Abstract

Whispering gallery mode (WGM) microtoroid optical resonators have been effectively used to sense low concentrations of biomolecules down to the single molecule limit. Optical WGM biochemical sensors such as the microtoroid operate by tracking changes in resonant frequency as particles enter the evanescent near field of the resonator. Previously, gold nanoparticles have been coupled to WGM resonators to increase the magnitude of resonance shifts via plasmonic enhancement of the electric field. However, this approach results in increased scattering from the WGM, which degrades its quality (Q) factor, making it less sensitive to extremely small frequency shifts caused by small molecules or protein conformational changes. Here, we show using simulation that precisely positioned trimer gold nanostructures generate dark modes that suppress radiation loss and can achieve high (>106)Q with an electric-field intensity enhancement of 4300, which far exceeds that of a single rod (2500 times). Through an overall evaluation of a combined enhancement factor, which includes the Q factor of the system, the sensitivity of the trimer system was improved 105× versus 84× for a single rod. Further simulations demonstrate that unlike a single rod system, the trimer is robust to orientation changes and has increased capture area. We also conduct stability tests to show that small positioning errors do not greatly impact the result.

© 2019 Chinese Laser Press

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References

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2018 (4)

Y. Gao, N. Zhou, Z. Shi, X. Guo, and L. Tong, “Dark dimer mode excitation and strong coupling with a nanorod dipole,” Photon. Res. 6, 887–892 (2018).
[Crossref]

T.-S. Deng, J. Parker, Y. Yifat, N. Shepherd, and N. F. Scherer, “Dark plasmon modes in symmetric gold nanoparticle dimers illuminated by focused cylindrical vector beams,” J. Phys. Chem. C 122, 27662–27672 (2018).
[Crossref]

F. Ruesink, H. M. Doeleman, E. Verhagen, and A. F. Koenderink, “Controlling nanoantenna polarizability through backaction via a single cavity mode,” Phys. Rev. Lett. 120, 206101 (2018).
[Crossref]

J. E. Melzer and E. McLeod, “Fundamental limits of optical tweezer nanoparticle manipulation speeds,” ACS Nano 12, 2440–2447 (2018).
[Crossref]

2017 (2)

J. Su, “Label-free biological and chemical sensing using whispering gallery mode optical resonators: past, present, and future,” Sensors 17, 540 (2017).
[Crossref]

Y. Zhi, X.-C. Yu, Q. Gong, L. Yang, and Y.-F. Xiao, “Single nanoparticle detection using optical microcavities,” Adv. Mater. 29, 1604920 (2017).
[Crossref]

2016 (1)

J. Su, A. F. Goldberg, and B. M. Stoltz, “Label-free detection of single nanoparticles and biological molecules using microtoroid optical resonators,” Light Sci. Appl. 5, e16001 (2016).
[Crossref]

2015 (2)

J. Su, “Label-free single exosome detection using frequency-locked microtoroid optical resonators,” ACS Photon. 2, 1241–1245 (2015).
[Crossref]

M. R. Foreman, J. D. Swaim, and F. Vollmer, “Whispering gallery mode sensors,” Adv. Opt. Photon. 7, 168–240 (2015).
[Crossref]

2014 (1)

M. D. Baaske, M. R. Foreman, and F. Vollmer, “Single-molecule nucleic acid interactions monitored on a label-free microcavity biosensor platform,” Nat. Nanotechnol. 9, 933–939 (2014).
[Crossref]

2013 (4)

A. Kaplan, M. Tomes, T. Carmon, M. Kozlov, O. Cohen, G. Bartal, and H. G. L. Schwefel, “Finite element simulation of a perturbed axial-symmetric whispering-gallery mode and its use for intensity enhancement with a nanoparticle coupled to a microtoroid,” Opt. Express 21, 14169–14180 (2013).
[Crossref]

D. E. Gómez, Z. Q. Teo, M. Altissimo, T. J. Davis, S. Earl, and A. Roberts, “The dark side of plasmonics,” Nano Lett. 13, 3722–3728 (2013).
[Crossref]

H. Chen, L. Shao, Q. Li, and J. Wang, “Gold nanorods and their plasmonic properties,” Chem. Soc. Rev. 42, 2679–2724 (2013).
[Crossref]

