Abstract

Label-free, single-object sensing with a microring resonator is investigated numerically using the finite difference time-domain (FDTD) method. A pulse with ultra-wide bandwidth that spans over several resonant modes of the ring and of the sensing object is used for simulation, enabling a single-shot simulation of the microring sensing. The FDTD simulation not only can describe the circulation of the light in a whispering-gallery-mode (WGM) microring and multiple interactions between the light and the sensing object, but also other important factors of the sensing system, such as scattering and radiation losses. The FDTD results show that the simulation can yield a resonant shift of the WGM cavity modes. Furthermore, it can also extract eigenmodes of the sensing object, and therefore information from deep inside the object. The simulation method is not only suitable for a single object (single molecule, nano-, micro-scale particle) but can be extended to the problem of multiple objects as well.

©2013 Optical Society of America

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References

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  1. A. M. Armani, R. P. Kulkarni, S. E. Fraser, R. C. Flagan, and K. J. Vahala, “Label-free, single-molecule detection with optical microcavities,” Science 317(5839), 783–787 (2007).
    [Crossref] [PubMed]
  2. F. Vollmer, D. Braun, A. Libchaber, M. Khoshsima, I. Teraoka, and S. Arnold, “Protein detection by optical shift of a resonant microcavity,” Appl. Phys. Lett. 80(21), 4057–4059 (2002).
    [Crossref]
  3. F. Vollmer and S. Arnold, “Whispering-gallery-mode biosensing: label-free detection down to single molecules,” Nat. Methods 5(7), 591–596 (2008).
    [Crossref] [PubMed]
  4. 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 microresonantor,” Nat. Photonics 4(1), 46–49 (2010).
    [Crossref]
  5. H. T. Beir, G. L. Cote, and K. E. Meissner, “Whispering-gallery-mode based biosensing using quantum dot-embedded microspheres,” in Colloidal Quantum Dots for Biomedical Applications V, edited by M. Osinski. Proc. SPIE 7575, 5750H (2010).
  6. F. Vollmer, ““Microcavity biosensing,” in Frontiers in Ultrafast Optics: Biomedical, Scientific, and Industrial Applications XI. Eds A. Heisterkamp, J. Neev, and S,” Nolte. Proc. SPIE 7925, 792502, 792502-4 (2011).
    [Crossref]
  7. B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonators channel dropping filters,” J. Lightwave Technol. 15(6), 998–1005 (1997).
    [Crossref]
  8. R.J. Hawkins, N. K. Maden, J.S. Kallman, M. D. Feit, C. C. Shang, B. W. Shore, and J. F. DeFord, “Full-wave simulation of the thumbtack laser,” in Integrated Photon. Res. Tech. Dig., 1993, Palm Springs, CA, 10, 116 - 119, Mar. 1993.
  9. B. J. Li and P. L. Liu, “Numerical analysis of whispering gallery modes by the finite –different time-domain method,” IEEE J. Quantum Electron. 32(9), 1583–1587 (1996).
    [Crossref]
  10. S. C. Hagness, D. Rafizadesh, S. T. Ho, and A. Taflove, “FDTD microcavity simulations: design and experimental realization of waveguide-coupled single-mode ring and whispering-gallery-mode disk resonators,” J. Lightwave Technol. 15(11), 2154–2165 (1997).
    [Crossref]
  11. S.-T. Chu and S. K. Chaudhuri, “A finite-difference time-domain method for the design and analysis of guided-wave optical structures,” J. Lightwave Technol. 7(12), 2033–2038 (1989).
    [Crossref]
  12. J.-P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114(2), 185–200 (1994).
    [Crossref]
  13. Dennis M. Sullivan, Electromagnetic Simulation using FDTD Method (Wiley-IEEE Press, July 2000).

