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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 16, Iss. 12 — Jun. 9, 2008
  • pp: 8421–8426
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Optical bistability in metal gap waveguide nanocavities

Yun Shen and Guo Ping Wang  »View Author Affiliations


Optics Express, Vol. 16, Issue 12, pp. 8421-8426 (2008)
http://dx.doi.org/10.1364/OE.16.008421


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Abstract

Metal-dielectric nanocavities constructed by filling a piece of nonlinear optical material into metal gap waveguides are introduced for realizing optical bistability in nanodomain. Finite-difference time-domain simulation reveal that such a structure can realize optical bistable effect with much weaker operating light power in a nanoscale nonlinear medium. We attribute it to the enhancement of local field intensity and nanoscale confinement of surface plasmon polaritons. Our results verify a feasible way for constructing nanoscale optical logical gates, switches, and all-optical transistors etc. for high density integration of optical circuits.

© 2008 Optical Society of America

1. Introduction

Optical bistability (OB) has attracted much attention since the seminal work of Gibbs in the late 1970s [1

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

] due to its widely potential applications in photonic devices such as optical logical gates, switches, optical regeneration, all-optical transistors, and memories etc [2

2. M. Soljacic, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, “Optimal bistable switching in nonlinear photonic crystals,” Phys. Rev. E 66, 055601(R) (2002). [CrossRef]

]. So far, OB has been theoretically predicted and experimentally demonstrated in various optical systems, including Fabry-Perot (F-P) cavities [1

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

], layered periodic dielectric structures [3

3. H. G. Winful, J. H. Marburger, and E. Garmire, “Theory of bistability in nonlinear distributed feedback structures,” Appl. Phys. Lett. 35, 379–381 (1979). [CrossRef]

], nonlinear prism coupler [4

4. G. I. Stegeman, G. Assanto, R. Zanoni, C. T. Seaton, E. Garmire, A. A. Maradudin, R. Reinisch, and G. Vitrant, “Bistability and switching in nonlinear prism coupling,” Appl. Phys. Lett. 52, 869–871 (1988). [CrossRef]

], and waveguide-ring resonators [5

5. G. Priem, P. Dumon, W. Bogaerts, D. Van Thourhoutm, G. Morthier, and R. Baets, “Optical bistability and pulsating behaviour in Silicon-On-Insulator ring resonator structures,” Opt. Express 13, 9623–9628 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-23-9623. [CrossRef] [PubMed]

]. However, in these systems, both relatively strong light power and/or large enough nonlinear optical material are generally needed to achieve a sizeable nonlinear response. To overcome these drawbacks, photonic crystal cavities [6–7

6. E. Centeno and D. Felbacq, “Optical bistability in finite-size nonlinear bidimensional photonic crystals doped by a microcavity,” Phys. Rev. B 62, R7683–R7686 (2000). [CrossRef]

] and quantum well structures [8

8. X. Chen, “Intrinsic optical intersubband bistability and saturation in a quantum well microcavity structure,” J. Opt. B: Quantum Semiclass. Opt. 1, 524–528 (1999). [CrossRef]

] etc. were proposed to enhance the nonlinear effects so as to reduce the material volume. With the assistance of surface plasmon polaritons (SPPs) to the effects of confining and enhancing the local optical field intensity, OB has also been demonstrated in different metal nanostructures such SPP crystals, metal-dielectric multilayers, and metal gratings etc [9–11

9. G. A. Wurtz, R. Pollard, and A. V. Zayats, “Optical bistability in Nonlinear Surface-Plasmon Polaritonic Crystals,” Phys. Rev. Lett. 97, 057402 (2006). [CrossRef] [PubMed]

].

