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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 20 — Sep. 26, 2011
  • pp: 19415–19421
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Optical bistability effect in plasmonic racetrack resonator with high extinction ratio

Xiaolei Wang, Houqiang Jiang, Junxue Chen, Pei Wang, Yonghua Lu, and Hai Ming  »View Author Affiliations


Optics Express, Vol. 19, Issue 20, pp. 19415-19421 (2011)
http://dx.doi.org/10.1364/OE.19.019415


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Abstract

In this paper, optical bistability effect in an ultracompact plasmonic racetrack resonator with nonlinear optical Kerr medium is investigated both analytically and numerically. The properties of optical bistability and pump threshold are studied at 1.55µm with various detuning parameters by an analytical model. The transmission switch from the upper branch to the lower branch with a pulse is also demonstrated by a finite-difference time-domain method. An extinction ratio of 97.8% and a switching time of 0.38ps can be achieved with proper detuning parameter. Such a plasmonic resonator design provides a promising realization for highly effective optical modulators and switch.

© 2011 OSA

1. Introduction

Highly integrated optical communication circuits require practical realization of ultracompact optical resonant cavities [1

1. V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431(7012), 1081–1084 (2004). [CrossRef] [PubMed]

, 2

2. S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440(7083), 508–511 (2006). [CrossRef] [PubMed]

]. Traditional optical micro-cavities made of dielectric or semiconducting materials have large footprints due to the rapidly increasing radiated loss with the decreasing cavities dimensions. Plasmonics is a promising field that can merge photonics and electronics at nanoscale dimensions [3

3. S. A. Maier and H. A. Atwater, “Plasmonics: Localization and guiding of electromagnetic energy in metal/dielectric structures,” J. Appl. Phys. 98(1), 011101 (2005). [CrossRef]

6

6. E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311(5758), 189–193 (2006). [CrossRef] [PubMed]

]. Plasmonic cavities that integrate surface plasmon polariton (SPP) with optical cavities can realize ultracompact optical resonators [7

7. M. Kuttge, F. J. García de Abajo, and A. Polman, “Ultrasmall mode volume plasmonic nanodisk resonators,” Nano Lett. 10(5), 1537–1541 (2010). [CrossRef] [PubMed]

12

12. Z. Han, V. Van, W. N. Herman, and P. T. Ho, “Aperture-coupled MIM plasmonic ring resonators with sub-diffraction modal volumes,” Opt. Express 17(15), 12678–12684 (2009). [CrossRef] [PubMed]

]. Plasmonic cavity not only is beyond the diffraction limit, but also achieve large local field enhancement within it. This strong field enhancement at nanoscale volume can be exploited to manipulate light-matter interactions [13

13. S. A. Maier, “Effective Mode Volume of Nanoscale Plasmon Cavities,” Opt. Quantum Electron. 38(1-3), 257–267 (2006). [CrossRef]

, 14

14. S.-H. Kwon, J.-H. Kang, C. Seassal, S.-K. Kim, P. Regreny, Y.-H. Lee, C. M. Lieber, and H.-G. Park, “Subwavelength plasmonic lasing from a semiconductor nanodisk with silver nanopan cavity,” Nano Lett. 10(9), 3679–3683 (2010). [CrossRef] [PubMed]

] and improve the performance of photonic devices based on optical nonlinear effect, such as optical bistability and all-optical plasmonic modulators and switching. Owing to its many potential applications, various plasmonic cavity structures have been investigated recently [9

9. S. S. Xiao, L. Liu, and M. Qiu, “Resonator channel drop filters in a plasmon-polaritons metal,” Opt. Express 14(7), 2932–2937 (2006). [CrossRef] [PubMed]

, 11

11. A. Hosseini and Y. Massoud, “Nanoscale surface plasmon based resonator using rectangular geometry,” Appl. Phys. Lett. 90(18), 181102 (2007). [CrossRef]