2011 (1)

F. Vollmer, ““Microcavity biosensing,” in Frontiers in Ultrafast Optics: Biomedical, Scientific, and Industrial Applications XI. Eds A. Heisterkamp, J. Neev, and S,” Nolte. Proc. SPIE 7925, 792502, 792502-4 (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 microresonantor,” Nat. Photonics 4(1), 46–49 (2010).
[Crossref]

2008 (1)

F. Vollmer and S. Arnold, “Whispering-gallery-mode biosensing: label-free detection down to single molecules,” Nat. Methods 5(7), 591–596 (2008).
[Crossref] [PubMed]

2007 (1)

A. M. Armani, R. P. Kulkarni, S. E. Fraser, R. C. Flagan, and K. J. Vahala, “Label-free, single-molecule detection with optical microcavities,” Science 317(5839), 783–787 (2007).
[Crossref] [PubMed]

2002 (1)

F. Vollmer, D. Braun, A. Libchaber, M. Khoshsima, I. Teraoka, and S. Arnold, “Protein detection by optical shift of a resonant microcavity,” Appl. Phys. Lett. 80(21), 4057–4059 (2002).
[Crossref]

1997 (2)

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonators channel dropping filters,” J. Lightwave Technol. 15(6), 998–1005 (1997).
[Crossref]

S. C. Hagness, D. Rafizadesh, S. T. Ho, and A. Taflove, “FDTD microcavity simulations: design and experimental realization of waveguide-coupled single-mode ring and whispering-gallery-mode disk resonators,” J. Lightwave Technol. 15(11), 2154–2165 (1997).
[Crossref]

1996 (1)

B. J. Li and P. L. Liu, “Numerical analysis of whispering gallery modes by the finite –different time-domain method,” IEEE J. Quantum Electron. 32(9), 1583–1587 (1996).
[Crossref]

1994 (1)

J.-P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114(2), 185–200 (1994).
[Crossref]

1989 (1)

S.-T. Chu and S. K. Chaudhuri, “A finite-difference time-domain method for the design and analysis of guided-wave optical structures,” J. Lightwave Technol. 7(12), 2033–2038 (1989).
[Crossref]

Armani, A. M.

A. M. Armani, R. P. Kulkarni, S. E. Fraser, R. C. Flagan, and K. J. Vahala, “Label-free, single-molecule detection with optical microcavities,” Science 317(5839), 783–787 (2007).
[Crossref] [PubMed]

Arnold, S.

F. Vollmer and S. Arnold, “Whispering-gallery-mode biosensing: label-free detection down to single molecules,” Nat. Methods 5(7), 591–596 (2008).
[Crossref] [PubMed]

F. Vollmer, D. Braun, A. Libchaber, M. Khoshsima, I. Teraoka, and S. Arnold, “Protein detection by optical shift of a resonant microcavity,” Appl. Phys. Lett. 80(21), 4057–4059 (2002).
[Crossref]

Berenger, J.-P.

J.-P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114(2), 185–200 (1994).
[Crossref]

Braun, D.

F. Vollmer, D. Braun, A. Libchaber, M. Khoshsima, I. Teraoka, and S. Arnold, “Protein detection by optical shift of a resonant microcavity,” Appl. Phys. Lett. 80(21), 4057–4059 (2002).
[Crossref]

Chaudhuri, S. K.

S.-T. Chu and S. K. Chaudhuri, “A finite-difference time-domain method for the design and analysis of guided-wave optical structures,” J. Lightwave Technol. 7(12), 2033–2038 (1989).
[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 microresonantor,” Nat. Photonics 4(1), 46–49 (2010).
[Crossref]

Chu, S. T.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonators channel dropping filters,” J. Lightwave Technol. 15(6), 998–1005 (1997).
[Crossref]

Chu, S.-T.

S.-T. Chu and S. K. Chaudhuri, “A finite-difference time-domain method for the design and analysis of guided-wave optical structures,” J. Lightwave Technol. 7(12), 2033–2038 (1989).
[Crossref]

Flagan, R. C.

A. M. Armani, R. P. Kulkarni, S. E. Fraser, R. C. Flagan, and K. J. Vahala, “Label-free, single-molecule detection with optical microcavities,” Science 317(5839), 783–787 (2007).
[Crossref] [PubMed]

Foresi, J.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonators channel dropping filters,” J. Lightwave Technol. 15(6), 998–1005 (1997).
[Crossref]

Fraser, S. E.