Recent experimental result shows that SPPs can be confined into two parallel metal films sandwiched SiO2 nanocavities s (≈ 0.001λ3) with much shorter effective wavelength (several tens of nanometers) than that of the incident wavelength in free space [12

12. H. T. Miyazaki and Y. Kurokawa, “Squeezing Visible Light Waves into a 3-nm-Thick and 55-nm-Long Plasmon Cavity,” Phys. Rev. Lett. 96, 097401 (2006). [CrossRef] [PubMed]

]. In terms of this idea, here we introduce an alternative plasmonic nanocavity for realizing the OB effect. The nanocavity is constructed by filling a piece of nonlinear optical medium into the metal gap waveguides (MGWs). Finite-difference time-domain (FDTD) simulations show that this structure can produce obvious OB effect with greatly reduced incident light power in a nanoscale nonlinear optical medium.

2. Design and theory

Fig. 1. Scheme of MGW F-P nanocavities for OB effect.

The proposed structure is schematically shown in Fig. 1. A piece of GaAs layer with thickness w and length L is filled into Ag film-constructed MGWs. Where hm is the thickness of the metal films, ε 1, ε 2, and ε m denote the dielectric constants of air, GaAs, and the metal films, respectively. The Ag-GaAs-Ag waveguide region forms a plasmonic cavity and the interfaces between air and GaAs layer in the MGWs form two mirrors. Hence the structure can function as a F-P cavity. The physics of OB occurred in the F-P cavities is due to the intrinsic positive feedback resulted from the optical Kerr effect [13

13. H. M. Gibbs, S. L. McCall, T. N. C. Venkatesan, A. C. Gossard, A. Passner, and W. Wiegmann, “Optical bistability in semiconductors,” Appl. Phys. Lett. 35, 451–453 (1979). [CrossRef]

].

For an ordinary F-P cavity filled with a nonlinear material, the transmittance T can be written as [14

14. D. A. B. Miller, “Refractive Fabry-Perot Bistability with Linear Absorption: Theory of Operation and Cavity Optimizeion,” IEEE J. Quantum Electron. QE-17, 306–311 (1981). [CrossRef]

]:

T=A11+Fsin2ϕ(I)̅2
(1)

and

T=BI̅Iin
(2)

ϕ(I̅)=4πRe(neff2)·Lλ0
(3)

where λ 0 is the wavelength of the incident light in air, Re(n eff2) is the real part of effective refractive index n eff2 of the cavity to SPPs. The n eff2 can be defined as [16

16. I. P. Kaminow, W. L. Mammel, and H. P. Weber, “Metal-Clad Optical Waveguides: Analytical and Experimental Study,” Appl. Opt. 13, 396–405 (1974). [CrossRef] [PubMed]

, 17

17. B. Wang and G. P. Wang, “Plasmon Bragg reflectors and nanocavities on flat metallic surfaces,” Appl. Phys. Lett. 87, 013107 (2005). [CrossRef]

]:

neff2=βspp2(ε2)k0
(4)

ε2=ε2(0)+Ddχ(3)E2
(5)

Equations (1) and (2) respectively represent a usual periodic Airy function and a linear relations between the transmission T and the average optical intensity . Geometrically, the OB effect can be regarded as the case where the straight line of transmittance from Eq. (2) has multiple intersections with the periodic Ariy curve from Eq. (1). By changing Iin one can modulate the transmission to produce multiple intersections between the curves and straight line from Eqs. (1) and (2), respectively.

Generally,, n eff2 of the interface between metals and dielectrics to SPPs is much lager than (ε 2)1/2 of the dielectrics [20

20. B. Wang and G. Ping Wang, “Metal heterowaveguides for nanometric focusing of light,” Appl. Phys. Lett. 85, 3599–3601 (2004). [CrossRef]

]. Therefore, the n eff2 is more sensitive to the change of ε 2, and so the nanocavity structure provides a feasible way to achieve sufficiently strong nonlinear response in a nonlinear medium with small size and low operating light power [From Eq. (1) and Eqs. (3) – (5)].