V. R. Dantham, S. Holler, C. Barbre, D. Keng, V. Kolchenko, and S. Arnold, “Label-free detection of single protein using a nanoplasmonic-photonic hybrid microcavity,” Nano Lett. 13, 3347–3351 (2013).
[Crossref]

2012 (1)

F. Vollmer and L. Yang, “Review label-free detection with high-Q microcavities: a review of biosensing mechanisms for integrated devices,” Nanophotonics 1, 267–291 (2012).
[Crossref]

2011 (3)

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

S. I. Shopova, R. Rajmangal, S. Holler, and S. Arnold, “Plasmonic enhancement of a whispering-gallery-mode biosensor for single nanoparticle detection,” Appl. Phys. Lett. 98, 243104 (2011).
[Crossref]

A. M. Funston, T. J. Davis, C. Novo, and P. Mulvaney, “Coupling modes of gold trimer superstructures,” Philos. Trans. R. Soc. A 369, 3472–3482 (2011).
[Crossref]

2010 (5)

S. L. Teo, V. K. Lin, R. Marty, N. Large, E. A. Llado, A. Arbouet, C. Girard, J. Aizpurua, S. Tripathy, and A. Mlayah, “Gold nanoring trimers: a versatile structure for infrared sensing,” Opt. Express 18, 22271–22282 (2010).
[Crossref]

T. J. Davis, D. E. Gómez, and K. C. Vernon, “Simple model for the hybridization of surface plasmon resonances in metallic nanoparticles,” Nano Lett. 10, 2618–2625 (2010).
[Crossref]

D. E. Gómez, K. C. Vernon, and T. J. Davis, “Symmetry effects on the optical coupling between plasmonic nanoparticles with applications to hierarchical structures,” Phys. Rev. B 81, 075414 (2010).
[Crossref]

J.-S. Huang, J. Kern, P. Geisler, P. Weinmann, M. Kamp, A. Forchel, P. Biagioni, and B. Hecht, “Mode imaging and selection in strongly coupled nanoantennas,” Nano Lett. 10, 2105–2110 (2010).
[Crossref]

J. Zhu, S. K. 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 (2010).
[Crossref]

2009 (1)

T. J. Davis, K. C. Vernon, and D. E. Gómez, “Designing plasmonic systems using optical coupling between nanoparticles,” Phys. Rev. B 79, 155423 (2009).
[Crossref]

2008 (1)

J. Alegret, T. Rindzevicius, T. Pakizeh, Y. Alaverdyan, L. Gunnarsson, and M. Käll, “Plasmonic properties of silver trimers with trigonal symmetry fabricated by electron-beam lithography,” J. Phys. Chem. C 112, 14313–14317 (2008).
[Crossref]

2007 (4)

D. P. Sprünken, H. Omi, K. Furukawa, H. Nakashima, I. Sychugov, Y. Kobayashi, and K. Torimitsu, “Influence of the local environment on determining aspect-ratio distributions of gold nanorods in solution using Gans theory,” J. Phys. Chem. C 111, 14299–14306 (2007).
[Crossref]

L. Novotny, “Effective wavelength scaling for optical antennas,” Phys. Rev. Lett. 98, 266802 (2007).
[Crossref]

B. Min, L. Yang, and K. Vahala, “Perturbative analytic theory of an ultrahigh-Q toroidal microcavity,” Phys. Rev. A 76, 013823 (2007).
[Crossref]

M. Oxborrow, “Traceable 2-D finite-element simulation of the whispering-gallery modes of axisymmetric electromagnetic resonators,” IEEE Trans. Microwave Theory Tech. 55, 1209–1218 (2007).
[Crossref]

2006 (1)

S. W. Prescott and P. Mulvaney, “Gold nanorod extinction spectra,” J. Appl. Phys. 99, 123504 (2006).
[Crossref]

2004 (1)

W. Suh, Z. Wang, and S. Fan, “Temporal coupled-mode theory and the presence of non-orthogonal modes in lossless multimode cavities,” IEEE J. Quantum Electron. 40, 1511–1518 (2004).
[Crossref]

2003 (3)

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]

F. Vollmer, S. Arnold, D. Braun, I. Teraoka, and A. Libchaber, “Multiplexed DNA quantification by spectroscopic shift of two microsphere cavities,” Biophys. J. 85, 1974–1979 (2003).
[Crossref]

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421, 925–928 (2003).
[Crossref]

2000 (1)

A. Yariv, “Universal relations for coupling of optical power between microresonators and dielectric waveguides,” Electron. Lett. 36, 321–322 (2000).
[Crossref]

1997 (1)

B. E. Little, S. T. Chu, and H. A. Haus, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997).
[Crossref]

1996 (1)

1994 (1)

J.-P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994).
[Crossref]

1986 (1)

1972 (1)

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[Crossref]

1960 (1)

R. A. Waldron, “Perturbation theory of resonant cavities,” Proc. IEE 107, 272–274 (1960).
[Crossref]

Aizpurua, J.

