident wavelength and aspect ratio in (a) nonlocal and (b) local conditions, respectively. Two real solutions means there existing optical bistability. The outer radii of the inclusions are fixed at b = 10 nm .
Fig. 4
Fig. 4 (a) Transmittance (T) and reflectance (R) spectra of the slab composed of liner composite material with thickness d = 100 nm at normal incidence ( θ = 0 ). Solid and dashed lines denote the nonlocal and local cases respectively. The inserts in (a): (left) | E | 2 s as the function of incident wavelength; (right) the schematic diagram of the model. (b) R and T versus the incident angle θ at λ = 324 nm . The volume factor is f = 0.01 .
Fig. 5
Fig. 5 (a): Dependence of transmittance on external incident field in nonlocal (Red) and local (Black) cases. The incident wavelength λ = 328.5 nm and the aspect ratio η = 0.5 . (b): Switching up and switching down threshold fields for the transmittance of the slab in the function of aspect ratio η at λ = 328.5 nm . Blank space between the upper and lower lines shows the bistable region.
Fig. 6
Fig. 6 Dependence of transmittance on the incident wavelength at different incident field intensity (a) E 0 = 5 × 10 7 V m 1 , (b) E 0 = 10 × 10 7 V m 1 and (c) E 0 = 20 × 10 7 V m 1 . Other parameters are the same as in Fig. (5).

Equations (20)

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V h ( r ) = E 0 ( r D r b 2 ) cos θ .
V s ( r ) = E 0 ( A r + B r a 2 ) cos θ .
D c = 0 × Ε c = 0 ,
D c ( r ) = ε ( r r ' , ω ) E ( r ' ) d 2 r ' .
2 V Dc ( r ) = C δ ( r a ) cos θ ,
D c ( r ) = V Dc ( r ) ,
V Dc ( k ) = i C 2 π a J 1 ( k a ) k 2 cos θ k ,
V Dc ( r ) = C r 2 cos θ .
V c ( r ) = C a cos θ J 1 ( k a ) J 1 ( k r ) k ε ( k , ω ) d k .
V c | r = a = V s | r = a V s | r = b = V h | r = b r V Dc | r = a = ε s r V s | r = a ε s r V s | r = b = ε h r V h | r = b .
( a 1 / a a / [ 2 f ( a , a ) ] 0 b 1 / b 0 1 / b ε s ε s / a 2 1 / 2 0 ε s ε s / b 2 0 ε h / b 2 ) × ( A B C D ) = ( 0 b 0 ε h ) ,
f ( x , y ) = [ 2 y x J 1 ( k x ) J 1 ( k y ) k ε ( k , ω ) d k ] 1 , ( x < y ) .
A = 2 ε h [ ε s + f ( a , a ) ] [ ε s + f ( a , a ) ] ( ε s + ε h ) ( a / b ) 2 [ ε s f ( a , a ) ] ( ε s ε h ) B = 2 ε h [ ε s f ( a , a ) ] [ ε s + f ( a , a ) ] ( ε s + ε h ) ( a / b ) 2 [ ε s f ( a , a ) ] ( ε s ε h ) C = 8 ε h f ( a , a ) ε s [ ε s + f ( a , a ) ] ( ε s + ε h ) ( a / b ) 2 [ ε s f ( a , a ) ] ( ε s ε h ) . D = [ f ( a , a ) + ε s ] ( ε s ε h ) ( a / b ) 2 [ ε s f ( a , a ) ] ( ε s + ε h ) [ ε s + f ( a , a ) ] ( ε s + ε h ) ( a / b ) 2 [ ε s f ( a , a ) ] ( ε s ε h )
ε ˜ s = ε s + χ s | Ε s | 2 .
ε ˜ s ε s + χ s | E | 2 s ,
| E | 2 s = 1 S s S s ( | E s | 2 ) d S = 1 π ( b 2 a 2 ) a b 0 2 π V s * V s r d r d θ , = ( | A | 2 + η 2 | B | 2 ) | E 0 | 2
| E 0 | 2 = | E | 2 s ( | A ˜ | 2 + η 2 | B ˜ | 2 ) .
0 = ( | E | 2 s ( | A ˜ | 2 + η 2 | B ˜ | 2 ) ) / | E | 2 s .
ε e = ε h + 2 f ε h D ˜ ,
R = | k 0 2 k e 2 + ( k e 2 k 0 2 ) e i 2 k e d ( k e + k 0 ) 2 ( k e k 0 ) 2 e i 2 k e d | 2 , T = | k e k 0 4 e i ( k 0 k e ) d ( k e + k 0 ) 2 ( k e k 0 ) 2 e i 2 k e d | 2 ,

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