Optical bistability in metal-insulator-metal plasmonic waveguide with nanodisk resonator containing Kerr nonlinear medium Guoxi Wang, Hua Lu, Xueming Liu,* Yongkang Gong, and Leiran Wang State Key Laboratory of Transient Optics and Photonics, Xi’an Institute of Optics and Precision Mechanics, Chinese Academy of Sciences, Xi’an 710119, China *Corresponding author:
[email protected] Received 22 April 2011; revised 19 June 2011; accepted 28 July 2011; posted 8 August 2011 (Doc. ID 146375); published 15 September 2011
We numerically investigate the optical bistability effect in the metal-insulator-metal waveguide with a nanodisk resonator containing a Kerr nonlinear medium. It is found that the increase of the refractive index, which is induced by enhancing the incident intensity, can cause a redshift for the resonance wavelength. The local resonant field excited in the nanodisk cavity can significantly increase the Kerr nonlinear effect. In addition, an obvious bistability loop is observed in the proposed structure. This nonlinear structure can find important applications for all-optical switching in highly integrated optical circuits. © 2011 Optical Society of America OCIS codes: 240.6680, 190.1450, 140.4780, 130.3120.
1. Introduction
Surface plasmon polaritons (SPPs) are electromagnetic waves that propagate along a metal-dielectric interface with an exponentially decaying field in both sides and are coupled to the free electrons in the metal. The unique properties of SPPs are overcoming the diffraction limit in conventional optics and the ability of light manipulation on the subwavelength scale [1,2]. The characteristics of SPPs can be easily tailored by changing the structure of metallic surfaces, which provides the potential for developing types of photonic devices [2]. In recent years, numerous devices based on SPPs have been numerically investigated and experimentally demonstrated, such as Bragg reflectors [3–5], wavelength demultiplexers [6,7], filters [8,9], Mach–Zehnder interferometers [10,11], Y-shaped combiners [12], couplers [13], splitters [14], superlens [15], and sensors [16,17]. As an important optical phenomenon, nonlinear optics has attracted increasing interest and atten0003-6935/11/275287-04$15.00/0 © 2011 Optical Society of America
tion of scientists. Some devices based on nonlinear materials have been investigated, such as all-optical switching [18], modulators [19], and amplifiers [20]. Nowadays, achieving active control signals in nanoscale devices has been a great challenge [21]. As an exciting new technology, SPPs exploit the unique optical properties of metallic nanostructures to realize the miniature of optical components [1,2,22]. Nonlinear optical devices based on subwavelength metallic structures have been proposed and investigated, such as metallic nano-optic lens [23], subwavelength metallic grating [24], and nonlinear SPPs crystals [25]. All-optical signal processing in integrated photonic circuits and its applications in optical communications and computing require the ability to control light with light [25,26]. Optical bistability is one of the most important nonlinear effects and is usually considered before the design of alloptical switching and other nonlinear optical devices [27]. There are two important kinds of plasmonic waveguides, i.e., insulator-metal-insulator (IMI) and metal-insulator-metal (MIM) waveguide. The IMI waveguide possesses less loss but poor capability to confine light on subwavelength scale [28], while MIM 20 September 2011 / Vol. 50, No. 27 / APPLIED OPTICS