3. Simulation and discussion

In the following, we perform FDTD numerical simulations to demonstrate the OB property of the plasmonic nanostructures, where w=30 nm, L=300 nm, hm=150 nm, ε 1=1, Dd=3, and χ (3)=6.5×10-4 esu (9.0757×10-12 (m/V)2) [15

15. R. W. Boyd, Nonlinear Optics (Academic, New York, 1992).

]. ε (0) 2 of the GaAs is from the measured values [21

21. E. D. Palik, Handbook of Optical Constants of Solids (Academic, London, 1985).

], which is from 13.8425 to 12.2657 in the wavelength range of from 750 nm to 1010 nm [21

21. E. D. Palik, Handbook of Optical Constants of Solids (Academic, London, 1985).

, 22

22. T. Skauli, P. S. Kuo, K. L. Vodopyanov, T. J. Pinguet, O. Levi, L. A. Eyres, J. S. Harris, and M. M. Fejer, “Improved dispersion relations for GaAs and applications to nonlinear optics,” J. Appl. Phys. 94, 6447–6455 (2003). [CrossRef]

]. The dielectric function of Ag films is deduced from the fitting of the measured values in the visible and near-infrared range by using the Drude model [21

21. E. D. Palik, Handbook of Optical Constants of Solids (Academic, London, 1985).

] εm=ε -ω 2 p/(ω 2+jγω) with (ε , ωp, γ) (1, 7.75 eV, 0.08267 eV). The incident light used to excite SPPs is a TM-polarized (the magnetic field is parallel to the z axis) plane wave. It should be noted that as w=30 nm, our calculated results (not shown here) reveal that SPPs excited by the frequencies of the illuminating field above a vacuum wavelength of 623 nm would not be supported in the GaAs region due to the absence of coupling between the SPPs on the surfaces of two Ag films. Therefore, in our case, we choose the excitation wavelength beyond 700 nm so as to achieve the observable plasmonic bistability. In the FDTD simulation, the spatial and temporal steps are set at Δx=4 nm, Δy=2 nm, and Δty/2c, respectively, and the magnetic field intensity |Hz|2 in (|Hz|2 out) at the center of a plane outside the F-P cavity 8 nm (1 nm) away from the front (back) mirror is used to represent the optical field intensity of the incident light Iin (output light Iout).

Fig. 2. Transmission spectra of MGW F-P nanocavities as the |Hz|2 in of the incident light is (a) 1.18 (A/m)2, (b) 4.73×105 (A/m)2, (c) 1.06×106 (A/m)2, respectively.

Figure 2 shows the calculated transmission spectra of the F-P cavity structure as the incident wavelength is in the range of from 750 nm to 1010 nm. Optical field intensity of the incident light |Hz|2 in is assumed to be (a) 1.18 (A/m)2, (b) 4.73×105 (A/m)2, (c) 1.06×106 (A/m)2, respectively. The transmittance T is defined as |Hz|2 out/|Hz|2 in. From the figure we see that the transmission peaks show a red shift and become to be more asymmetric with the increasing intensity of the incident light, indicating the feasible of OB effect [5

5. G. Priem, P. Dumon, W. Bogaerts, D. Van Thourhoutm, G. Morthier, and R. Baets, “Optical bistability and pulsating behaviour in Silicon-On-Insulator ring resonator structures,” Opt. Express 13, 9623–9628 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-23-9623. [CrossRef] [PubMed]

, 13

13. H. M. Gibbs, S. L. McCall, T. N. C. Venkatesan, A. C. Gossard, A. Passner, and W. Wiegmann, “Optical bistability in semiconductors,” Appl. Phys. Lett. 35, 451–453 (1979). [CrossRef]