Alaverdyan, Y.

J. Alegret, T. Rindzevicius, T. Pakizeh, Y. Alaverdyan, L. Gunnarsson, and M. Käll, “Plasmonic properties of silver trimers with trigonal symmetry fabricated by electron-beam lithography,” J. Phys. Chem. C 112, 14313–14317 (2008).
[Crossref]

Alegret, J.

J. Alegret, T. Rindzevicius, T. Pakizeh, Y. Alaverdyan, L. Gunnarsson, and M. Käll, “Plasmonic properties of silver trimers with trigonal symmetry fabricated by electron-beam lithography,” J. Phys. Chem. C 112, 14313–14317 (2008).
[Crossref]

Altissimo, M.

D. E. Gómez, Z. Q. Teo, M. Altissimo, T. J. Davis, S. Earl, and A. Roberts, “The dark side of plasmonics,” Nano Lett. 13, 3722–3728 (2013).
[Crossref]

Arbouet, A.

Armani, D. K.

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421, 925–928 (2003).
[Crossref]

Arnold, S.

V. R. Dantham, S. Holler, C. Barbre, D. Keng, V. Kolchenko, and S. Arnold, “Label-free detection of single protein using a nanoplasmonic-photonic hybrid microcavity,” Nano Lett. 13, 3347–3351 (2013).
[Crossref]

S. I. Shopova, R. Rajmangal, S. Holler, and S. Arnold, “Plasmonic enhancement of a whispering-gallery-mode biosensor for single nanoparticle detection,” Appl. Phys. Lett. 98, 243104 (2011).
[Crossref]

F. Vollmer, S. Arnold, D. Braun, I. Teraoka, and A. Libchaber, “Multiplexed DNA quantification by spectroscopic shift of two microsphere cavities,” Biophys. J. 85, 1974–1979 (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]

Ashkin, A.

Baaske, M. D.

M. D. Baaske, M. R. Foreman, and F. Vollmer, “Single-molecule nucleic acid interactions monitored on a label-free microcavity biosensor platform,” Nat. Nanotechnol. 9, 933–939 (2014).
[Crossref]

Barbre, C.

V. R. Dantham, S. Holler, C. Barbre, D. Keng, V. Kolchenko, and S. Arnold, “Label-free detection of single protein using a nanoplasmonic-photonic hybrid microcavity,” Nano Lett. 13, 3347–3351 (2013).
[Crossref]

Bartal, G.

Berenger, J.-P.

J.-P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994).
[Crossref]

Biagioni, P.

J.-S. Huang, J. Kern, P. Geisler, P. Weinmann, M. Kamp, A. Forchel, P. Biagioni, and B. Hecht, “Mode imaging and selection in strongly coupled nanoantennas,” Nano Lett. 10, 2105–2110 (2010).
[Crossref]

Bjorkholm, J. E.

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 2008).

Bowen, W. P.

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

Braun, D.

F. Vollmer, S. Arnold, D. Braun, I. Teraoka, and A. Libchaber, “Multiplexed DNA quantification by spectroscopic shift of two microsphere cavities,” Biophys. J. 85, 1974–1979 (2003).
[Crossref]

Carmon, T.

Chen, D.-R.

J. Zhu, S. K. 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 (2010).
[Crossref]

Chen, H.

H. Chen, L. Shao, Q. Li, and J. Wang, “Gold nanorods and their plasmonic properties,” Chem. Soc. Rev. 42, 2679–2724 (2013).
[Crossref]

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[Crossref]

Chu, S.

Chu, S. T.

B. E. Little, S. T. Chu, and H. A. Haus, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997).
[Crossref]

Cohen, O.

Dantham, V. R.