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waveguide exhibits the strong light confinement and acceptable propagation length for SPPs [29]. Quite recently, the optical bistability in metal gap waveguide nanocavities has been proposed [30]. However, the waveguide-filtering function is not evident due to the weak resonant effect of simple F-P cavity. In this paper, a MIM waveguide with nanodisk resonator containing Kerr nonlinear medium has been proposed and investigated numerically. The optical bistability can be generated at some optical resonant structure containing nonlinear medium [21,31]. In our structure, the resonant mode in the nanodisk resonator can enhance the nonlinear effect and produces the optical bistability. Because of the Kerr nonlinear effect, the resonance wavelength of the cavity exhibits a redshift with the increasing of the incident intensity. The transmission spectrum of this plasmonic structure possesses obvious and sharp peak. At the transmission peak, the local resonant mode is excited and, thus, enhances the nonlinear effect of the cavity. Additionally, an obvious bistability loop is achieved. It is well-known that optical bistability is one of the most important nonlinear optical effect and can be used to design optical devices such as alloptical switching [26,31]. So our structure has potential applications for nonlinear optical devices in highly integrated optical circuits. 2. Structures and Model
Figure 1 shows the schematic diagram of the plasmonic structure, which is composed of inputting and outgoing waveguides as well as a nanodisk resonator in the middle of the MIM structure. The dielectric in the metal slit is air with refractive index n ¼ 1 and the yellow area in the nanodisk resonator represents Kerr nonlinear medium. The metal is chosen to be sliver, whose frequency-dependent relative permittivity is characterized by the Drude model [32]: εm ðωÞ ¼ ε∞ −
ω2p : ωðω þ iγÞ
ð1Þ
of these parameters can be set as ε∞ ¼ 3:7, γ ¼ 0:018 eV, and ωp ¼ 9:1 eV, respectively [5]. ω is the angular frequency of the incident light. A TMpolarized plane wave is used to excite the SPPs in the waveguide. The transmission efficiency is defined as T ¼ T t =T i [33], where T i is the total incident power and T t is the transmission power. 3. Simulation Results and Discussion
The parameters of the structure are set as r ¼ 150 nm, w ¼ 50 nm, and dt ¼ 20 nm. These parameters are used for all following results. We utilize the finite difference time-domain (FDTD) method to investigate the transmission response of this structure [34]. In the simulations, the grid sizes are set to be Δx ¼ Δy ¼ 5 nm and the temporal step is Δt ¼ Δx=ð2cÞ. Here, c is the velocity of light in vacuum. The perfectly matched layer is used in the x and y directions [35]. Figure 2(a) shows the transmission spectra with different refraction indices in the nanodisk cavity. It reveals that the center wavelength has a redshift when the refractive index increases. As shown in Fig. 2(b), the transmitted-peak wavelength increases linearly with the refractive index in a wide spectral range. Figures. 2(c) and 2(d) show the field distributions of jH z j2 at the wavelength of 1025 nm with n ¼ 1:6 and n ¼ 1:5, respectively. It can be seen that the incident light can pass through the cavity with n ¼ 1:6, whereas is prohibited when n is 1.5. This is consistent with results in Fig. 2(a). Successively, the nanodisk resonator is filled with Kerr medium whose dielectric constant depends on the intensity of the incident light [26] εd ¼ εl þ χ ð3Þ jEj2 ;
ð2Þ
where εd is the dielectric constant of Kerr medium, εl is the linear dielectric constant and set as 2.25, and χ ð3Þ stands for the third-order nonlinear susceptibility. Here, the Kerr medium is chosen as InGaAsP
Here ε∞ is the dielectric constant at infinite angular frequency, ωp is the bulk plasma frequency, which represents the natural frequency of the oscillations of free conduction electrons, and γ represents the damping frequency of the oscillations. The value
Fig. 1. (Color online) Schematic diagram of the MIM plasmonic waveguide with a nanodisk resonator. r: the radius of the resonator, w: the width of the waveguide, dt : the coupling length between the waveguide and resonator. 5288
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Fig. 2. (Color online) (a) Transmission spectra with different refractive indices with r ¼ 150 nm, w ¼ 50 nm, and dt ¼ 20 nm. (b) Transmitted-peak wavelength of the nanodisk resonator versus refractive index. Contour profiles of field jH z j2 at the wavelength of 1025 nm with n ¼ 1:6 (c) and n ¼ 1:5 (d).
