Analytical model for optical bistability in nonlinear metal nano-antennae involving Kerr materials

doi:10.1364/OE.18.013337

Analytical model for optical bistability in nonlinear metal nano-antennae involving Kerr materials

Fei Zhou, Ye Liu, Zhi-Yuan Li, and Younan Xia »View Author Affiliations

Optics Express, Vol. 18, Issue 13, pp. 13337-13344 (2010)
http://dx.doi.org/10.1364/OE.18.013337

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Abstract

Optical bistability at nanoscale is a promising way to realize optical switching, a key component of integrated nanophotonic devices. In this work we present an analytical model for optical bistability in a metal nano-antenna involving Kerr nonlinear medium based on detailed analysis of the correlation between the incident and extinction light intensity under surface plasmon resonance (SPR). The model allows one to construct a clear picture on how the threshold, contrast, and other characteristics of optical bistability are influenced by the nonlinear coefficient, incident light intensity, local field enhancement factor, SPR peak width, and other physical parameters of the nano-antenna. It shows that the key towards low threshold power and high contrast optical bistability in the nanosystem is to reduce the SPR peak width. This can be achieved by reducing the absorption of metal materials or introducing gain media into nanosystems.

OCIS Codes
(190.1450) Nonlinear optics : Bistability
(190.3270) Nonlinear optics : Kerr effect
(240.6680) Optics at surfaces : Surface plasmons

ToC Category:
Nonlinear Optics

History
Original Manuscript: April 16, 2010
Revised Manuscript: May 22, 2010
Manuscript Accepted: May 25, 2010
Published: June 7, 2010

Citation
Fei Zhou, Ye Liu, Zhi-Yuan Li, and Younan Xia, "Analytical model for optical bistability in nonlinear metal nano-antennae involving Kerr materials," Opt. Express 18, 13337-13344 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-13-13337