, 14

14. S.-H. Kwon, J.-H. Kang, C. Seassal, S.-K. Kim, P. Regreny, Y.-H. Lee, C. M. Lieber, and H.-G. Park, “Subwavelength plasmonic lasing from a semiconductor nanodisk with silver nanopan cavity,” Nano Lett. 10(9), 3679–3683 (2010). [CrossRef] [PubMed]

19

19. X. S. Lin, J. H. Yan, Y. B. Zheng, L. J. Wu, and S. Lan, “Bistable switching in the lossy side-coupled plasmonic waveguide-cavity structures,” Opt. Express 19(10), 9594–9599 (2011). [CrossRef] [PubMed]

]. In those various plasmonic structures, circular cavity has relatively low loss [16

16. B. Min, E. Ostby, V. Sorger, E. Ulin-Avila, L. Yang, X. Zhang, and K. Vahala, “High-Q surface-plasmon-polariton whispering-gallery microcavity,” Nature 457(7228), 455–458 (2009). [CrossRef] [PubMed]

, 18

18. H. Lu, X. M. Liu, L. R. Wang, Y. K. Gong, and D. Mao, “Ultrafast all-optical switching in nanoplasmonic waveguide with Kerr nonlinear resonator,” Opt. Express 19(4), 2910–2915 (2011). [CrossRef] [PubMed]

] owing to its smooth surface, while rectangle cavity can offer large coupling efficiency [11

11. A. Hosseini and Y. Massoud, “Nanoscale surface plasmon based resonator using rectangular geometry,” Appl. Phys. Lett. 90(18), 181102 (2007). [CrossRef]

, 19

19. X. S. Lin, J. H. Yan, Y. B. Zheng, L. J. Wu, and S. Lan, “Bistable switching in the lossy side-coupled plasmonic waveguide-cavity structures,” Opt. Express 19(10), 9594–9599 (2011). [CrossRef] [PubMed]

] because of its long coupling region. Plasmonic racetrack resonator that combine plasmonic cirular resonator with plasmonic rectangle resonator can realize more excellent plasmonic device [20

20. X. Wang, P. Wang, C. Chen, J. Chen, Y. Lu, H. Ming, and Q. Zhan, “Plasmonic racetrack resonator with high extinction ratio under critical coupling condition,” J. Appl. Phys. 107(12), 124517 (2010). [CrossRef]

]. Among many characteristics of nonlinear plasmonic modulators and switching, the extinction ratio is a very important figure of merit [21

21. A. V. Krasavin, K. F. MacDonald, N. I. Zheludev, and A. V. Zayats, “High-contrast modulation of light with light by control of surface plasmon polariton wave coupling,” Appl. Phys. Lett. 85(16), 3369–3371 (2004). [CrossRef]

, 22

22. S. W. Liu and M. Xiao, “Electro-optic switch in ferroelectric thin films mediated by surface plasmons,” Appl. Phys. Lett. 88(14), 143512 (2006). [CrossRef]

] that should be investigated in details to make these devices suitable for practical applications.

In this work, we propose and investigate a bistable switching with high extinction ratio based on plasmonic racetrack resonator with nonlinear optical Kerr material. Taking into account perturbations caused by the Kerr nonlinearity, the properties of optical bistability and pump threshold are studied at resonant mode at 1.55µm with various detuning parameters by coupling mode theory. A numerical model is developed by the finite-difference time-domain (FDTD) method to confirm the theoretical results. The bistable switching from the upper branch to the lower branch with an extinction ratio of 97.8% and a switching time of 0.38ps is also demonstrated by the FDTD method.