with a typical third-order nonlinear susceptibility: χ ð3Þ ¼ 1 × 10−18 m2 =V2 : [5]. Figure 3(a) shows the transmission spectra at different intensities of the incident light and the parameters of the structure are the same as that in Fig. 2. The intensity is determined by jEj2, which represents the square of amplitude (peak value) of the incident light and jEj2 are chosen as 1 × 1014, 1 × 1016 , 3 × 1016 V2 =m2 . From Fig. 3(a), we can see that the transmitted peak has a redshift with the increase of the intensity of the incident light. The transmission curves in Fig. 3(a) for larger incident intensity are asymmetric and lower. This phenomenon may be due to the nonuniform refractive index of the nanodisk resonator induced by the nonuniform distribution of electric field in the nanodisk resonator at high incident intensity. The increase of the incident intensity will augment the refractive index of Kerr medium, and thus results in the redshift of the resonance wavelength according to the result in Fig. 2(b). Our structure possesses higher transmission and more obvious wavelength-filtering function than that in [30]. Figure 3(b) shows the transmission contrast ratio, which is defined as 10log10 ðT 1 =T 0 Þ. Here, T 1 and T 0 are the transmission values at the intensity of I 1 ¼ 3 × 1016 V2 =m2 and I 0 ¼ 1 × 1014 V2 =m2 , respectively. It can be found that the transmission contrast ratio at the resonant wavelength is 6:358 dB. To further verify the transmission response at different inputting intensity, the contour profiles of field jH z j2 with the intensities of 1 × 1014 and 3 × 1016 V2 =m2 at the wavelength of 988 nm are plotted in Figs. 3(c) and 3(d), respectively. It is obviously shown that the
Fig. 3. (Color online) (a) Transmission spectra at the incident intensities of 1 × 1014, 1 × 1016 , and 3 × 1016 V2 =m2 . The inset is the transmitted-peak wavelength versus the incident intensity. (b) Transmission contrast ratio between the intensity of 1 × 1014 V2 =m2 and 3 × 1016 V2 =m2 . Contour profiles of field jH z j2 with the incident electric intensity of (c) 1 × 1014 V2 =m2 and (d) 3 × 1016 V2 =m2 at the wavelength of 988 nm.
incident light of 1 × 1014 V2 =m2 is reflected, while when the intensity is selected as 3 × 1016 V2 =m2 the incident light can pass through the waveguides. Furthermore, the optical bistability in this MIM waveguide with nanodisk resonator containing Kerr medium is investigated by the FDTD simulations. For comparison, we calculated the optical bistability for different radii, which are chosen as 140 nm, 150 nm, and 160 nm. The incident wavelengths for the three radii are chosen as 937:5 nm, 988 nm, and 1035 nm. The other parameters are the same as that in Fig. 2(a). The optical bistability loop is obtained and shown in Fig. 4. The red and blue curves represent the transmission efficiency with the decrease and increase of incident intensities. For the radius of the nanodisk is 150 nm, with the increase of the light intensity, the transmission keeps a rather low level for a long range until the intensity reaches to about 2:341 × 1016 V2 =m2 , when the transmission jumps to a much higher value. By contrast, with the decrease of the light intensity, the transmission keeps a high value for a long range and then drops to a low value at the incident intensity of about 2:191 × 1016 V2 =m2 . From Fig. 4, it is found that the obvious optical bistability loop can be observed for larger radius. This may be due to the fact that the Q-factor is higher for the larger radius, and thus the decay time of the resonant mode is longer and the induced nonlinear effect is more intense, which gives rise to the obvious optical bistability. It should be noted that in our structure, the properties of optical bistability and nonlinear effect can also be modulated by the other parameters of the system, including the structure parameters ðw; dt Þ and the resonant modes in the nanodisk. Especially, the parameters such as the radius, coupling length, and refractive index of the nanodisk resonator could be optimized to get the best contrast ratio of transmission in our structure.