]. This can be understood from the following analysis. On the one hand, when the intensity of the incident light is increased, the dielectric constant ε 2 of nonlinear medium (GaAs) will increase due to the Kerr effect [Eq. (5)]. Correspondingly, the effective refractive index n eff2 of F-P cavity to SPPs will increase [Eq. (4)], which results in the phase shift ϕ of the light field in the cavity [Eq. (3)]. On the other hand, a higher input light intensity will produce a stronger electric field intensity in the nonlinear medium, which results in the increase of both the dielectric constant ε 2 of nonlinear material [Eq. (5)] and the effective refractive index n eff2 of the cavity to SPPs [Eq. (4)]. As a result, the transmission peak (corresponding to a fixed phase ϕ) will shift to longer wavelength [Eq. (3)]. In addition, from Eqs. (1) and (3) we see that the transmittance T shows a nonlinear dependence on the phase ϕ and hence on the wavelength of the incident light. Consequently, more asymmetric shape of transmission peaks appears in transmission spectra at longer wavelengths as the intensity of the incident light is increased (Fig. 2).

Fig. 3. Output-input intensity relation of MGW F-P nanocavities as the incident light is with wavelength λ0=(a) 860 nm, (b) 870 nm, (c) 880 nm, (d) 956 nm, (e) 966 nm, and (f) 976 nm, respectively. Inset, magnified view of the hysteresis loop as the incident light is with λ0=976 nm.

Figure 3 displays the output-input intensity relation of the SPP cavity as the intensity of the incident light with wavelength λ0=(a) 860 nm, (b) 870 nm, (c) 880 nm, (d) 956 nm, (e) 966 nm, and (f) 976 nm is increased and decreased, respectively. The figure shows a series of hysteresis loops, manifesting the occurrence of OB around different incident wavelengths. For instance, as the incident light is with λ0=976 nm, we can see that the OB occurs as the light intensity is around |Hz|2 in=1.18×106 (A/m)2, corresponding to Iin=37.14 kW/cm 2 [Inset of Fig. 3]. The occurrence of the hysteresis loops means that the transmission spectra resulted from Eqs. (1) and (2) show two intersections around λ0=976 nm. On the other hand, Fig. 3 shows that there are two sets of hysteresis loops in the output-input intensity relation of the plasmonic cavity. The lower set corresponds to three weaker transmission peaks while the upper one to three stronger peaks of Fig. 2. And furthermore, only around the asymmetric transmission peaks are the hysteresis loops formed. The stronger the asymmetry of the transmission peaks, the larger the hysteresis loops [13

13. H. M. Gibbs, S. L. McCall, T. N. C. Venkatesan, A. C. Gossard, A. Passner, and W. Wiegmann, “Optical bistability in semiconductors,” Appl. Phys. Lett. 35, 451–453 (1979). [CrossRef]

, 23

23. P. Wen, M. Sanchez, M. Gross, and S. Esener, “Observation of bistability in a Vertical-Cavity Semiconductor Optical Amplifier (VCSOA),” Opt. Express 10, 1273–1278 (2002). [PubMed]

, 24

24. J. A. Porto, L. Martin-Moreno, and F. J. Garcia-Vidal, “Optical bistability in subwavelength slit apertures containing nonlinear media,” Phys. Rev. B 70, 081402(R) (2004). [CrossRef]

].

Regarding to the OB effect observed in conventional metal-dielectric optical systems, we see that much stronger incident power and/or larger nonlinear optical materials are needed. For instance, a metal-dielectric multilayer structure requires 2.5 GW/cm 2 light power and 1.17 µm thick nonlinear materials for obtaining a visible nonlinear response [10

10. A. Husakou and J. Herrmann, “Steplike Transmission of Light through a Metal-Dielectric Multilayer Structure due to an Intensity-Dependent Sign of the Effective Dielectric Constant,” Phys. Rev. Lett. 99, 127402 (2007). [CrossRef] [PubMed]

], while a metallic grating coated with about 880 nm thick nonlinear materials requires more than 1×1016 (V 2/m 2) (Iin=1.33 GW/cm 2) light power to achieve the OB [11

11. C. J. Min, P. Wang, X. J. Jiao, Y. Deng, and H. Ming, “Optical bistability in subwavelength metallic grating coated by nonlinear material,” Opt. Express 15, 12368–12373 (2007), http://www.opticsexpress.org/abstract.cfm?uri=OE-15-19-12368. [CrossRef] [PubMed]

]. In contrast, in our case, only about Iin=37.14 kW/cm 2 light power and 300 nm long nonlinear medium can realize a remarkable plasmonic bistability at λ0=976 nm.