2. Analytical model

The proposed configuration consists of a single mode metal-dielectric-metal (MDM) plasmonic gap waveguide side-coupled to a plasmonic racetrack cavity with nonlinear optical Kerr material, which is illustrated in Fig. 1
Fig. 1 Schematic configuration of the nonlinear plasmonic racetrack resonator.
. Silver is chosen for its low absorption. The Drude model is used to describe the dispersion of Ag that is used in the device.
ε=ε+ωp22iνcωω2,
(1)
where ε=3.7, ωp=1.3826×1016rad/s, νc=−1.3674×1013s−1 [12

12. Z. Han, V. Van, W. N. Herman, and P. T. Ho, “Aperture-coupled MIM plasmonic ring resonators with sub-diffraction modal volumes,” Opt. Express 17(15), 12678–12684 (2009). [CrossRef] [PubMed]

]. The core index of the coupling MDM plasmonic waveguide is chosen as 1.52 (e.g. fused silica). The gap of racetrack cavity is filled with nonlinear organic polymer, the linear refractive index nl = 1.52, and the third-order susceptibility is χ(3)=1.4×107esu1015m2/V2. The width of the coupling plasmonic waveguide and the racetrack resonator is w, the distance between the boundaries of the racetrack and waveguide is g, and the outer radius of curve section is R while the length of straight section is Lc considered as the coupling length. The amplitudes of incident light and transmitted light are denoted by S+ and S-, which are normalized such that p in = |S + |2 and p out = |S-|2 are the incident and transmitted power. Power exchange dominantly takes place in the coupling area (the dashed box). For the resonant system, the coupling of modes formalism [23

23. H. A. Haus and Y. Lai, “Theory of Cascaded Quarter Wave Shifted Distributed Feedback Resonators,” IEEE J. Quantum Electron. 28(1), 205–213 (1992). [CrossRef]

] can be expressed as:
dadt=jω0a(1τ0+1τe)a+2τes+,
(2)
where a is the amplitude of the peak electric field in the racetrack cavity, which is normalized such that |a|2 gives the energy in the cavity mode. The frequency ω 0 is the interest eignfrequency of the plasmonic resonator, and 1/τ0 denotes the decay rate due to the internal loss in the resonator, while 1/τe denotes the decay rate due to the escaping power. If the incident light is at frequency ω (S+exp(iωt)), according to Eq. (2), a can be expressed as:
a=2τes+/[j(ωω0)+(1τ0+1τe)],
(3)
When the system is linear, S- is the sum of a term proportional to S+ and a term proportional to a:

s=css++caa,
(4)

Applying the property of time reversibility and energy conservation to Eqs. (2) and (4), we can obtain

s=s++2τea,
(5)

Then the transmission efficiency of the resonator in the steady state is derived from Eqs. (3) and (5):

T=|ss+|2=(1τe1τ0)2+(ωω0)2(1τe+1τ0)2+(ωω0)2,
(6)

Taking into account perturbations caused by the Kerr nonlinearity, the eigenfreqency of the plasmonic resonator ω 0 will change into ω 0ω, and the transmission efficiency Eq. (6) can be written as:
T=(δ+ωγ)21+(δ+ωγ)2,
(8)
where δ =(ω-ω 0)/γ is a detuning parameter, which is the detuning of the incident excited frequency ω from the plasmonic resonator ω 0.According to first-order perturbation theory of the eignmode in the plasmonic resonator and the characteristics of the system [24

24. M. Soljačić, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, “Optimal bistable switching in nonlinear photonic crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(5), 055601 (2002). [CrossRef] [PubMed]

], the change in the resonant frequency of the mode can be given by
ωγ=(PinPout)ω0cκQ2n2(r)|max,
(9)
where κ is the nonlinear feedback parameter determined by the overlap of the plasmonic cavity mode with the nonlinear material. n 2(r) and c are the local Kerr coefficient and the speed of light in vacuum respectively. We definepin'=pin/p0andpout'=pout/p0, then applying Eq. (9) to Eq. (8), the transmission efficiency becomes
T=pout'pin'=111+(pin'pout'δ)2,
(10)
where p 0 (p 0=c/(ω 0 κQ 2 n 2(r)|max)) is the characteristic power of the resonator. The Eq. (10) shows that the resonant system has bistable phenomenon or not, depending on the value of the detuning parameter δ. According to Eq. (10) and the assumption of p 0=0.73MW/cm2 which can be achieved with a particular set of parameters to be detailed later, the transmission efficiency p out/ p in as a function of incident power p in with different detuning parameter is shown in Fig. (2)
Fig. 2 The transmission efficiency as a function of the incident power at different detuning parameter δ. The blue lines and green lines denote the transmission respective obtained from increasing and decreasing intensity of incident light.
. It shows that δ=3 is the minimum detuning requirement for the presence of bistability, and the bistable loop becomes more obvious with increasing the detuning parameter, while the threshold of the incident light power increase. We also note that one state of every bistable loop can possess a near zero transmission efficiency, so the extinction ratio can be extremely high. It can be used to design bistable switching with high extinction ratio.