Fig. 4. (Color online) Transmission coefficients by increasing (blue curve) and decreasing (red curve) the incident intensity with different radii of the nanodisk resonator. 20 September 2011 / Vol. 50, No. 27 / APPLIED OPTICS
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4. Conclusions
In this paper, the optical bistability effect in a MIM waveguide with nanodisk resonator containing a Kerr medium is proposed and investigated. The FDTD simulations show that the transmitted-peak can be tuned by changing the intensity of the incident light. The local resonant field excited in the nanodisk cavity significantly enhances the Kerr nonlinear effect. The incident light with high intensity can pass through the waveguides, whereas the incident light with low intensity is reflected without exciting resonant field in the cavity. In addition, an obvious bistability loop is observed in this structure. Our structure can find potential applications in all-optical switching in highly integrated optical circuits and optical computing. This work was supported by the Hundreds of Talents Programs of the Chinese Academy of Sciences (CAS) and by the National Natural Science Foundation (NSFC) of China under grants 10874239 and 10604066. References 1. R. Zia, J. A. Schuller, and M. L. Brongersma, “Plasmonics: The next chip-scale technology,” Mater. Today 9, 20–27 (2006). 2. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003). 3. Y. Gong, L. Wang, X. Hu, X. Li, and X. Liu, “Broad-bandgap and low-sidelobe surface plasmon polariton reflector with Bragg-grating-based MIM waveguide,” Opt. Express 17, 13727–13736 (2009). 4. J. Liu, L. Wang, M. He, W. Huang, D. Wang, B. Zou, and S. Wen, “A wide bandgap plasmonic Bragg reflector,” Opt. Express 16, 4888–4894 (2008). 5. Z. H. Han, E. Forsberg, and S. He, “Surface plasmon Bragg gratings formed in metal-insulator-metal waveguides,” IEEE Photon. Technol. Lett. 19, 91–93 (2007). 6. G. Wang, H. Lu, X. Liu, D. Mao, and L. Duan, “Tunable multichannel wavelength demultiplexer based on MIM plasmonic nanodisk resonators at telecommunication regime,” Opt. Express 19, 3513–3518 (2011). 7. J. Tao, X. Huang, and J. Zhu, “A wavelength demultiplexing structure based on metal-dielectric-metal plasmonic nanocapillary resonators,” Opt. Express 18, 11111–11116 (2010). 8. H. Lu, X. M. Liu, D. Mao, L. R. Wang, and Y. K. Gong, “Tunable band-pass plasmonic waveguide filters with nanodisk resonators,” Opt. Express 18, 17922–17927 (2010). 9. Y. Gong, X. Liu, and L. Wang, “High channel-count plasmonic filter with the metal-insulator-metal Fibonacci-sequence gratings,” Opt. Lett. 35, 285–287 (2010). 10. M. Pu, N. Yao, C. Hu, X. Xin, Z. Zhao, C. Wang, and X. Luo, “Directional coupler and nonlinear Mach-Zehnder interferometer based on metal-insulator-metal plasmonic waveguide,” Opt. Express 18, 21030–21037 (2010). 11. B. Wang and G. P. Wang, “Surface plasmon polariton propagation in nanoscale metal gap waveguides,” Opt. Lett. 29, 1992–1994 (2004). 12. H. Gao, H. Shi, C. Wang, C. Du, X. Luo, Q. Deng, Y. Lv, X. Lin, and H. Yao, “Surface plasmon polariton propagation and combination in Y-shaped metallic channels,” Opt. Express 13, 10795–10800 (2005). 13. H. Zhao, X. Guang, and J. Huang, “Novel optical directional coupler based on surface plasmon polaritons,” Physica E 40, 3025–3029 (2008).
