Abstract

Ultra-high quality (Q) whispering gallery mode (WGM) microtoroid optical resonators have demonstrated highly sensitive biomolecular detection down to the single molecule limit; however, the lack of a robust coupling method has prevented their widespread adoption outside the laboratory. We demonstrate through simulation that a phased array of nanorods can enable free-space coupling of light both into and out of a microtoroid while maintaining a high Q. To simulate large nanostructured WGM resonators, we developed a new approach known as FloWBEM, which is an efficient and compact 3D wedge model with custom boundary conditions that accurately simulate the resonant Fano interference between the traveling WGM waves and a nanorod array. Depending on the excitation conditions, we find loaded Q factors of the driven system as high as 2.1×107 and signal-to-background ratios as high as 3.86%, greater than the noise levels of many commercial detectors. These results can drive future experimental implementation.

© 2019 Chinese Laser Press

Full Article  |  PDF Article
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References

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2019 (1)

2018 (7)

S. H. Huang, X. Jiang, B. Peng, C. Janisch, A. Cocking, Ş. K. Özdemir, Z. Liu, and L. Yang, “Surface-enhanced Raman scattering on dielectric microspheres with whispering gallery mode resonance,” Photon. Res. 6, 346–356 (2018).
[Crossref]

F. Shu, X. Jiang, G. Zhao, and L. Yang, “A scatterer-assisted whispering-gallery-mode microprobe,” Nanophotonics 7, 1455–1460 (2018).
[Crossref]

Y. Zhang, T. Zhou, B. Han, A. Zhang, and Y. Zhao, “Optical bio-chemical sensors based on whispering gallery mode resonators,” Nanoscale 10, 13832–13856 (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]

Y. Xu, S.-J. Tang, X.-C. Yu, Y.-L. Chen, D. Yang, Q. Gong, and Y.-F. Xiao, “Mode splitting induced by an arbitrarily shaped Rayleigh scatterer in a whispering-gallery microcavity,” Phys. Rev. A 97, 063828 (2018).
[Crossref]

W. Chen, H. Xiao, Z. Liu, X. Han, M. Liao, T. Zhao, and Y. Tian, “Experimental realization of mode-splitting resonance using microring resonator with a feedback coupled waveguide,” Appl. Phys. Express 11, 092201 (2018).
[Crossref]

2017 (4)

M. F. Limonov, M. V. Rybin, A. N. Poddubny, and Y. S. Kivshar, “Fano resonances in photonics,” Nat. Photonics 11, 543–554 (2017).
[Crossref]

Z. Chen, Y. Zhou, and J.-T. Shen, “Dissipation-induced photonic-correlation transition in waveguide-QED systems,” Phys. Rev. A 96, 053805 (2017).
[Crossref]

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

X. Jiang, L. Shao, S. X. Zhang, X. Yi, J. Wiersig, L. Wang, Q. Gong, M. Lončar, L. Yang, and Y. F. Xiao, “Chaos-assisted broadband momentum transformation in optical microresonators,” Science 358, 344–347 (2017).
[Crossref]

2016 (4)

X.-F. Jiang, C.-L. Zou, L. Wang, Q. Gong, and Y.-F. Xiao, “Whispering-gallery microcavities with unidirectional laser emission,” Laser Photon. Rev. 10, 40–61 (2016).
[Crossref]

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]

A. Gopinath, E. Miyazono, A. Faraon, and P. W. K. Rothemund, “Engineering and mapping nanocavity emission via precision placement of DNA origami,” Nature 535, 401–405 (2016).
[Crossref]

Z. Chen, Y. Zhou, and J.-T. Shen, “Photon antibunching and bunching in a ring-resonator waveguide quantum electrodynamics system,” Opt. Lett. 41, 3313–3316 (2016).
[Crossref]

2015 (5)

R. Halir, P. J. Bock, P. Cheben, A. Ortega‐Moñux, C. Alonso‐Ramos, J. H. Schmid, J. Lapointe, D.-X. Xu, J. G. Wangüemert‐Pérez, Í. Molina‐Fernández, and S. Janz, “Waveguide sub-wavelength structures: a review of principles and applications,” Laser Photon. Rev. 9, 25–49 (2015).
[Crossref]