A. M. Armani, R. P. Kulkarni, S. E. Fraser, R. C. Flagan, and K. J. Vahala, “Label-free, single-molecule detection with optical microcavities,” Science 317(5839), 783–787 (2007).
[Crossref] [PubMed]

Hagness, S. C.

S. C. Hagness, D. Rafizadesh, S. T. Ho, and A. Taflove, “FDTD microcavity simulations: design and experimental realization of waveguide-coupled single-mode ring and whispering-gallery-mode disk resonators,” J. Lightwave Technol. 15(11), 2154–2165 (1997).
[Crossref]

Haus, H. A.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonators channel dropping filters,” J. Lightwave Technol. 15(6), 998–1005 (1997).
[Crossref]

He, L.

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 microresonantor,” Nat. Photonics 4(1), 46–49 (2010).
[Crossref]

Ho, S. T.

S. C. Hagness, D. Rafizadesh, S. T. Ho, and A. Taflove, “FDTD microcavity simulations: design and experimental realization of waveguide-coupled single-mode ring and whispering-gallery-mode disk resonators,” J. Lightwave Technol. 15(11), 2154–2165 (1997).
[Crossref]

Khoshsima, M.

F. Vollmer, D. Braun, A. Libchaber, M. Khoshsima, I. Teraoka, and S. Arnold, “Protein detection by optical shift of a resonant microcavity,” Appl. Phys. Lett. 80(21), 4057–4059 (2002).
[Crossref]

Kulkarni, R. P.

A. M. Armani, R. P. Kulkarni, S. E. Fraser, R. C. Flagan, and K. J. Vahala, “Label-free, single-molecule detection with optical microcavities,” Science 317(5839), 783–787 (2007).
[Crossref] [PubMed]

Laine, J.-P.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonators channel dropping filters,” J. Lightwave Technol. 15(6), 998–1005 (1997).
[Crossref]

Li, B. J.

B. J. Li and P. L. Liu, “Numerical analysis of whispering gallery modes by the finite –different time-domain method,” IEEE J. Quantum Electron. 32(9), 1583–1587 (1996).
[Crossref]

Li, L.

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 microresonantor,” Nat. Photonics 4(1), 46–49 (2010).
[Crossref]

Libchaber, A.

F. Vollmer, D. Braun, A. Libchaber, M. Khoshsima, I. Teraoka, and S. Arnold, “Protein detection by optical shift of a resonant microcavity,” Appl. Phys. Lett. 80(21), 4057–4059 (2002).
[Crossref]

Little, B. E.

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonators channel dropping filters,” J. Lightwave Technol. 15(6), 998–1005 (1997).
[Crossref]

Liu, P. L.

B. J. Li and P. L. Liu, “Numerical analysis of whispering gallery modes by the finite –different time-domain method,” IEEE J. Quantum Electron. 32(9), 1583–1587 (1996).
[Crossref]

Ozdemir, S. K.

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 microresonantor,” Nat. Photonics 4(1), 46–49 (2010).
[Crossref]

Rafizadesh, D.

S. C. Hagness, D. Rafizadesh, S. T. Ho, and A. Taflove, “FDTD microcavity simulations: design and experimental realization of waveguide-coupled single-mode ring and whispering-gallery-mode disk resonators,” J. Lightwave Technol. 15(11), 2154–2165 (1997).
[Crossref]

Taflove, A.

S. C. Hagness, D. Rafizadesh, S. T. Ho, and A. Taflove, “FDTD microcavity simulations: design and experimental realization of waveguide-coupled single-mode ring and whispering-gallery-mode disk resonators,” J. Lightwave Technol. 15(11), 2154–2165 (1997).
[Crossref]

Teraoka, I.

F. Vollmer, D. Braun, A. Libchaber, M. Khoshsima, I. Teraoka, and S. Arnold, “Protein detection by optical shift of a resonant microcavity,” Appl. Phys. Lett. 80(21), 4057–4059 (2002).
[Crossref]

Vahala, K. J.