3. Numerical simulation results and discussions

FDTD simulation is used to verify feasibility of the theoretical model for the nonlinear plasmonic racetrack resonator. In the FDTD simulation, the grid size is 4nm for Δx, 5nm for Δy and 3nm/c for the time step, which are found to be sufficient for the convergence of numerical results. Firstly, when nonlinear plasmonic racetrack resonator doesn’t present nonlinear effect (optical intensity is very weak in racetrack cavity), we choose appropriate structure parameters which result in critical coupling resonance at 1.55µm in the nonlinear resonator system. Using a similar procedure to achieve critical coupling resonance which outlined in Ref [20

20. X. Wang, P. Wang, C. Chen, J. Chen, Y. Lu, H. Ming, and Q. Zhan, “Plasmonic racetrack resonator with high extinction ratio under critical coupling condition,” J. Appl. Phys. 107(12), 124517 (2010). [CrossRef]

], the optimal structure parameters can be obtained, which are w=180nm, R=Lc=500nm, and g=20nm. To verify the correctness of chosen parameter, a 5.2fs broadband Gaussian pulse with a center wavelength of 1.55µm is used to scan the transmission efficiency spectrum of the structure with the chosen structure parameters. The frequency scope of a broadband pulse should contain several resonant wavelengths of the device. Figure 3
Fig. 3 The transmission efficiency as a function of the incident wavelength with parameters w=180nm, R= Lc =500nm, and g =20nm.
shows that 1.55µm is one of the resonant wavelengths, and the structure achieves the critical coupling condition.

The bistable curves are studied at resonant mode at 1.55µm with different detuning. For comparing the simulated results with theoretical results, the detuning in simulation are the same with theoretical analysis, which are 1.566µm (δ=3), 1.5697µm (δ=1.333), and 1.571µm (δ=1.43) respectively. The bistability loops with these detuning are shown in Fig. (4)
Fig. 4 The transmission efficiency as a function of the incident power at different detuning parameter δ. The down and up arrow represent the increasing and decreasing intensity of incident light.
, the up and down arrows represent the decreasing and increasing of incident light intensity. According to Fig. (4), the cut-off value of detuning for the presence of bistability and the change of bistable loops with increasing of detuning are the same with theoretical results, so the agreements between the coupled mode equation in time and FDTD simulations are excellent.

Based on the results of the bistable phenomenon of the nonlinear plasmonic racetrack resonator, the bistable switching is studied with FDTD. The bistable loops reveal that the transmission efficiency can be switched to the lower branch from the upper branch with a pulse. The pulse bandwidth should be chosen appropriate, since photon has cavity lifetime in cavity. At the 1.55µm resonant wavelength, the nonlinear plasmonic racetrack resonator has a full-width-at-half-maximum (FWHM) of 12.56nm and a quality factor Q=123, the corresponding cavity lifetime can be achieved by

τ=λ22πcλ=0.1ps,
(11)