V. R. Dantham, S. Holler, C. Barbre, D. Keng, V. Kolchenko, and S. Arnold, “Label-free detection of single protein using a nanoplasmonic-photonic hybrid microcavity,” Nano Lett. 13, 3347–3351 (2013).
[Crossref]

Davis, T. J.

D. E. Gómez, Z. Q. Teo, M. Altissimo, T. J. Davis, S. Earl, and A. Roberts, “The dark side of plasmonics,” Nano Lett. 13, 3722–3728 (2013).
[Crossref]

A. M. Funston, T. J. Davis, C. Novo, and P. Mulvaney, “Coupling modes of gold trimer superstructures,” Philos. Trans. R. Soc. A 369, 3472–3482 (2011).
[Crossref]

T. J. Davis, D. E. Gómez, and K. C. Vernon, “Simple model for the hybridization of surface plasmon resonances in metallic nanoparticles,” Nano Lett. 10, 2618–2625 (2010).
[Crossref]

D. E. Gómez, K. C. Vernon, and T. J. Davis, “Symmetry effects on the optical coupling between plasmonic nanoparticles with applications to hierarchical structures,” Phys. Rev. B 81, 075414 (2010).
[Crossref]

T. J. Davis, K. C. Vernon, and D. E. Gómez, “Designing plasmonic systems using optical coupling between nanoparticles,” Phys. Rev. B 79, 155423 (2009).
[Crossref]

Deng, T.-S.

T.-S. Deng, J. Parker, Y. Yifat, N. Shepherd, and N. F. Scherer, “Dark plasmon modes in symmetric gold nanoparticle dimers illuminated by focused cylindrical vector beams,” J. Phys. Chem. C 122, 27662–27672 (2018).
[Crossref]

Doeleman, H. M.

F. Ruesink, H. M. Doeleman, E. Verhagen, and A. F. Koenderink, “Controlling nanoantenna polarizability through backaction via a single cavity mode,” Phys. Rev. Lett. 120, 206101 (2018).
[Crossref]

Dziedzic, J. M.

Earl, S.

D. E. Gómez, Z. Q. Teo, M. Altissimo, T. J. Davis, S. Earl, and A. Roberts, “The dark side of plasmonics,” Nano Lett. 13, 3722–3728 (2013).
[Crossref]

Fan, S.

W. Suh, Z. Wang, and S. Fan, “Temporal coupled-mode theory and the presence of non-orthogonal modes in lossless multimode cavities,” IEEE J. Quantum Electron. 40, 1511–1518 (2004).
[Crossref]

Forchel, A.

J.-S. Huang, J. Kern, P. Geisler, P. Weinmann, M. Kamp, A. Forchel, P. Biagioni, and B. Hecht, “Mode imaging and selection in strongly coupled nanoantennas,” Nano Lett. 10, 2105–2110 (2010).
[Crossref]

Foreman, M. R.

M. R. Foreman, J. D. Swaim, and F. Vollmer, “Whispering gallery mode sensors,” Adv. Opt. Photon. 7, 168–240 (2015).
[Crossref]

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ACS Nano (1)

J. E. Melzer and E. McLeod, “Fundamental limits of optical tweezer nanoparticle manipulation speeds,” ACS Nano 12, 2440–2447 (2018).
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Adv. Mater. (1)

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Adv. Opt. Photon. (1)

Appl. Phys. Lett. (2)

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Biophys. J. (1)

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Chem. Soc. Rev. (1)

H. Chen, L. Shao, Q. Li, and J. Wang, “Gold nanorods and their plasmonic properties,” Chem. Soc. Rev. 42, 2679–2724 (2013).
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Electron. Lett. (1)

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IEEE J. Quantum Electron. (1)

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J. Phys. Chem. C (3)

J. Alegret, T. Rindzevicius, T. Pakizeh, Y. Alaverdyan, L. Gunnarsson, and M. Käll, “Plasmonic properties of silver trimers with trigonal symmetry fabricated by electron-beam lithography,” J. Phys. Chem. C 112, 14313–14317 (2008).
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Figures (6)

