Abstract

The modulation of resonance features in microcavities is important to applications in nanophotonics. Based on the asymmetric whispering-gallery modes (WGMs) in a plasmonic resonator, we theoretically studied the mode evolution in an asymmetric WGM plasmonic system. Exploiting the gap or nano-scatter in the plasmonic ring cavity, the symmetry of the system will be broken and the standing wave in the cavity will be tunable. Based on this asymmetric structure, the output coupling rate between the two cavity modes can also be tuned. Moreover, the proposed method could further be applied for sensing and detecting the position of defects in a WGM system.

© 2017 Chinese Laser Press

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References

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    [Crossref]
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2016 (1)

2014 (5)

X. C. Yu, B. B. Li, P. Wang, L. Tong, X. F. Jiang, Y. Li, Q. Gong, and Y. F. Xiao, “Single nanoparticle detection and sizing using a nanofiber pair in an aqueous environment,” Adv. Mater. 26, 7462–7467 (2014).
[Crossref]

Ş. Özdemir, J. Zhu, X. Yang, B. Peng, H. Yilmaz, L. He, F. Monifi, S. H. Huang, G. L. Long, and L. Yang, “Highly sensitive detection of nanoparticles with a self-referenced and self-heterodyned whispering-gallery Raman microlaser,” Proc. Natl. Acad. Sci. USA 111, E3836–E3844 (2014).
[Crossref]

B. B. Li, W. Clements, X. C. Yu, K. Shi, Q. Gong, and Y. F. Xiao, “Single nanoparticle detection using split-mode microcavity Raman lasers,” Proc. Natl. Acad. Sci. USA 111, 14657–14662 (2014).
[Crossref]

E. Arbabi, S. Kamali, S. Arnold, and L. Goddard, “Hybrid whispering gallery mode/plasmonic chain ring resonators for biosensing,” Appl. Phys. Lett. 105, 231107 (2014).
[Crossref]

B. Peng, Ş. K. Özdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. Fan, F. Nori, C. M. Bender, and L. Yang, “Parity-time-symmetric whispering-gallery microcavities,” Nat. Phys. 10, 394–398 (2014).
[Crossref]

2013 (1)

M. Tame, K. McEnery, Ş. Özdemir, J. Lee, S. Maier, and M. Kim, “Quantum plasmonics,” Nat. Phys. 9, 329–340 (2013).
[Crossref]

2012 (2)

M. Luchansky and R. Bailey, “High-Q optical sensors for chemical and biological analysis,” Anal. Chem. 84, 793–821 (2012).
[Crossref]

A. Cetin and H. Altug, “Fano resonant ring/disk plasmonic nanocavities on conducting substrates for advanced biosensing,” ACS Nano 6, 9989–9995 (2012).
[Crossref]

2011 (2)

L. He, Ş. K. Özdemir, J. Zhu, W. Kim, and L. Yang, “Detecting single viruses and nanoparticles using whispering gallery microlasers,” Nat. Nanotechnol. 6, 428–432 (2011).
[Crossref]

J. Swaim, J. Knittel, and W. Bowen, “Detection limits in whispering gallery biosensors with plasmonic enhancement,” Appl. Phys. Lett. 99, 243109 (2011).
[Crossref]

2010 (2)

H. Hunt and A. Armani, “Label-free biological and chemical sensors,” Nanoscale 2, 1544–1559 (2010).
[Crossref]

S. Weis, R. Rivière, S. Deléglise, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanically induced transparency,” Science 330, 1520–1523 (2010).
[Crossref]

2009 (2)

J. Zhu, S. Ozdemir, Y.-F. Xiao, L. Li, L. He, D.-R. Chen, and L. Yang, “On-chip single nanoparticle detection and sizing by mode splitting in an ultrahigh-Q microresonator,” Nat. Photonics 4, 46–49 (2009).
[Crossref]

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, 455–458 (2009).
[Crossref]

2008 (4)

F. Vollmer and S. Arnold, “Whispering-gallery-mode biosensing: label-free detection down to single molecules,” Nat. Methods 5, 591–596 (2008).
[Crossref]

F. Vollmer, S. Arnold, and D. Keng, “Single virus detection from the reactive shift of a whispering-gallery mode,” Proc. Natl. Acad. Sci. USA 105, 20701–20704 (2008).
[Crossref]