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14. G. Veronis and S. Fan, “Bends and splitters in metaldielectric-metal subwavelength plasmonic waveguides,” Appl. Phys. Lett. 87, 131102 (2005). 15. G. Tremblay and Y. L. Sheng, “Improving imaging performance of a metallic superlens using the long-range surface plasmon polariton mode cutoff technique,” Appl. Opt. 49, A36–A41 (2010). 16. K. Donghyun, “Effect of the azimuthal orientation on the performance of grating-coupled surface-plasmon resonancebiosensors,” Appl. Opt. 44, 3218–3223 (2005). 17. W. Kuo and C. Chang, “Phase detection sensitivity enhancement of surface plasmon resonance sensor in a heterodyne interferometer system,” Appl. Opt. 50, 1345–1349 (2011). 18. I. V. Kabakova, C. M. de Sterke, and B. J. Eggleton, “Performance of field-enhanced optical switching in fiber Bragg gratings,” J. Opt. Soc. Am. B 27, 1343–1352 (2010). 19. H. Chen, J. Su, J. Wang, and X. Zhao, “Optically-controlled high-speed terahertz wave modulator based on nonlinear photonic crystals,” Opt. Express 19, 3599–3603 (2011). 20. F. R. Jeffrey and W. S. Steven, “The impact of nonlinearity on degenerate parametric amplifiers,” Appl. Phys. Lett. 96, 234101 (2010). 21. C. Min, P. Wang, X. Jiao, Y. Deng, and H. Ming, “Optical bistability in subwavelength metallic grating coated by nonlinear material,” Opt. Express 15, 12368–12373 (2007). 22. A. V. Krasavin and A. V. Zayats, “Silicon-based plasmonic waveguides,” Opt. Express 18, 11791–11799 (2010). 23. C. Min, P. Wang, X. Jiao, Y. Deng, and H. Ming, “Beam manipulating by metallic nano-optic lens containing nonlinear media,” Opt. Express 15, 9541–9546 (2007). 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). 25. G. Wurtz, R. Pollard, and A. Zayats, “Optical bistability in nonlinear surface-plasmon polaritonic crystals,” Phys. Rev. Lett. 97, 057402 (2006). 26. C. Min, P. Wang, C. Chen, Y. Deng, Y. Lu, H. Ming, T. Ning, Y. Zhou, and G. Yang, “All-optical switching in subwavelength metallic grating structure containing nonlinear optical materials,” Opt. Lett. 33, 869–871 (2008). 27. J. Chen, P. Wang, X. Wang, Y. Lu, R. Zheng, H. Ming, and Q. Zhan, “Optical bistability enhanced by highly localized bulk plasmon polariton modes in subwavelength metal-nonlinear dielectric multilayer structure,” Appl. Phys. Lett. 94, 081117 (2009). 28. J. W. Mu and W. P. Huang, “A low-loss surface plasmonic Bragg grating,” J. Lightwave Technol. 27, 436–439 (2009). 29. J. Park, H. Kim, and B. Lee, “High order plasmonic Bragg reflection in the metal-insulator-metal waveguide Bragg grating,” Opt. Express 16, 413–425 (2008). 30. Y. Shen and G. Wang, “Optical bistability in metal gap waveguide nanocavities,” Opt. Express 16, 8421–8426 (2008). 31. H. Lu, X. Liu, L. Wang, Y. Gong, and D. Mao, “Ultrafast all-optical switching in nanoplasmonic waveguide with Kerr nonlinear resonator,” Opt. Express 19, 2910–2915 (2011). 32. X. Lin and X. Huang, “Tooth-shaped plasmonic waveguide filters with nanometeric sizes,” Opt. Lett. 33, 2874–2876 (2008). 33. T. Wang, X. Wen, C. Yin, and H. Wang, “The transmission characteristics of surface plasmon polaritons in ring resonator,” Opt. Express 17, 24096–24101 (2009). 34. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 2nd ed. (Artech House, 2000). 35. Z. Zhong, Y. Xu, S. Lan, Q. Dai, and L. Wu, “Sharp and asymmetric transmission response in metal-dielectric-metal plasmonic waveguides containing Kerr nonlinear media,” Opt. Express 18, 79–86 (2010).