Fig. 1.
Fig. 1. Schematic of a microtoroid cavity. (a) The E-field is normalized by the amplitude of the maximum field in the evanescent zone of the bare WGM toroid [Eo(r)]. (b) A rendering of a gold nanorod placed parallel to the TE polarization of the WGM cavity mode. The resonance frequency of a single rod is tuned by adjusting its aspect ratio, which is defined as the ratio of the length to the width (diameter) of the rod. (c) Field distribution of the excited dipole mode around a nanorod.
Fig. 2.
Fig. 2. (a) Blue shift or red shift of the cavity mode around on-resonance coupling. (b) The relationship between the linewidth corresponding to system loss and the resonance of a single rod. (c) Q factor and enhancement factor as functions of the resonance for a single nanorod. The trend for the enhancement factor is similar to the linewidth change in (b). Extremely strong enhancements are shown for on-resonance coupling. Due to the light–matter interaction, a very strong hot spot is generated between the plasmonic nanorod and the biomolecule. (d) The relationship between the combined enhancement factor (fC) and the resonance frequency of the rod.
Fig. 3.
Fig. 3. (a) Q factors obtained through both numerical simulations and coupled mode theory are consistent for the systems involving multiple nanorods and no direct inter-rod coupling. (b) Top view of multiple rods coupled to the cavity mode. (b) and Fig. 2(c) share the same color bar.
Fig. 4.
Fig. 4. (a) Plane wave excitation for three isolated rods and a gold trimer. (b) Spectral comparison of the total extinction cross section of the lateral dark mode versus the three isolated rods from (a). The lateral dark mode is excited at the peak wavelength of the red curve. The illustrations show the charge distribution of the breathing and lateral dark modes at different wavelengths. Because the coupling between the breathing dark mode and free-space radiation is so small, no peak is visible at its resonance around 725 nm. (c) Quality and intensity enhancement factors as functions of the aspect ratios of each individual rod. The red arrows show the current density direction obtained in COMSOL. The inset shows the field distribution of the excited lateral dark mode. The characteristic dark spot between the ends of the bottom two rods is clearly visible. (d) Plot of the fC of the trimer. The lateral dark mode exhibits a higher combined enhancement value than that obtained from the coupling of a single rod to the cavity alone.
Fig. 5.
Fig. 5. Influence of different perturbations on the trimer’s combined enhancement factor. (a) and (b) Small changes in angle and length can maintain the fC. (c) To ensure that the gap space is large enough for particles to bind, we study the effect of the spacing on the system when the spacing is greater than 5 nm. The illustrations for the trimer field distribution use the same color bar as in Fig. 3. (d) The fC of a single rod system decreases with increasing rotation angle. When the rod is rotated 90 deg, that is, perpendicular to the polarization of the TE mode, the overall system improvement fC is only 4. The white area in the inset shows where the magnitude of the E-field is 10× greater than that of a bare cavity. (e) The rotation of the trimer has little effect on fC. The white area in the inset shows where the magnitude of the E-field is 10× greater than that of a bare cavity. The enhancement area provided by the trimer in (e) is slightly more than twice that of a single rod in (d).
Fig. 6.
Fig. 6. (a) Schematic of the wedge model. (b) E-field distribution of a particle coupled to a toroid cavity (top view). The particle is placed at the antinode. (c) A zoom-in of near-field enhancement. (d) and (e) show the SM and ASM of the coupled system obtained by the whole 3D model using the eigenfrequency solver, respectively. The corresponding detuning frequency between the SM and ASM modes is 200 MHz.

Tables (1)

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Table 1. Q-Factor of the Coupled System for Different Wedge Anglesa

Equations (11)

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Δωω=ΔV[E0ε0Δε(r)E+H0μ0Δμ(r)H]dVV[ε0ε(r)E0·E+μ0μ(r)H0·H]dVεbE0α(ω)E02ε0εrVm|E0|max2,
α(ω)=(α000α000α),
α,=ΔVε0εmεbG,εm+(1G,)εb,
G=Rs1e2e2[1+12eln(1+e1e)],
G=1G2,
fE=ΔV|Ec(r)|2dVΔV|E(r)|2dV,
fC=fQfE=QcQ0fE,
dbWGMdt=(iΩWGMΓWGM)bWGM+iκb1+iκb2++iκbn,db1dt=(iΩ1Γ1)b1+iκbWGM,dbndt=(iΩnΓn)bn+iκbWGM,
H=[ΩWGM+iΓWGMκκκΩ1+iΓ1000κ0Ωn+iΓn].
θ=Nπm,
κ=[(ΩWGM+iΓWGMΩcouplediΓcoupled)(Ω1+iΓ1ΩcouplediΓcoupled)]12.

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