We choose pulse bandwidth of 0.155ps in simulation. The bistable loop with detuning wavelength of 1.5697µm is used based on weighing the threshold of incident light intensity and the bistable phenomenon. Figure (5a)
Fig. 5 (a) The switching process with a pulse, with a peak power 1.748MW/cm2, the same carrier frequency as that of CW, which is superimposed upon the CW excitation. (b) and (c) is the magnetic field distribution of the states of switching on and switching off respectively.
shows switching process with pulse. As the incident continuous wave (CW) is increased to the stable power level of 1.748MW/cm2 for some cavity period, the resonator system is at a high transmission state that is at the upper branch of bistable loop. Then the switching occurs after a pulse with a peak power 1.748MW/cm2, the same carrier frequency as that of CW, which is superimposed upon the CW excitation. The pulse make the stored light intensity in cavity exceed the bistable threshold. After the pulse has passed through the plasmonic racetrack resonator, the system switches to the low transmission state. According to Fig. (5a), the system has a switching time of 0.38ps, and a high extinction ratio of 97.8%. In the simulation, the time delay of the nonlinear material is not considered, so the switching time of 0.38ps is only determined by the feedback of the structure, which represents the shortest switching time of the structure. To make the states of switching on and off visible, we give the magnetic field distributions in Fig. (5b) and Fig. (5c). The switching on state shown in Fig. (5b) has most of the power transmits through the waveguide, and Fig. (5c) corresponds to the off state which has most of the power confined in plasmonic racetrack cavity.

4. Conclusions

In conclusions, we studied optical bistability phenomenon in an ultracompact nonlinear plasmonic racetrack resonator by theoretical analyses and FDTD method. The analytical model clearly demonstrates that optical bistability and the threshold of incident light intensity have close relationship with detuning parameter δ, and the simulated results are consistent with theoretical analysis. Thus, it shows that the nonlinear dynamics in plasmonic racetrack resonator can be completely accounted for using coupled mode theory, which provides a convenient framework for analyzing complex nonlinear processes. The bistable switch with an extinction ratio of 97.8% and a switching time of 0.38ps can be achieved with proper detuning parameter. Such a nonlinear plasmonic resonator design provides a foundation for realizing low threshold of incident light intensity, fast switching time and highly effective optical modulators and switch.

Acknowledgments

This work is supported by the Key Program of National Natural Science Foundation of China No. 61036005 and National Natural Science Foundation of China No. 60977019, 11074241.

References and links

1.

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431(7012), 1081–1084 (2004). [CrossRef] [PubMed]

2.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440(7083), 508–511 (2006). [CrossRef] [PubMed]

3.

S. A. Maier and H. A. Atwater, “Plasmonics: Localization and guiding of electromagnetic energy in metal/dielectric structures,” J. Appl. Phys. 98(1), 011101 (2005). [CrossRef]

4.

R. Zia, J. Schuller, A. Chandran, and M. Brongersma, “Plasmonics: the next chip-scale technology,” Mater. Today 9(7–8), 20–27 (2006). [CrossRef]

5.

A. Hryciw, Y. C. Jun, and M. L. Brongersma, “Plasmonics: Electrifying plasmonics on silicon,” Nat. Mater. 9(1), 3–4 (2010). [CrossRef] [PubMed]

6.

E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311(5758), 189–193 (2006). [CrossRef] [PubMed]

7.

M. Kuttge, F. J. García de Abajo, and A. Polman, “Ultrasmall mode volume plasmonic nanodisk resonators,” Nano Lett. 10(5), 1537–1541 (2010). [CrossRef] [PubMed]

8.

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(9), 097401 (2006). [CrossRef] [PubMed]

9.

S. S. Xiao, L. Liu, and M. Qiu, “Resonator channel drop filters in a plasmon-polaritons metal,” Opt. Express 14(7), 2932–2937 (2006). [CrossRef] [PubMed]

10.

S. A. Maier, “Plasmonic field enhancement and SERS in the effective mode volume picture,” Opt. Express 14(5), 1957–1964 (2006). [CrossRef] [PubMed]

11.

A. Hosseini and Y. Massoud, “Nanoscale surface plasmon based resonator using rectangular geometry,” Appl. Phys. Lett. 90(18), 181102 (2007). [CrossRef]

12.

Z. Han, V. Van, W. N. Herman, and P. T. Ho, “Aperture-coupled MIM plasmonic ring resonators with sub-diffraction modal volumes,” Opt. Express 17(15), 12678–12684 (2009). [CrossRef] [PubMed]

13.