4. Conclusion

Acknowledgments

This work is financially supported by the National Basic Research Program (Grant No. 2007CB935300), NSFC (Grant Nos. 10774116, 60736041, and 10574101) and the program of NCET (Grant No. 04-0678).

References and links

1.

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

2.

M. Soljacic, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, “Optimal bistable switching in nonlinear photonic crystals,” Phys. Rev. E 66, 055601(R) (2002). [CrossRef]

3.

H. G. Winful, J. H. Marburger, and E. Garmire, “Theory of bistability in nonlinear distributed feedback structures,” Appl. Phys. Lett. 35, 379–381 (1979). [CrossRef]

4.

G. I. Stegeman, G. Assanto, R. Zanoni, C. T. Seaton, E. Garmire, A. A. Maradudin, R. Reinisch, and G. Vitrant, “Bistability and switching in nonlinear prism coupling,” Appl. Phys. Lett. 52, 869–871 (1988). [CrossRef]

5.

G. Priem, P. Dumon, W. Bogaerts, D. Van Thourhoutm, G. Morthier, and R. Baets, “Optical bistability and pulsating behaviour in Silicon-On-Insulator ring resonator structures,” Opt. Express 13, 9623–9628 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-23-9623. [CrossRef] [PubMed]

6.

E. Centeno and D. Felbacq, “Optical bistability in finite-size nonlinear bidimensional photonic crystals doped by a microcavity,” Phys. Rev. B 62, R7683–R7686 (2000). [CrossRef]

7.

M. G. Banaee, A. R. Cowan, and J. F. Young, “Third-order nonlinear influence on the specular reflectivity of two-dimensional waveguide-based photonic crystals,” J. Opt. Soc. Am. B. 19, 2224–2231 (2002). [CrossRef]

8.

X. Chen, “Intrinsic optical intersubband bistability and saturation in a quantum well microcavity structure,” J. Opt. B: Quantum Semiclass. Opt. 1, 524–528 (1999). [CrossRef]

9.

G. A. Wurtz, R. Pollard, and A. V. Zayats, “Optical bistability in Nonlinear Surface-Plasmon Polaritonic Crystals,” Phys. Rev. Lett. 97, 057402 (2006). [CrossRef] [PubMed]

10.

A. Husakou and J. Herrmann, “Steplike Transmission of Light through a Metal-Dielectric Multilayer Structure due to an Intensity-Dependent Sign of the Effective Dielectric Constant,” Phys. Rev. Lett. 99, 127402 (2007). [CrossRef] [PubMed]

11.

C. J. Min, P. Wang, X. J. Jiao, Y. Deng, and H. Ming, “Optical bistability in subwavelength metallic grating coated by nonlinear material,” Opt. Express 15, 12368–12373 (2007), http://www.opticsexpress.org/abstract.cfm?uri=OE-15-19-12368. [CrossRef] [PubMed]

12.

H. T. Miyazaki and Y. Kurokawa, “Squeezing Visible Light Waves into a 3-nm-Thick and 55-nm-Long Plasmon Cavity,” Phys. Rev. Lett. 96, 097401 (2006). [CrossRef] [PubMed]

13.

H. M. Gibbs, S. L. McCall, T. N. C. Venkatesan, A. C. Gossard, A. Passner, and W. Wiegmann, “Optical bistability in semiconductors,” Appl. Phys. Lett. 35, 451–453 (1979). [CrossRef]

14.

D. A. B. Miller, “Refractive Fabry-Perot Bistability with Linear Absorption: Theory of Operation and Cavity Optimizeion,” IEEE J. Quantum Electron. QE-17, 306–311 (1981). [CrossRef]

15.

R. W. Boyd, Nonlinear Optics (Academic, New York, 1992).

16.