A. M. Armani, R. P. Kulkarni, S. E. Fraser, R. C. Flagan, and K. J. Vahala, “Label-free, single-molecule detection with optical microcavities,” Science 317(5839), 783–787 (2007).
[Crossref] [PubMed]

Vollmer, F.

F. Vollmer, ““Microcavity biosensing,” in Frontiers in Ultrafast Optics: Biomedical, Scientific, and Industrial Applications XI. Eds A. Heisterkamp, J. Neev, and S,” Nolte. Proc. SPIE 7925, 792502, 792502-4 (2011).
[Crossref]

F. Vollmer and S. Arnold, “Whispering-gallery-mode biosensing: label-free detection down to single molecules,” Nat. Methods 5(7), 591–596 (2008).
[Crossref] [PubMed]

F. Vollmer, D. Braun, A. Libchaber, M. Khoshsima, I. Teraoka, and S. Arnold, “Protein detection by optical shift of a resonant microcavity,” Appl. Phys. Lett. 80(21), 4057–4059 (2002).
[Crossref]

Xiao, Y.-F.

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 microresonantor,” Nat. Photonics 4(1), 46–49 (2010).
[Crossref]

Yang, L.

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 microresonantor,” Nat. Photonics 4(1), 46–49 (2010).
[Crossref]

Zhu, J.

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 microresonantor,” Nat. Photonics 4(1), 46–49 (2010).
[Crossref]

Appl. Phys. Lett. (1)

F. Vollmer, D. Braun, A. Libchaber, M. Khoshsima, I. Teraoka, and S. Arnold, “Protein detection by optical shift of a resonant microcavity,” Appl. Phys. Lett. 80(21), 4057–4059 (2002).
[Crossref]

IEEE J. Quantum Electron. (1)

B. J. Li and P. L. Liu, “Numerical analysis of whispering gallery modes by the finite –different time-domain method,” IEEE J. Quantum Electron. 32(9), 1583–1587 (1996).
[Crossref]

J. Comput. Phys. (1)

J.-P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114(2), 185–200 (1994).
[Crossref]

J. Lightwave Technol. (3)

S. C. Hagness, D. Rafizadesh, S. T. Ho, and A. Taflove, “FDTD microcavity simulations: design and experimental realization of waveguide-coupled single-mode ring and whispering-gallery-mode disk resonators,” J. Lightwave Technol. 15(11), 2154–2165 (1997).
[Crossref]

S.-T. Chu and S. K. Chaudhuri, “A finite-difference time-domain method for the design and analysis of guided-wave optical structures,” J. Lightwave Technol. 7(12), 2033–2038 (1989).
[Crossref]

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonators channel dropping filters,” J. Lightwave Technol. 15(6), 998–1005 (1997).
[Crossref]

Nat. Methods (1)

F. Vollmer and S. Arnold, “Whispering-gallery-mode biosensing: label-free detection down to single molecules,” Nat. Methods 5(7), 591–596 (2008).
[Crossref] [PubMed]

Nat. Photonics (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 microresonantor,” Nat. Photonics 4(1), 46–49 (2010).
[Crossref]

Nolte. Proc. SPIE (1)

F. Vollmer, ““Microcavity biosensing,” in Frontiers in Ultrafast Optics: Biomedical, Scientific, and Industrial Applications XI. Eds A. Heisterkamp, J. Neev, and S,” Nolte. Proc. SPIE 7925, 792502, 792502-4 (2011).
[Crossref]

Science (1)

A. M. Armani, R. P. Kulkarni, S. E. Fraser, R. C. Flagan, and K. J. Vahala, “Label-free, single-molecule detection with optical microcavities,” Science 317(5839), 783–787 (2007).
[Crossref] [PubMed]

Other (3)

R.J. Hawkins, N. K. Maden, J.S. Kallman, M. D. Feit, C. C. Shang, B. W. Shore, and J. F. DeFord, “Full-wave simulation of the thumbtack laser,” in Integrated Photon. Res. Tech. Dig., 1993, Palm Springs, CA, 10, 116 - 119, Mar. 1993.