S. A. Maier, “Effective Mode Volume of Nanoscale Plasmon Cavities,” Opt. Quantum Electron. 38(1-3), 257–267 (2006). [CrossRef]

14.

S.-H. Kwon, J.-H. Kang, C. Seassal, S.-K. Kim, P. Regreny, Y.-H. Lee, C. M. Lieber, and H.-G. Park, “Subwavelength plasmonic lasing from a semiconductor nanodisk with silver nanopan cavity,” Nano Lett. 10(9), 3679–3683 (2010). [CrossRef] [PubMed]

15.

T. Holmgaard, Z. Chen, S. I. Bozhevolnyi, L. Markey, and A. Dereux, “Dielectric-loaded plasmonic waveguide-ring resonators,” Opt. Express 17(4), 2968–2975 (2009). [CrossRef] [PubMed]

16.

B. Min, E. Ostby, V. Sorger, E. Ulin-Avila, L. Yang, X. Zhang, and K. Vahala, “High-Q surface-plasmon-polariton whispering-gallery microcavity,” Nature 457(7228), 455–458 (2009). [CrossRef] [PubMed]

17.

B. Wang and G. P. Wang, “Plasmonic waveguide ring resonator at terahertz frequencies,” Appl. Phys. Lett. 89(13), 133106 (2006). [CrossRef]

18.

H. Lu, X. M. Liu, L. R. Wang, Y. K. Gong, and D. Mao, “Ultrafast all-optical switching in nanoplasmonic waveguide with Kerr nonlinear resonator,” Opt. Express 19(4), 2910–2915 (2011). [CrossRef] [PubMed]

19.

X. S. Lin, J. H. Yan, Y. B. Zheng, L. J. Wu, and S. Lan, “Bistable switching in the lossy side-coupled plasmonic waveguide-cavity structures,” Opt. Express 19(10), 9594–9599 (2011). [CrossRef] [PubMed]

20.

X. Wang, P. Wang, C. Chen, J. Chen, Y. Lu, H. Ming, and Q. Zhan, “Plasmonic racetrack resonator with high extinction ratio under critical coupling condition,” J. Appl. Phys. 107(12), 124517 (2010). [CrossRef]

21.

A. V. Krasavin, K. F. MacDonald, N. I. Zheludev, and A. V. Zayats, “High-contrast modulation of light with light by control of surface plasmon polariton wave coupling,” Appl. Phys. Lett. 85(16), 3369–3371 (2004). [CrossRef]

22.

S. W. Liu and M. Xiao, “Electro-optic switch in ferroelectric thin films mediated by surface plasmons,” Appl. Phys. Lett. 88(14), 143512 (2006). [CrossRef]

23.

H. A. Haus and Y. Lai, “Theory of Cascaded Quarter Wave Shifted Distributed Feedback Resonators,” IEEE J. Quantum Electron. 28(1), 205–213 (1992). [CrossRef]

24.

M. Soljačić, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, “Optimal bistable switching in nonlinear photonic crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(5), 055601 (2002). [CrossRef] [PubMed]

OCIS Codes
(190.4360) Nonlinear optics : Nonlinear optics, devices
(230.5750) Optical devices : Resonators
(250.5403) Optoelectronics : Plasmonics

ToC Category:
Integrated Optics

History
Original Manuscript: June 14, 2011
Revised Manuscript: August 13, 2011
Manuscript Accepted: August 14, 2011
Published: September 22, 2011

Citation
Xiaolei Wang, Houqiang Jiang, Junxue Chen, Pei Wang, Yonghua Lu, and Hai Ming, "Optical bistability effect in plasmonic racetrack resonator with high extinction ratio," Opt. Express 19, 19415-19421 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-20-19415


