## Optical bistability effect in plasmonic racetrack resonator with high extinction ratio |

Optics Express, Vol. 19, Issue 20, pp. 19415-19421 (2011)

http://dx.doi.org/10.1364/OE.19.019415

Acrobat PDF (881 KB)

### 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

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]

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]

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]

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

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]

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. 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]

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

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]

## 2. Analytical model

*ε*=3.7,

_{∞}*ω*=1.3826×10

_{p}^{16}rad/s,

*ν*=−1.3674×10

_{c}^{13}s

^{−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]

*n*= 1.52, and the third-order susceptibility is

_{l}*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

*L*considered as the coupling length. The amplitudes of incident light and transmitted light are denoted by S+ and S-, which are normalized such that

_{c}*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]

^{2}gives the energy in the cavity mode. The frequency

*ω*

_{0}is the interest eignfrequency of the plasmonic resonator, and 1/τ

_{0}denotes the decay rate due to the internal loss in the resonator, while 1/τ

_{e}denotes the decay rate due to the escaping power. If the incident light is at frequency

*ω*(

*ω*

_{0}will change into

*ω*

_{0}-Δ

*ω*, and the transmission efficiency Eq. (6) can be written as: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]

*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 define

*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/cm

^{2}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) . It shows that

## 3. Numerical simulation results and discussions

*x*, 5nm for Δ

*y*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 1.55

*µm*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]

*w=*180

*nm, R*=

*L*500

_{c}=*nm,*and

*g=*20

*nm.*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 shows that 1.55

*µm*is one of the resonant wavelengths, and the structure achieves the critical coupling condition.

*5µm*with different detuning. For comparing the simulated results with theoretical results, the detuning in simulation are the same with theoretical analysis, which are 1.566

*µm*(

*µm*(

*µm*(

*µm*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

*µm*is used based on weighing the threshold of incident light intensity and the bistable phenomenon. Figure (5a) shows switching process with pulse. As the incident continuous wave (CW) is increased to the stable power level of 1.748MW/cm

^{2}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/cm

^{2}, 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

## Acknowledgments

## 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 |

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 |

3. | S. A. Maier and H. A. Atwater, “Plasmonics: Localization and guiding of electromagnetic energy in metal/dielectric structures,” J. Appl. Phys. |

4. | R. Zia, J. Schuller, A. Chandran, and M. Brongersma, “Plasmonics: the next chip-scale technology,” Mater. Today |

5. | A. Hryciw, Y. C. Jun, and M. L. Brongersma, “Plasmonics: Electrifying plasmonics on silicon,” Nat. Mater. |

6. | E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science |

7. | M. Kuttge, F. J. García de Abajo, and A. Polman, “Ultrasmall mode volume plasmonic nanodisk resonators,” Nano Lett. |

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. |

9. | S. S. Xiao, L. Liu, and M. Qiu, “Resonator channel drop filters in a plasmon-polaritons metal,” Opt. Express |

10. | S. A. Maier, “Plasmonic field enhancement and SERS in the effective mode volume picture,” Opt. Express |

11. | A. Hosseini and Y. Massoud, “Nanoscale surface plasmon based resonator using rectangular geometry,” Appl. Phys. Lett. |

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 |

13. | S. A. Maier, “Effective Mode Volume of Nanoscale Plasmon Cavities,” Opt. Quantum Electron. |

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. |

15. | T. Holmgaard, Z. Chen, S. I. Bozhevolnyi, L. Markey, and A. Dereux, “Dielectric-loaded plasmonic waveguide-ring resonators,” Opt. Express |

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 |

17. | B. Wang and G. P. Wang, “Plasmonic waveguide ring resonator at terahertz frequencies,” Appl. Phys. Lett. |

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. | 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 |

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. |

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. |

22. | S. W. Liu and M. Xiao, “Electro-optic switch in ferroelectric thin films mediated by surface plasmons,” Appl. Phys. Lett. |

23. | H. A. Haus and Y. Lai, “Theory of Cascaded Quarter Wave Shifted Distributed Feedback Resonators,” IEEE J. Quantum Electron. |

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. |

**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

- 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]
- 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]
- 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]
- R. Zia, J. Schuller, A. Chandran, and M. Brongersma, “Plasmonics: the next chip-scale technology,” Mater. Today9(7–8), 20–27 (2006). [CrossRef]
- A. Hryciw, Y. C. Jun, and M. L. Brongersma, “Plasmonics: Electrifying plasmonics on silicon,” Nat. Mater.9(1), 3–4 (2010). [CrossRef] [PubMed]
- E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science311(5758), 189–193 (2006). [CrossRef] [PubMed]
- 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]
- 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]
- 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]
- S. A. Maier, “Plasmonic field enhancement and SERS in the effective mode volume picture,” Opt. Express14(5), 1957–1964 (2006). [CrossRef] [PubMed]
- A. Hosseini and Y. Massoud, “Nanoscale surface plasmon based resonator using rectangular geometry,” Appl. Phys. Lett.90(18), 181102 (2007). [CrossRef]
- 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]
- S. A. Maier, “Effective Mode Volume of Nanoscale Plasmon Cavities,” Opt. Quantum Electron.38(1-3), 257–267 (2006). [CrossRef]
- 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]
- 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]
- 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]
- B. Wang and G. P. Wang, “Plasmonic waveguide ring resonator at terahertz frequencies,” Appl. Phys. Lett.89(13), 133106 (2006). [CrossRef]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]

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