I. P. Kaminow, W. L. Mammel, and H. P. Weber, “Metal-Clad Optical Waveguides: Analytical and Experimental Study,” Appl. Opt. 13, 396–405 (1974). [CrossRef] [PubMed]

17.

B. Wang and G. P. Wang, “Plasmon Bragg reflectors and nanocavities on flat metallic surfaces,” Appl. Phys. Lett. 87, 013107 (2005). [CrossRef]

18.

R. M. Joseph and A. Taflove, “FDTD Maxwell’s Equations Models for Nonlinear Electrodynamics and Optics,” IEEE Trans. Antennas Propag. 45, 364–374 (1997). [CrossRef]

19.

S. Martellucci and A. N. Chester, Integrated Optics Physics and Applications (Plenum, New York, 1983).

20.

B. Wang and G. Ping Wang, “Metal heterowaveguides for nanometric focusing of light,” Appl. Phys. Lett. 85, 3599–3601 (2004). [CrossRef]

21.

E. D. Palik, Handbook of Optical Constants of Solids (Academic, London, 1985).

22.

T. Skauli, P. S. Kuo, K. L. Vodopyanov, T. J. Pinguet, O. Levi, L. A. Eyres, J. S. Harris, and M. M. Fejer, “Improved dispersion relations for GaAs and applications to nonlinear optics,” J. Appl. Phys. 94, 6447–6455 (2003). [CrossRef]

23.

P. Wen, M. Sanchez, M. Gross, and S. Esener, “Observation of bistability in a Vertical-Cavity Semiconductor Optical Amplifier (VCSOA),” Opt. Express 10, 1273–1278 (2002). [PubMed]

24.

J. A. Porto, L. Martin-Moreno, and F. J. Garcia-Vidal, “Optical bistability in subwavelength slit apertures containing nonlinear media,” Phys. Rev. B 70, 081402(R) (2004). [CrossRef]

OCIS Codes
(190.1450) Nonlinear optics : Bistability
(230.7370) Optical devices : Waveguides
(240.6680) Optics at surfaces : Surface plasmons
(260.3910) Physical optics : Metal optics

ToC Category:
Nonlinear Optics

History
Original Manuscript: April 16, 2008
Revised Manuscript: May 13, 2008
Manuscript Accepted: May 13, 2008
Published: May 23, 2008

Citation
Yun Shen and Guo Ping Wang, "Optical bistability in metal gap waveguide nanocavities," Opt. Express 16, 8421-8426 (2008)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-12-8421