E. Verhagen, J. Dionne, L. Kuipers, H. Atwater, and A. Polman, “Near-field visualization of strongly confined surface plasmon polaritons in metal-insulator-metal waveguides,” Nano Lett. 8, 2925–2929 (2008).
[Crossref]

T. Kippenberg and K. Vahala, “Cavity optomechanics: back-action at the mesoscale,” Science 321, 1172–1176 (2008).
[Crossref]

2007 (2)

P. DelHaye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450, 1214–1217 (2007).
[Crossref]

A. Armani, R. Kulkarni, S. Fraser, R. Flagan, and K. Vahala, “Label-free, single-molecule detection with optical microcavities,” Science 317, 783–787 (2007).
[Crossref]

2006 (2)

H. 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]

I. Grudinin, V. Ilchenko, and L. Maleki, “Ultrahigh optical Q factors of crystalline resonators in the linear regime,” Phys. Rev. A 74, 063806 (2006).
[Crossref]

2003 (2)

S. Spillane, T. Kippenberg, O. Painter, and K. Vahala, “Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics,” Phys. Rev. Lett. 91, 043902 (2003).
[Crossref]

S. Arnold, M. Khoshsima, I. Teraoka, S. Holler, and F. Vollmer, “Shift of whispering-gallery modes in microspheres by protein adsorption,” Opt. Lett. 28, 272–274 (2003).
[Crossref]

2000 (1)

M. Cai, O. Painter, and K. Vahala, “Observation of critical coupling in a fiber taper to a silica-microsphere whispering-gallery mode system,” Phys. Rev. Lett. 85, 74–77 (2000).
[Crossref]

1999 (1)

J. Porto, F. Garcia-Vidal, and J. Pendry, “Transmission resonances on metallic gratings with very narrow slits,” Phys. Rev. Lett. 83, 2845–2848 (1999).
[Crossref]

1991 (1)

H. Haus and W. P. Huang, “Coupled-mode theory,” Proc. IEEE 79, 1505–1518 (1991).
[Crossref]

1973 (1)

A. Yariv, “Coupled-mode theory for guided-wave optics,” IEEE J. Quantum Electron. 9, 919–933 (1973).
[Crossref]

1909 (1)

P. Debye, “Der lichtdruck auf kugeln von beliebigem material,” Ann. Phys. 335, 57–136 (1909).

1908 (1)

G. Mie, “Beiträge zur optik trüber medien, speziell kolloidaler metallösungen,” Ann. Phys. 330, 377–445 (1908).

Altug, H.

A. Cetin and H. Altug, “Fano resonant ring/disk plasmonic nanocavities on conducting substrates for advanced biosensing,” ACS Nano 6, 9989–9995 (2012).
[Crossref]

Arbabi, E.

E. Arbabi, S. Kamali, S. Arnold, and L. Goddard, “Hybrid whispering gallery mode/plasmonic chain ring resonators for biosensing,” Appl. Phys. Lett. 105, 231107 (2014).
[Crossref]

Arcizet, O.

S. Weis, R. Rivière, S. Deléglise, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanically induced transparency,” Science 330, 1520–1523 (2010).
[Crossref]

P. DelHaye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450, 1214–1217 (2007).
[Crossref]

Armani, A.

H. Hunt and A. Armani, “Label-free biological and chemical sensors,” Nanoscale 2, 1544–1559 (2010).
[Crossref]

A. Armani, R. Kulkarni, S. Fraser, R. Flagan, and K. Vahala, “Label-free, single-molecule detection with optical microcavities,” Science 317, 783–787 (2007).
[Crossref]

Arnold, S.

E. Arbabi, S. Kamali, S. Arnold, and L. Goddard, “Hybrid whispering gallery mode/plasmonic chain ring resonators for biosensing,” Appl. Phys. Lett. 105, 231107 (2014).
[Crossref]

F. Vollmer and S. Arnold, “Whispering-gallery-mode biosensing: label-free detection down to single molecules,” Nat. Methods 5, 591–596 (2008).
[Crossref]

F. Vollmer, S. Arnold, and D. Keng, “Single virus detection from the reactive shift of a whispering-gallery mode,” Proc. Natl. Acad. Sci. USA 105, 20701–20704 (2008).
[Crossref]

S. Arnold, M. Khoshsima, I. Teraoka, S. Holler, and F. Vollmer, “Shift of whispering-gallery modes in microspheres by protein adsorption,” Opt. Lett. 28, 272–274 (2003).
[Crossref]

Atwater, H.