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References

H. M. Gibbs, Optical Bistability: Controlling Light with Light, Quantum electronics–principles and applications (Academic Press, 1985)
H. Nihei and A. Okamoto, “Photonic crystal systems for high-speed optical memory device on an atomic scale,” Proc. SPIE 4416, 470–473 (2001). [CrossRef]
G. Assanto, Z. Wang, D. J. Hagan, and E. W. Vanstryland, “All-optical modulation via nonlinear cascading in type II second-harmonic generation,” Appl. Phys. Lett. 67(15), 2120–2122 (1995). [CrossRef]
D. A. Mazurenko, R. Kerst, J. I. Dijkhuis, A. V. Akimov, V. G. Golubev, D. A. Kurdyukov, A. B. Pevtsov, and A. V. Sel’kin, “Ultrafast optical switching in three-dimensional photonic crystals,” Phys. Rev. Lett. 91(21), 213903 (2003). [CrossRef] [PubMed]
G. Priem, P. Dumon, W. Bogaerts, D. Van Thourhout, G. Morthier, and R. Baets, “Optical bistability and pulsating behaviour in silicon-on-insulator ring resonator structures,” Opt. Express 13(23), 9623–9628 (2005). [CrossRef] [PubMed]
F. Y. Wang, G. X. Li, H. L. Tam, K. W. Cheah, and S. N. Zhu, “Optical bistability and multistability in one-dimensional periodic metal-dielectric photonic crystal,” Appl. Phys. Lett. 92(21), 211109 (2008). [CrossRef]
M. F. Yanik, S. H. Fan, and M. Soljacic, “High-contrast all-optical bistable switching in photonic crystal microcavities,” Appl. Phys. Lett. 83(14), 2739–2741 (2003). [CrossRef]
M. F. Yanik, S. H. Fan, M. Soljacić, and J. D. Joannopoulos, “All-optical transistor action with bistable switching in a photonic crystal cross-waveguide geometry,” Opt. Lett. 28(24), 2506–2508 (2003). [CrossRef] [PubMed]
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]
C. J. Min, P. Wang, C. C. Chen, Y. Deng, Y. H. Lu, H. Ming, T. Y. Ning, Y. L. Zhou, and G. Z. Yang, “All-optical switching in subwavelength metallic grating structure containing nonlinear optical materials,” Opt. Lett. 33(8), 869–871 (2008). [CrossRef] [PubMed]
Y. Shen and G. P. Wang, “Optical bistability in metal gap waveguide nanocavities,” Opt. Express 16(12), 8421–8426 (2008). [CrossRef] [PubMed]
N. Large, M. Abb, J. Aizpurua, and O. L. Muskens, “Photoconductively loaded plasmonic nanoantenna as building block for ultracompact optical switches,” Nano Lett. 10(5), 1741–1746 (2010). [CrossRef] [PubMed]
P. Mühlschlegel, H. J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308(5728), 1607–1609 (2005). [CrossRef] [PubMed]
O. L. Muskens, V. Giannini, J. A. Sánchez-Gil, and J. Gómez Rivas, “Strong enhancement of the radiative decay rate of emitters by single plasmonic nanoantennas,” Nano Lett. 7(9), 2871–2875 (2007). [CrossRef] [PubMed]
J. W. Liaw, “Analysis of a bowtie nanoantenna for the enhancement of spontaneous emission,” IEEE J. Sel. Top. Quantum Electron. 14(6), 1441–1447 (2008). [CrossRef]
Y. Liu, F. Qin, F. Zhou, and Z. Y. Li, “Ultrafast and low-power photonic crystal all-optical switching with resonant cavities,” J. Appl. Phys. 106(8), 083102 (2009). [CrossRef]
B. T. Draine and P. J. Flatau, “Discrete-dipole approximation for scattering calculations,” J. Opt. Soc. Am. A 11(4), 1491–1499 (1994). [CrossRef]
F. Zhou, Z. Y. Li, Y. Liu, and Y. N. Xia, “Quantitative analysis of dipole and quadrupole excitation in the surface plasmon resonance of metal nanoparticles,” J. Phys. Chem. C 112(51), 20233–20240 (2008). [CrossRef]
A. Alù and N. Engheta, “Tuning the scattering response of optical nanoantennas with nanocircuit loads,” Nat. Photonics 2(5), 307–310 (2008). [CrossRef]
J. Berthelot, A. Bouhelier, C. Huang, J. Margueritat, G. Colas-des-Francs, E. Finot, J.-C. Weeber, A. Dereux, S. Kostcheev, H. I. E. Ahrach, A.-L. Baudrion, J. Plain, R. Bachelot, P. Royer, and G. P. Wiederrecht, “Tuning of an optical dimer nanoantenna by electrically controlling its load impedance,” Nano Lett. 9(11), 3914–3921 (2009). [CrossRef] [PubMed]
Z. Y. Li and Y. N. Xia, “Metal nanoparticles with gain toward single-molecule detection by surface-enhanced Raman scattering,” Nano Lett. 10(1), 243–249 (2010). [CrossRef]

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[1] H. M. Gibbs, Optical Bistability: Controlling Light with Light, Quantum electronics–principles and applications (Academic Press, 1985)

[2] H. Nihei and A. Okamoto, “Photonic crystal systems for high-speed optical memory device on an atomic scale,” Proc. SPIE 4416, 470–473 (2001). [CrossRef]

[3] G. Assanto, Z. Wang, D. J. Hagan, and E. W. Vanstryland, “All-optical modulation via nonlinear cascading in type II second-harmonic generation,” Appl. Phys. Lett. 67(15), 2120–2122 (1995). [CrossRef]

[4] D. A. Mazurenko, R. Kerst, J. I. Dijkhuis, A. V. Akimov, V. G. Golubev, D. A. Kurdyukov, A. B. Pevtsov, and A. V. Sel’kin, “Ultrafast optical switching in three-dimensional photonic crystals,” Phys. Rev. Lett. 91(21), 213903 (2003). [CrossRef] [PubMed]

[5] G. Priem, P. Dumon, W. Bogaerts, D. Van Thourhout, G. Morthier, and R. Baets, “Optical bistability and pulsating behaviour in silicon-on-insulator ring resonator structures,” Opt. Express 13(23), 9623–9628 (2005). [CrossRef] [PubMed]