F. Ruesink, H. M. Doeleman, R. Hendrikx, A. F. Koenderink, and E. Verhagen, “Perturbing open cavities: anomalous resonance frequency shifts in a hybrid cavity-nanoantenna system,” Phys. Rev. Lett. 115, 203904 (2015).
[Crossref]

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

E. McLeod, Q. Wei, and O. Aydogan, “Democratization of nanoscale imaging and sensing tools using photonics,” Anal. Chem. 87, 6434–6445 (2015).
[Crossref]

F. Gu, Z. Li, Y. Zhu, and H. Zeng, “Free-space coupling of nanoantennas and whispering-gallery microcavities with narrowed linewidth and enhanced sensitivity,” Laser Photon. Rev. 9, 682–688 (2015).
[Crossref]

2014 (2)

J. Zhu, Ş. K. Özdemir, H. Yilmaz, B. Peng, M. Dong, M. Tomes, T. Carmon, and L. Yang, “Interfacing whispering-gallery microresonators and free space light with cavity enhanced Rayleigh scattering,” Sci. Rep. 4, 6396 (2014).
[Crossref]

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 (7)

L. Shao, X.-F. Jiang, X.-C. Yu, B.-B. Li, W. R. Clements, F. Vollmer, W. Wang, Y.-F. Xiao, and Q. Gong, “Detection of single nanoparticles and lentiviruses using microcavity resonance broadening,” Adv. Mater. 25, 5616–5620 (2013).
[Crossref]

Y. Zhou, D. Zhu, X. Yu, W. Ding, and F. Luan, “Fano resonances in metallic grating coupled whispering gallery mode resonator,” Appl. Phys. Lett. 103, 151108 (2013).
[Crossref]

Z.-P. Liu, X.-F. Jiang, Y. Li, Y.-F. Xiao, L. Wang, J.-L. Ren, S.-J. Zhang, H. Yang, and Q. Gong, “High-Q asymmetric polymer microcavities directly fabricated by two-photon polymerization,” Appl. Phys. Lett. 102, 221108 (2013).
[Crossref]

X.-F. Jiang, Y.-F. Xiao, Q.-F. Yang, L. Shao, W. R. Clements, and Q. Gong, “Free-space coupled, ultralow-threshold Raman lasing from a silica microcavity,” Appl. Phys. Lett. 103, 101102 (2013).
[Crossref]

L. Shao, L. Wang, W. Xiong, X.-F. Jiang, Q.-F. Yang, and Y.-F. Xiao, “Ultrahigh-Q, largely deformed microcavities coupled by a free-space laser beam,” Appl. Phys. Lett. 103, 121102 (2013).
[Crossref]

A. Kaplan, M. Tomes, T. Carmon, M. Kozlov, O. Cohen, G. Bartal, and H. G. 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]

M. A. C. Shirazi, W. Yu, S. Vincent, and T. Lu, “Cylindrical beam propagation modelling of perturbed whispering-gallery mode microcavities,” Opt. Express 21, 30243–30254 (2013).
[Crossref]

2012 (2)

X.-F. Jiang, Y.-F. Xiao, C.-L. Zou, L. He, C.-H. Dong, B.-B. Li, Y. Li, F.-W. Sun, L. Yang, and Q. Gong, “Highly unidirectional emission and ultralow-threshold lasing from on-chip ultrahigh-Q microcavities,” Adv. Mater. 24, OP260–OP264 (2012).
[Crossref]

Y.-C. Liu, Y.-F. Xiao, X.-F. Jiang, B.-B. Li, Y. Li, and Q. Gong, “Cavity-QED treatment of scattering-induced free-space excitation and collection in high-Q whispering-gallery microcavities,” Phys. Rev. A 85, 013843 (2012).
[Crossref]

2011 (1)

C. M. Soukoulis and M. Wegener, “Past achievements and future challenges in the development of three-dimensional photonic metamaterials,” Nat. Photonics 5, 523–530 (2011).
[Crossref]

2010 (1)

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]

2008 (3)

S. I. Shopova, I. M. White, Y. Sun, H. Zhu, X. Fan, G. Frye-Mason, A. Thompson, and S. Ja, “On-column micro gas chromatography detection with capillary-based optical ring resonators,” Anal. Chem. 80, 2232–2238 (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]

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

2007 (2)

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]

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]

2006 (1)

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

2005 (1)

S. H. Liu and M. Y. Han, “Synthesis, functionalization, and bioconjugation of monodisperse, silica-coated gold nanoparticles: robust bioprobes,” Adv. Funct. Mater. 15, 961–967 (2005).
[Crossref]

2003 (2)

1997 (1)

1995 (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. IEEE C 107, 272–274 (1960).
[Crossref]

Alonso-Ramos, C.