E. Verhagen, J. Dionne, L. Kuipers, H. Atwater, and A. Polman, “Near-field visualization of strongly confined surface plasmon polaritons in metal-insulator-metal waveguides,” Nano Lett. 8, 2925–2929 (2008).
[Crossref]

Bailey, R.

M. Luchansky and R. Bailey, “High-Q optical sensors for chemical and biological analysis,” Anal. Chem. 84, 793–821 (2012).
[Crossref]

Bender, C. M.

B. Peng, Ş. K. Özdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. Fan, F. Nori, C. M. Bender, and L. Yang, “Parity-time-symmetric whispering-gallery microcavities,” Nat. Phys. 10, 394–398 (2014).
[Crossref]

Bowen, W.

J. Swaim, J. Knittel, and W. Bowen, “Detection limits in whispering gallery biosensors with plasmonic enhancement,” Appl. Phys. Lett. 99, 243109 (2011).
[Crossref]

Cai, M.

M. Cai, O. Painter, and K. Vahala, “Observation of critical coupling in a fiber taper to a silica-microsphere whispering-gallery mode system,” Phys. Rev. Lett. 85, 74–77 (2000).
[Crossref]

Cetin, A.

A. Cetin and H. Altug, “Fano resonant ring/disk plasmonic nanocavities on conducting substrates for advanced biosensing,” ACS Nano 6, 9989–9995 (2012).
[Crossref]

Chen, D.-R.

J. Zhu, S. Ozdemir, Y.-F. Xiao, L. Li, L. He, D.-R. Chen, and L. Yang, “On-chip single nanoparticle detection and sizing by mode splitting in an ultrahigh-Q microresonator,” Nat. Photonics 4, 46–49 (2009).
[Crossref]

Clements, W.

B. B. Li, W. Clements, X. C. Yu, K. Shi, Q. Gong, and Y. F. Xiao, “Single nanoparticle detection using split-mode microcavity Raman lasers,” Proc. Natl. Acad. Sci. USA 111, 14657–14662 (2014).
[Crossref]

College, R.

D. Griffiths and R. College, Introduction to Electrodynamics (Prentice-Hall, 1999), Vol. 3.

Debye, P.

P. Debye, “Der lichtdruck auf kugeln von beliebigem material,” Ann. Phys. 335, 57–136 (1909).

Deléglise, S.

S. Weis, R. Rivière, S. Deléglise, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanically induced transparency,” Science 330, 1520–1523 (2010).
[Crossref]

DelHaye, P.

P. DelHaye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450, 1214–1217 (2007).
[Crossref]

Dionne, J.

E. Verhagen, J. Dionne, L. Kuipers, H. Atwater, and A. Polman, “Near-field visualization of strongly confined surface plasmon polaritons in metal-insulator-metal waveguides,” Nano Lett. 8, 2925–2929 (2008).
[Crossref]

Fan, S.

B. Peng, Ş. K. Özdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. Fan, F. Nori, C. M. Bender, and L. Yang, “Parity-time-symmetric whispering-gallery microcavities,” Nat. Phys. 10, 394–398 (2014).
[Crossref]

Flagan, R.

A. Armani, R. Kulkarni, S. Fraser, R. Flagan, and K. Vahala, “Label-free, single-molecule detection with optical microcavities,” Science 317, 783–787 (2007).
[Crossref]

Fraser, S.

A. Armani, R. Kulkarni, S. Fraser, R. Flagan, and K. Vahala, “Label-free, single-molecule detection with optical microcavities,” Science 317, 783–787 (2007).
[Crossref]

Gao, M.

Garcia-Vidal, F.

J. Porto, F. Garcia-Vidal, and J. Pendry, “Transmission resonances on metallic gratings with very narrow slits,” Phys. Rev. Lett. 83, 2845–2848 (1999).
[Crossref]

Gavartin, E.

S. Weis, R. Rivière, S. Deléglise, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanically induced transparency,” Science 330, 1520–1523 (2010).
[Crossref]

Gianfreda, M.

B. Peng, Ş. K. Özdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. Fan, F. Nori, C. M. Bender, and L. Yang, “Parity-time-symmetric whispering-gallery microcavities,” Nat. Phys. 10, 394–398 (2014).
[Crossref]

Goddard, L.

E. Arbabi, S. Kamali, S. Arnold, and L. Goddard, “Hybrid whispering gallery mode/plasmonic chain ring resonators for biosensing,” Appl. Phys. Lett. 105, 231107 (2014).
[Crossref]

Gong, Q.