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References

  1. H. M. Gibbs, Optical Bistability: Controlling Light with Light (Academic, New York, 1985).
  2. M. Soljacic, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, "Optimal bistable switching in nonlinear photonic crystals," Phys. Rev. E 66, 055601(R) (2002).. H. G. Winful, J. H. Marburger, and E. Garmire, "Theory of bistability in nonlinear distributed feedback structures," Appl. Phys. Lett. 35, 379-381 (1979). [CrossRef]
  3. G. I. Stegeman, G. Assanto, R. Zanoni, C. T. Seaton, E. Garmire, A. A. Maradudin, R. Reinisch, and G. Vitrant, "Bistability and switching in nonlinear prism coupling," Appl. Phys. Lett. 52, 869-871 (1988). [CrossRef]
  4. G. Priem, P. Dumon, W. Bogaerts, D. Van Thourhoutm, G. Morthier, and R. Baets, "Optical bistability and pulsating behaviour in Silicon-On-Insulator ring resonator structures," Opt. Express 13, 9623-9628 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-23-9623. [CrossRef]
  5. E. Centeno and D. Felbacq, "Optical bistability in finite-size nonlinear bidimensional photonic crystals doped by a microcavity," Phys. Rev. B 62, R7683-R7686 (2000). [CrossRef] [PubMed]
  6. M. G. Banaee, A. R. Cowan, and J. F. Young, "Third-order nonlinear influence on the specular reflectivity of two-dimensional waveguide-based photonic crystals," J. Opt. Soc. Am. B. 19, 2224-2231 (2002). [CrossRef]
  7. X. Chen, "Intrinsic optical intersubband bistability and saturation in a quantum well microcavity structure," J. Opt. B: Quantum Semiclass. Opt. 1, 524-528 (1999). [CrossRef]
  8. G. A. Wurtz, R. Pollard, and A. V. Zayats, "Optical bistability in Nonlinear Surface-Plasmon Polaritonic Crystals," Phys. Rev. Lett. 97, 057402 (2006). [CrossRef]
  9. A. Husakou and J. Herrmann, "Steplike Transmission of Light through a Metal-Dielectric Multilayer Structure due to an Intensity-Dependent Sign of the Effective Dielectric Constant," Phys. Rev. Lett. 99, 127402 (2007). [CrossRef] [PubMed]
  10. C. J. Min, P. Wang, X. J. Jiao, Y. Deng, and H. Ming, "Optical bistability in subwavelength metallic grating coated by nonlinear material," Opt. Express 15, 12368-12373 (2007), http://www.opticsexpress.org/abstract.cfm?uri=OE-15-19-12368. [CrossRef] [PubMed]
  11. H. T. Miyazaki and Y. Kurokawa, "Squeezing Visible Light Waves into a 3-nm-Thick and 55-nm-Long Plasmon Cavity," Phys. Rev. Lett. 96, 097401 (2006). [CrossRef] [PubMed]
  12. H. M. Gibbs, S. L. McCall, T. N. C. Venkatesan, A. C. Gossard, A. Passner, and W. Wiegmann, "Optical bistability in semiconductors," Appl. Phys. Lett. 35, 451-453 (1979). [CrossRef] [PubMed]
  13. D. A. B. Miller, "Refractive Fabry-Perot Bistability with Linear Absorption: Theory of Operation and Cavity Optimizeion," IEEE J. Quantum Electron. QE- 17, 306-311 (1981). [CrossRef]
  14. R. W. Boyd, Nonlinear Optics (Academic, New York, 1992). [CrossRef]
  15. I. P. Kaminow, W. L. Mammel, and H. P. Weber, "Metal-Clad Optical Waveguides: Analytical and Experimental Study," Appl. Opt. 13, 396-405 (1974).
  16. B. Wang and G. P. Wang, "Plasmon Bragg reflectors and nanocavities on flat metallic surfaces," Appl. Phys. Lett. 87, 013107 (2005). [CrossRef] [PubMed]
  17. R. M. Joseph and A. Taflove, "FDTD Maxwell?s Equations Models for Nonlinear Electrodynamics and Optics," IEEE Trans. Antennas Propag. 45, 364-374 (1997). [CrossRef]
  18. S. Martellucci and A. N. Chester, Integrated Optics Physics and Applications (Plenum, New York, 1983). [CrossRef]
  19. B. Wang and G. Ping Wang, "Metal heterowaveguides for nanometric focusing of light," Appl. Phys. Lett. 85, 3599-3601 (2004).
  20. E. D. Palik, Handbook of Optical Constants of Solids (Academic, London, 1985). [CrossRef]
  21. T. Skauli, P. S. Kuo, K. L. Vodopyanov, T. J. Pinguet, O. Levi, L. A. Eyres, J. S. Harris, and M. M. Fejer, "Improved dispersion relations for GaAs and applications to nonlinear optics," J. Appl. Phys. 94, 6447-6455 (2003).
  22. P. Wen, M. Sanchez, M. Gross, and S. Esener, "Observation of bistability in a Vertical-Cavity Semiconductor Optical Amplifier (VCSOA)," Opt. Express 10, 1273-1278 (2002). [CrossRef]
  23. J. A. Porto, L. Martin-Moreno, and F. J. Garcia-Vidal, "Optical bistability in subwavelength slit apertures containing nonlinear media," Phys. Rev. B 70, 081402(R) (2004). [PubMed]

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