R. Halir, P. J. Bock, P. Cheben, A. Ortega‐Moñux, C. Alonso‐Ramos, J. H. Schmid, J. Lapointe, D.-X. Xu, J. G. Wangüemert‐Pérez, Í. Molina‐Fernández, and S. Janz, “Waveguide sub-wavelength structures: a review of principles and applications,” Laser Photon. Rev. 9, 25–49 (2015).
[Crossref]

Arnold, S.

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]

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

Aydogan, O.

E. McLeod, Q. Wei, and O. Aydogan, “Democratization of nanoscale imaging and sensing tools using photonics,” Anal. Chem. 87, 6434–6445 (2015).
[Crossref]

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]

Bartal, G.

Birks, T. A.

Bock, P. J.

R. Halir, P. J. Bock, P. Cheben, A. Ortega‐Moñux, C. Alonso‐Ramos, J. H. Schmid, J. Lapointe, D.-X. Xu, J. G. Wangüemert‐Pérez, Í. Molina‐Fernández, and S. Janz, “Waveguide sub-wavelength structures: a review of principles and applications,” Laser Photon. Rev. 9, 25–49 (2015).
[Crossref]

Carmon, T.

J. Zhu, Ş. K. Özdemir, H. Yilmaz, B. Peng, M. Dong, M. Tomes, T. Carmon, and L. Yang, “Interfacing whispering-gallery microresonators and free space light with cavity enhanced Rayleigh scattering,” Sci. Rep. 4, 6396 (2014).
[Crossref]

A. Kaplan, M. Tomes, T. Carmon, M. Kozlov, O. Cohen, G. Bartal, and H. G. 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]

Cheben, P.

R. Halir, P. J. Bock, P. Cheben, A. Ortega‐Moñux, C. Alonso‐Ramos, J. H. Schmid, J. Lapointe, D.-X. Xu, J. G. Wangüemert‐Pérez, Í. Molina‐Fernández, and S. Janz, “Waveguide sub-wavelength structures: a review of principles and applications,” Laser Photon. Rev. 9, 25–49 (2015).
[Crossref]

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, L.

Chen, W.

W. Chen, H. Xiao, Z. Liu, X. Han, M. Liao, T. Zhao, and Y. Tian, “Experimental realization of mode-splitting resonance using microring resonator with a feedback coupled waveguide,” Appl. Phys. Express 11, 092201 (2018).
[Crossref]

Chen, Y.-L.

Y. Xu, S.-J. Tang, X.-C. Yu, Y.-L. Chen, D. Yang, Q. Gong, and Y.-F. Xiao, “Mode splitting induced by an arbitrarily shaped Rayleigh scatterer in a whispering-gallery microcavity,” Phys. Rev. A 97, 063828 (2018).
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Appl. Phys. Express (1)

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Figures (9)