B. B. Li, W. Clements, X. C. Yu, K. Shi, Q. Gong, and Y. F. Xiao, “Single nanoparticle detection using split-mode microcavity Raman lasers,” Proc. Natl. Acad. Sci. USA 111, 14657–14662 (2014).
[Crossref]

X. C. Yu, B. B. Li, P. Wang, L. Tong, X. F. Jiang, Y. Li, Q. Gong, and Y. F. Xiao, “Single nanoparticle detection and sizing using a nanofiber pair in an aqueous environment,” Adv. Mater. 26, 7462–7467 (2014).
[Crossref]

Griffiths, D.

D. Griffiths and R. College, Introduction to Electrodynamics (Prentice-Hall, 1999), Vol. 3.

Grudinin, I.

I. Grudinin, V. Ilchenko, and L. Maleki, “Ultrahigh optical Q factors of crystalline resonators in the linear regime,” Phys. Rev. A 74, 063806 (2006).
[Crossref]

Haus, H.

H. Haus and W. P. Huang, “Coupled-mode theory,” Proc. IEEE 79, 1505–1518 (1991).
[Crossref]

He, L.

Ş. Özdemir, J. Zhu, X. Yang, B. Peng, H. Yilmaz, L. He, F. Monifi, S. H. Huang, G. L. Long, and L. Yang, “Highly sensitive detection of nanoparticles with a self-referenced and self-heterodyned whispering-gallery Raman microlaser,” Proc. Natl. Acad. Sci. USA 111, E3836–E3844 (2014).
[Crossref]

L. He, Ş. K. Özdemir, J. Zhu, W. Kim, and L. Yang, “Detecting single viruses and nanoparticles using whispering gallery microlasers,” Nat. Nanotechnol. 6, 428–432 (2011).
[Crossref]

J. Zhu, S. Ozdemir, Y.-F. Xiao, L. Li, L. He, D.-R. Chen, and L. Yang, “On-chip single nanoparticle detection and sizing by mode splitting in an ultrahigh-Q microresonator,” Nat. Photonics 4, 46–49 (2009).
[Crossref]

Holler, S.

Holzwarth, R.

P. DelHaye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450, 1214–1217 (2007).
[Crossref]

Huang, S. H.

Ş. Özdemir, J. Zhu, X. Yang, B. Peng, H. Yilmaz, L. He, F. Monifi, S. H. Huang, G. L. Long, and L. Yang, “Highly sensitive detection of nanoparticles with a self-referenced and self-heterodyned whispering-gallery Raman microlaser,” Proc. Natl. Acad. Sci. USA 111, E3836–E3844 (2014).
[Crossref]

Huang, W. P.

H. Haus and W. P. Huang, “Coupled-mode theory,” Proc. IEEE 79, 1505–1518 (1991).
[Crossref]

Hunt, H.

H. Hunt and A. Armani, “Label-free biological and chemical sensors,” Nanoscale 2, 1544–1559 (2010).
[Crossref]

Ilchenko, V.

I. Grudinin, V. Ilchenko, and L. Maleki, “Ultrahigh optical Q factors of crystalline resonators in the linear regime,” Phys. Rev. A 74, 063806 (2006).
[Crossref]

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics (Wiley, 1988), Vol. 3.

Jiang, X. F.

X. C. Yu, B. B. Li, P. Wang, L. Tong, X. F. Jiang, Y. Li, Q. Gong, and Y. F. Xiao, “Single nanoparticle detection and sizing using a nanofiber pair in an aqueous environment,” Adv. Mater. 26, 7462–7467 (2014).
[Crossref]

Kamali, S.

E. Arbabi, S. Kamali, S. Arnold, and L. Goddard, “Hybrid whispering gallery mode/plasmonic chain ring resonators for biosensing,” Appl. Phys. Lett. 105, 231107 (2014).
[Crossref]

Keng, D.

F. Vollmer, S. Arnold, and D. Keng, “Single virus detection from the reactive shift of a whispering-gallery mode,” Proc. Natl. Acad. Sci. USA 105, 20701–20704 (2008).
[Crossref]

Khoshsima, M.

Kim, M.

M. Tame, K. McEnery, Ş. Özdemir, J. Lee, S. Maier, and M. Kim, “Quantum plasmonics,” Nat. Phys. 9, 329–340 (2013).
[Crossref]

Kim, W.