H. T. Beir, G. L. Cote, and K. E. Meissner, “Whispering-gallery-mode based biosensing using quantum dot-embedded microspheres,” in Colloidal Quantum Dots for Biomedical Applications V, edited by M. Osinski. Proc. SPIE 7575, 5750H (2010).

Dennis M. Sullivan, Electromagnetic Simulation using FDTD Method (Wiley-IEEE Press, July 2000).

Supplementary Material (4)

Media 1: AVI (3946 KB)     
Media 2: AVI (14900 KB)     
Media 3: AVI (3946 KB)     
Media 4: AVI (14900 KB)     

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Figures (8)
Fig. 1
Fig. 1 Schematic of a microring sensor: a ring resonator (radius R, width dR and index nR) coupled to a waveguide (width dW, index nW). The gap between the ring and the waveguide is g. A sensing object (radius rSO and index nSO) is adjacent to the ring (light blue microdisk).

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Fig. 2
Fig. 2 FDTD simulation of light field with frequency of 192 THz in a microring with R = 20μm, nR = nW = 1.46, dR = dW = 1μm . (a): without sensing object, and (b) with sensing object rSO = 2 μm, nSO = 3.6. The long waveguide around the sensing system acts to minimize the boundary reflection that can couple back into to the cavity during the resonant recirculation of the light.

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Fig. 3
Fig. 3 A general result from FDTD simulation of the pulse propagating in the waveguide and coupling to the microring. (a) E-field of the input pulse in time domain (TD), and (b) normalized intensity in frequency domain (FD). (c) E-field inside the cavity measured at position 2 in TD, and (d) relative intensity in FD showing the resonant modes of the ring without the sensing object. (e) E-field in TD and (f) transmission in FD (at position 3). Central: intensity of the light with frequency f = 192 THz which is closest to a resonant mode of the ring shown in (d).

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Fig. 4
Fig. 4 Intensity of the light with f = 192 THz in the microring (R = 20, dR = 1 μm, n = 1.46) with and without a sensing object. (a) without SO, (b) with SO r = 2 μm, nSO = 3.6, and (c) with SO r = 3 μm, nSO = 3.6, (d) relative intensity inside cavity, (e) transmission: without SO (red-curve), with SO r = 2 μm (blue), and with SO r = 3 μm (green); nSO = 3.6. Media 1 (or in large format, Media 2) is a short animation of light propagation in the microring adjacent to SO = 2micron described in Fig. 4(b).

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Fig. 5
Fig. 5 Eigenmodes of several SOs with different size and indices within the bandwidth of the light pulse that was used to simulate the microring sensing above. (a) r = 1μm, n = 3.6, (b) r = 2μm, n = 3.6, (c) r = 1μm, n = 4, and (d) r = 2μm, n = 2.0. The two SOs in (a) and (b) are used for the simulation of microring sensing shown in Figs. 4(b) and 4(c) above. Media 3 (or in large format, Media 4) is a short animation of light propagation in SO with r=2 m, n=3.6 (e.g., Fig. 5(b)).

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Fig. 6
Fig. 6 (a): Transmission T of the micro-sensing without (red) and without sensing object (blue). The microring (R = 20 μm, dR = 1μm, nR = 1.46); SO rSO = 2 μm and nSO = 3.6., and (b): Relative intensity inside microring without (red) and with (blue) sensing object, and inside the sensing object (green) which show the resonant modes in the systems. The SO has rSO = 2 μm and nSO = 3.6. The two green arrows indicate new modes that come from SO and can be detected in the transmission.

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Fig. 7
Fig. 7 Resonant modes of a microring with R = 20 μm and n = 1.46. (a) E field in time domain, 10 recirculations, (b) E field in time domain, 5 recirculations, and (c) relative intensity inside the microring in frequency domain: 5 recirculation (red) and 10 recirculation (blue).

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Fig. 8
Fig. 8 During the recirculation of light in the ring, each time it passes the coupling region, light can couple to and subsequently co-propagates in the waveguide. Left: first time, (central) second time, and (right) third time light passes the coupling region. (See the propagation of light in the system for the whole time in the Media 1).

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