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References

  1. V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature431(7012), 1081–1084 (2004). [CrossRef] [PubMed]
  2. S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature440(7083), 508–511 (2006). [CrossRef] [PubMed]
  3. S. A. Maier and H. A. Atwater, “Plasmonics: Localization and guiding of electromagnetic energy in metal/dielectric structures,” J. Appl. Phys.98(1), 011101 (2005). [CrossRef]
  4. R. Zia, J. Schuller, A. Chandran, and M. Brongersma, “Plasmonics: the next chip-scale technology,” Mater. Today9(7–8), 20–27 (2006). [CrossRef]
  5. A. Hryciw, Y. C. Jun, and M. L. Brongersma, “Plasmonics: Electrifying plasmonics on silicon,” Nat. Mater.9(1), 3–4 (2010). [CrossRef] [PubMed]
  6. E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science311(5758), 189–193 (2006). [CrossRef] [PubMed]
  7. M. Kuttge, F. J. García de Abajo, and A. Polman, “Ultrasmall mode volume plasmonic nanodisk resonators,” Nano Lett.10(5), 1537–1541 (2010). [CrossRef] [PubMed]
  8. 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(9), 097401 (2006). [CrossRef] [PubMed]
  9. S. S. Xiao, L. Liu, and M. Qiu, “Resonator channel drop filters in a plasmon-polaritons metal,” Opt. Express14(7), 2932–2937 (2006). [CrossRef] [PubMed]
  10. S. A. Maier, “Plasmonic field enhancement and SERS in the effective mode volume picture,” Opt. Express14(5), 1957–1964 (2006). [CrossRef] [PubMed]
  11. A. Hosseini and Y. Massoud, “Nanoscale surface plasmon based resonator using rectangular geometry,” Appl. Phys. Lett.90(18), 181102 (2007). [CrossRef]
  12. Z. Han, V. Van, W. N. Herman, and P. T. Ho, “Aperture-coupled MIM plasmonic ring resonators with sub-diffraction modal volumes,” Opt. Express17(15), 12678–12684 (2009). [CrossRef] [PubMed]
  13. S. A. Maier, “Effective Mode Volume of Nanoscale Plasmon Cavities,” Opt. Quantum Electron.38(1-3), 257–267 (2006). [CrossRef]
  14. S.-H. Kwon, J.-H. Kang, C. Seassal, S.-K. Kim, P. Regreny, Y.-H. Lee, C. M. Lieber, and H.-G. Park, “Subwavelength plasmonic lasing from a semiconductor nanodisk with silver nanopan cavity,” Nano Lett.10(9), 3679–3683 (2010). [CrossRef] [PubMed]
  15. T. Holmgaard, Z. Chen, S. I. Bozhevolnyi, L. Markey, and A. Dereux, “Dielectric-loaded plasmonic waveguide-ring resonators,” Opt. Express17(4), 2968–2975 (2009). [CrossRef] [PubMed]
  16. B. Min, E. Ostby, V. Sorger, E. Ulin-Avila, L. Yang, X. Zhang, and K. Vahala, “High-Q surface-plasmon-polariton whispering-gallery microcavity,” Nature457(7228), 455–458 (2009). [CrossRef] [PubMed]
  17. B. Wang and G. P. Wang, “Plasmonic waveguide ring resonator at terahertz frequencies,” Appl. Phys. Lett.89(13), 133106 (2006). [CrossRef]
  18. H. Lu, X. M. Liu, L. R. Wang, Y. K. Gong, and D. Mao, “Ultrafast all-optical switching in nanoplasmonic waveguide with Kerr nonlinear resonator,” Opt. Express19(4), 2910–2915 (2011). [CrossRef] [PubMed]
  19. X. S. Lin, J. H. Yan, Y. B. Zheng, L. J. Wu, and S. Lan, “Bistable switching in the lossy side-coupled plasmonic waveguide-cavity structures,” Opt. Express19(10), 9594–9599 (2011). [CrossRef] [PubMed]
  20. X. Wang, P. Wang, C. Chen, J. Chen, Y. Lu, H. Ming, and Q. Zhan, “Plasmonic racetrack resonator with high extinction ratio under critical coupling condition,” J. Appl. Phys.107(12), 124517 (2010). [CrossRef]
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