L. He, Ş. K. Özdemir, J. Zhu, W. Kim, and L. Yang, “Detecting single viruses and nanoparticles using whispering gallery microlasers,” Nat. Nanotechnol. 6, 428–432 (2011).
[Crossref]

Kippenberg, T.

T. Kippenberg and K. Vahala, “Cavity optomechanics: back-action at the mesoscale,” Science 321, 1172–1176 (2008).
[Crossref]

P. DelHaye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450, 1214–1217 (2007).
[Crossref]

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Figures (6)

Fig. 1.
Fig. 1. MIM structure studied in this paper. The waveguide and ring resonator have a width of 50 nm, the nearest distance between the two subjects is 10 nm, and the nanogap in the ring resonator is 2 nm. For convenience, here we give two points A and B to discuss later. The metal in this paper is A g . Its Drude parameter is high frequency relative permittivity ε = 3.7 , the plasma frequency is ω p = 9.1    eV , and the plasma decay is γ p = 0.018    eV .
Fig. 2.
Fig. 2. Electric field distribution of the input field with wavelength (a) 982 and (b) 1081 nm. Here we take the gap as the origin point and rotate around the ring resonator CCW with an angle of 2 π . The inset figure shows the field magnitude of the electric field.
Fig. 3.
Fig. 3. Electric field distribution of the ring resonator in Fig. 1. The resonance wavelengths are (a) 982 and (b) 1081 nm. Here the gap is rotated CCW around the ring resonator from point B .
Fig. 4.
Fig. 4. Transmission spectrum of (a) a perfect ring resonator. (b) The nanogap has an angle of π / 4 with point A in the CCW direction.
Fig. 5.
Fig. 5. Simulation of spectrum using the coupled mode theory (solid lines) and the FEM (dashed lines) with a different angle between the gap and point B . Here we take the CCW direction from B to the gap as the positive direction. The angle is selected as (a)  π / 2 , (b)  3 π / 4 , and (c)  π .
Fig. 6.
Fig. 6. Transmission spectrum of the inside wall defect, in-ring defect, and exinous defect. Here we plot the transmission spectrum when the defects have an angle of 3 π / 4 with point B in the CCW direction. The inset figure shows the distribution of the electric field in this structure with input wavelength 1081 nm. (a) The defect is in the inside wall. (b) The defect is exinous. (c) The defect is all in the ring cavity but does not touch the periphery of the cavity. The inset figure shows the field magnitude of the electric field.

Equations (15)

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H = ω ( a cw a cw + a ccw a ccw ) + g ( a ccw a cw + a cw a ccw + a cw a cw + a ccw a ccw ) ,
d a cw d t = 1 i [ a cw , H ] κ 0 + κ out 2 a cw κ in a cw in ,
d a ccw d t = 1 i [ a ccw , H ] κ 0 + κ out 2 a ccw κ in a ccw in .
d a cw d t = i [ ( ω + g ) a cw + g a ccw ] κ 0 + κ out 2 a cw κ in a cw in ,
d a ccw d t = i [ ( ω + g ) a ccw + g a cw ] κ 0 + κ out 2 a ccw κ in a ccw in .
g = α f 2 ( r ) ω 2 V c , α = V p ϵ p ϵ m ϵ p + 2 ϵ m .
[ i ( Δ 2 g ) + κ out + κ 0 2 ] a + + κ in a + in = 0 ,
( i Δ + κ out + κ 0 2 ) a + κ in a in = 0 ,
t = 1 κ out ( λ , θ ) κ in β β 2 + g 2 , β = i ( Δ g ) + κ 0 + κ out 2 .
t = 1 ϕ ( λ , θ ) κ in β β 2 + g 2 .
E ( θ ) = E 0 sin ( θ + φ 1 ( θ scatter ) + φ 2 ( λ ) ) .
× × E μ ε k 2 E = 0 , E ( x , y , z ) = E ( x , y ) e i k z z .
E ( θ ) = E 0 sin ( θ + θ scatter + 10 7 π λ 2 + 0.15 ) ,
ϕ ( θ , λ ) = sin ( θ + θ scatter + π λ 10 7 2 + 0.15 ) .
T = | 1 ϕ ( λ , θ ) κ in β β 2 + g 2 | 2 , β = i ( Δ + g ) + κ 0 + κ out 2 , ϕ ( θ , λ ) = sin ( θ + θ scatter + π λ 10 7 2 + 0.15 ) .

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