Fig. 1.
Fig. 1. Free-space coupling to a WGM microtoroid optical resonator via a phased array of gold nanorods. (a) Schematic view. (b) Collection of far-field scattering from the grating shows the Fano resonance corresponding to the interference between the grating and WGM resonances. (c) Established 2D axisymmetric simulations identify a resonance of the bare WGM at λ2633  nm, corresponding to an azimuthal mode number m=660. (d) The FloWBEM simulation of the same bare toroid as in panel (c). Surfaces S1 and S2 are simulated with Floquet boundary conditions, and S3 is simulated with scattering boundary conditions. (e) For simulating the driven system, a far-field domain (S4) is added at the circumference, replacing the Floquet and scattering boundary conditions for that region. (f) Nanorods are placed in the equatorial plane, between the light source, which is incident at 45°, and the silica toroid. A field continuity condition is applied between the light source and the domain surrounding the toroid.
Fig. 2.
Fig. 2. Frequency domain simulations of the driven system. (a) Intracavity energy of the coupled TE WGM with a grating spaced d=1000  nm from the toroid. Zoom-in: ΔλFWHM=0.14  pm. (b) Intracavity energy of the coupled TM WGM with a grating-toroid spacing d=1000  nm. Zoom-in: ΔλFWHM=0.22  pm. (c) TE WGM backaction-mediated reflection spectrum corresponding to the same simulation as panel (a). (d) TM WGM backaction mediated reflection spectrum corresponding to the same simulation as panel (b). In all panels, the wavelength step is 0.5 nm for the broad spectrum, and between 0.005 pm and 2 pm in the vicinity of the resonance (insets). The SBR and δλFWHM values for panels (c) and (d) are given in Table 1.
Fig. 3.
Fig. 3. Effect of grating-WGM separation on linewidths. Loaded Q factors for both TE and TM polarizations depend on grating-toroid separation. Q factors are evaluated using three methods: eigenfrequency Re{fres}/(2Im{fres}) (solid circles and lines), eigenfrequency 2πfresW/(Pabs+Prad) (hollow circles), and frequency domain λres/ΔλFWHM (red stars). Owing to the increased computational costs of frequency domain simulations, only four points are shown.
Fig. 4.
Fig. 4. Mode field distributions of the driven coupled system. (a) 3D frequency domain simulation of the microtoroid coupled to the grating with various separation distances. The CCW mode is shown, which is selected through appropriate choice of the Floquet boundary conditions. The incident light is s-polarized, which drives a TE WGM. Field distributions are plotted as field amplitude |E|. (b) Same as panel (a), but with a separation of d=1000  nm. (c) Same as panel (b), but where the CW solution has been selected through the choice of Floquet boundary conditions with opposite sign. (d) The superposition of the field distributions in (b) and (c).
Fig. 5.
Fig. 5. Reflected spectrum exhibiting a Lorentzian lineshape, corresponding to the third column in Table 1 of the main text (d=700  nm). The SBR is 0.05%.
Fig. 6.
Fig. 6. Reflected spectrum exhibiting a Fano lineshape, corresponding to the fifth column in Table 1 of the main text (d=700  nm). The SBR is 1.18%.
Fig. 7.
Fig. 7. Far-field scattering from isolated nanorods and nanorod arrays without a WGM resonator. (a) Intensity of the far-field scattering of a single nanorod excited at the LSPR. (b) 3D grating of 10 nanorods with nonphase matched periodicity Λ=228.5  nm, excited at normal incidence and at the LSPR of the individual rods. (c) Same as (b), but at 45° incidence. (d) Same as (c), but with nine nanorods with periodicity Λ=264.8  nm that is perfectly phase-matched for backward scattering when excited at 45° incidence. For the case of finite-length nanorods positioned near the curved surface of the toroid, we expect only partial phase matching (see main text Fig. 4) and not perfect phase matching. (e) Same as (c), but excited with transverse polarization, which would correspond to a TM-polarized WGM. (f) Same as (d), but excited with transverse polarization. The six panels are solved in frequency domain at a wavelength of 630 nm. The dark orange arrows denote the incoming angle of the light.
Fig. 8.
Fig. 8. Intracavity energy spectra for the TE CCW mode (blue) and the TE CW mode (red). The CCW mode is dominant due to partial phase matching between the incident light, grating periodicity, and WGM mode.
Fig. 9.
Fig. 9. WGM frequency shift for a single nanorod as a function of nanorod aspect ratio (AR).

Tables (2)

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Table 1. Calculation Methods for Loaded Q of the Driven WGM Coupled to a Gratinga

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Table 2. Intracavity Energy of the Frequency Domain Driven TE CCW and CW Modes for Different Coupling Separation

Equations (7)

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kF=±2πλeffn^ϕ=±2π2πRmn^ϕ±mRn^x,
Udst=Usrcexp[ikF·(rdstrsrc)].
kinc,x+2πNΛ=2πMλeff,
2πnwaterλsin45°+2πNΛ=mMR
Δωω=nwater2α(AR)|E0|22ε0nSio22Vm|E0|max2,
α=ΔVε0εAunwater2GεAu+(1G)nwater2,
G=Rs1ec2ec2[1+12ecln(1+ec1ec)],