[6] F. Y. Wang, G. X. Li, H. L. Tam, K. W. Cheah, and S. N. Zhu, “Optical bistability and multistability in one-dimensional periodic metal-dielectric photonic crystal,” Appl. Phys. Lett. 92(21), 211109 (2008). [CrossRef]

[7] M. F. Yanik, S. H. Fan, and M. Soljacic, “High-contrast all-optical bistable switching in photonic crystal microcavities,” Appl. Phys. Lett. 83(14), 2739–2741 (2003). [CrossRef]

[8] M. F. Yanik, S. H. Fan, M. Soljacić, and J. D. Joannopoulos, “All-optical transistor action with bistable switching in a photonic crystal cross-waveguide geometry,” Opt. Lett. 28(24), 2506–2508 (2003). [CrossRef] [PubMed]

[9] 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]

[10] C. J. Min, P. Wang, C. C. Chen, Y. Deng, Y. H. Lu, H. Ming, T. Y. Ning, Y. L. Zhou, and G. Z. Yang, “All-optical switching in subwavelength metallic grating structure containing nonlinear optical materials,” Opt. Lett. 33(8), 869–871 (2008). [CrossRef] [PubMed]

[11] Y. Shen and G. P. Wang, “Optical bistability in metal gap waveguide nanocavities,” Opt. Express 16(12), 8421–8426 (2008). [CrossRef] [PubMed]

[12] N. Large, M. Abb, J. Aizpurua, and O. L. Muskens, “Photoconductively loaded plasmonic nanoantenna as building block for ultracompact optical switches,” Nano Lett. 10(5), 1741–1746 (2010). [CrossRef] [PubMed]

[13] P. Mühlschlegel, H. J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308(5728), 1607–1609 (2005). [CrossRef] [PubMed]

[14] O. L. Muskens, V. Giannini, J. A. Sánchez-Gil, and J. Gómez Rivas, “Strong enhancement of the radiative decay rate of emitters by single plasmonic nanoantennas,” Nano Lett. 7(9), 2871–2875 (2007). [CrossRef] [PubMed]

[15] J. W. Liaw, “Analysis of a bowtie nanoantenna for the enhancement of spontaneous emission,” IEEE J. Sel. Top. Quantum Electron. 14(6), 1441–1447 (2008). [CrossRef]

[16] Y. Liu, F. Qin, F. Zhou, and Z. Y. Li, “Ultrafast and low-power photonic crystal all-optical switching with resonant cavities,” J. Appl. Phys. 106(8), 083102 (2009). [CrossRef]

[17] B. T. Draine and P. J. Flatau, “Discrete-dipole approximation for scattering calculations,” J. Opt. Soc. Am. A 11(4), 1491–1499 (1994). [CrossRef]

[18] F. Zhou, Z. Y. Li, Y. Liu, and Y. N. Xia, “Quantitative analysis of dipole and quadrupole excitation in the surface plasmon resonance of metal nanoparticles,” J. Phys. Chem. C 112(51), 20233–20240 (2008). [CrossRef]

[19] A. Alù and N. Engheta, “Tuning the scattering response of optical nanoantennas with nanocircuit loads,” Nat. Photonics 2(5), 307–310 (2008). [CrossRef]

[20] J. Berthelot, A. Bouhelier, C. Huang, J. Margueritat, G. Colas-des-Francs, E. Finot, J.-C. Weeber, A. Dereux, S. Kostcheev, H. I. E. Ahrach, A.-L. Baudrion, J. Plain, R. Bachelot, P. Royer, and G. P. Wiederrecht, “Tuning of an optical dimer nanoantenna by electrically controlling its load impedance,” Nano Lett. 9(11), 3914–3921 (2009). [CrossRef] [PubMed]

[21] Z. Y. Li and Y. N. Xia, “Metal nanoparticles with gain toward single-molecule detection by surface-enhanced Raman scattering,” Nano Lett. 10(1), 243–249 (2010). [CrossRef]

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Analytical model for optical bistability in nonlinear metal nano-antennae involving Kerr materials