Abstract

The accurate characterization of single nanoparticles in colloidal solutions in terms of their size and morphology is important for medical diagnostics and aerosol investigations. However, it is challenging to achieve a high throughput for very small (sub-100 nm) particles. In particular, it is not well established what the fundamental limits are on the trade-off between speed and the smallest detectable particle. Here we study these limits for the case of refractive index sensing based on resonant photonic crystal cavities. Importantly, we have reached a regime where the fundamental thermal fluctuations set the intrinsic detection limit for acquisition sampling times tacq larger than 3 μs. Such an intrinsic fundamental limit corresponds to 1/2000th the linewidth of the optical spectrum of photonic crystal cavities of effective mode volume as small as 0.06  μm3. The results of this work indicate that it is possible to monitor up to 33 million particles per second with a particle size down to 34 nm, making it a promising technique for fast real-time biosensing.

© 2017 Optical Society of America

Full Article  |  PDF Article

Corrections

Kumar Saurav and Nicolas Le Thomas, "Probing the fundamental detection limit of photonic crystal cavities: erratum," Optica 4, 1305-1305 (2017)
https://www.osapublishing.org/optica/abstract.cfm?uri=optica-4-10-1305

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References

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  1. K. J. Vahala, “Optical microcavities,” Nature 424, 839–846 (2003).
    [Crossref]
  2. M. G. Scullion, T. F. Krauss, and A. Di Falco, “Slotted photonic crystal sensors,” Sensors 13, 3675–3710 (2013).
    [Crossref]
  3. 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]
  4. S. Rosenblum, Y. Lovsky, L. Arazi, F. Vollmer, and B. Dayan, “Cavity ring-up spectroscopy for ultrafast sensing with optical microresonators,” Nat. Commun. 6, 6788 (2015).
    [Crossref]
  5. M. Tardif, J.-B. Jager, P. R. Marcoux, K. Uchiyamada, E. Picard, E. Hadji, and D. Peyrade, “Single-cell bacterium identification with a SOI optical microcavity,” Appl. Phys. Lett. 109, 133510 (2016).
    [Crossref]
  6. F. Priolo, T. Gregorkiewicz, M. Galli, and T. F. Krauss, “Silicon nanostructures for photonics and photovoltaics,” Nat. Nanotechnol. 9, 19–32 (2014).
    [Crossref]
  7. D. Keng, S. McAnanama, I. Teraoka, and S. Arnold, “Resonance fluctuations of a whispering gallery mode biosensor by particles undergoing Brownian motion,” Appl. Phys. Lett. 91, 103902 (2007).
    [Crossref]
  8. From the local intensity |E|2 of the cavity mode and the dielectric map ε of the photonic structure, the effective volume can be defined as Veff=∫ε|E|2dV/max{ε|E|2}, where the max function takes the maximum value over the entire space. The numerical value Veff=0.06  μm3 has been determined with a finite difference time-domain method.
  9. X. Zhou, L. Zhang, and W. Pang, “Performance and noise analysis of optical microresonator-based biochemical sensors using intensity detection,” Opt. Express 24, 18197–18208 (2016).
    [Crossref]
  10. J. Hu, X. Sun, A. Agarwal, and L. C. Kimerling, “Design guidelines for optical resonator biochemical sensors,” J. Opt. Soc. Am. B 26, 1032–1041 (2009).
    [Crossref]
  11. Note that the current definition of the acquisition time is much more restrictive than the conventional definition of the rise time, which amounts to 6  μs for a load resistance of 1 MΩ with the current photodetector bandwidth of 1.2 GHz at Rload=50  Ω.
  12. Y. Akahane, T. Asano, B.-S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944–947 (2003).
    [Crossref]
  13. Y. Akahane, T. Asano, B.-S. Song, and S. Noda, “Fine-tuned high-Q photonic-crystal nanocavity,” Opt. Express 13, 1202–1214 (2005).
    [Crossref]
  14. L. D. Landau and E. M. Lifshitz, Statistical Physics, Part 1, 3rd ed. (Pergamon, 1980), § 114.
  15. In view of the value of the thermal expansion coefficient of the silicon, the impact of the density fluctuations can be neglected here.
  16. M. L. Gorodetsky and I. S. Grudinin, “Fundamental thermal fluctuations in microspheres,” J. Opt. Soc. Am. B 21, 697–705 (2004).
    [Crossref]
  17. J. Komma, C. Schwarz, G. Hofmann, D. Heinert, and R. Nawrodta, “Thermo-optic coefficient of silicon at 1550  nm and cryogenic temperatures,” Appl. Phys. Lett. 101, 041905 (2012).
    [Crossref]
  18. As a first-order approximation, we assume that mode is located within a homogeneous medium whose index equals the effective index of the 215  nm thick silicon slab waveguide. The optical index of the silicon is 3.45.
  19. G. Gagliardi, M. Salza, S. Avino, P. Ferraro, and P. De Natale, “Probing the ultimate limit of fiber-optic strain sensing,” Science 330, 1081–1084 (2010).
    [Crossref]
  20. G. A. Cranch and S. Foster, “Comment on probing the ultimate limit of fiber-optic strain sensing,” Science 335, 286 (2012).
    [Crossref]
  21. G. Gagliardi, M. Salza, S. Avino, P. Ferraro, and P. De Natale, “Response to comment on probing the ultimate limit of fiber-optic strain sensing,” Science 335, 286 (2012).
    [Crossref]
  22. J. Dong, J. Huang, T. Li, and L. Liu, “Observation of fundamental thermal noise in optical fibers down to infrasonic frequencies,” Appl. Phys. Lett. 108, 021108 (2016).
    [Crossref]
  23. J. Knittel, J. D. Swaim, D. L. McAuslan, G. A. Brawley, and W. P. Bowen, “Back-scatter based whispering gallery mode sensing,” Sci. Rep. 3, 2974 (2013).
    [Crossref]
  24. We have implemented a scanning near-field technique making use of silica nanotips to map the cavity near field, which will be discussed elsewhere.
  25. Note that even if the total quality factor appears as a parameter in Eq. (4), it has no impact on δω/Δω|min, as expected from the normalization by Δω, which confers to this quantity a figure of merit character.
  26. F. Vollmer and L. Yang, “Label-free detection with high-Q microcavities: a review of biosensing mechanisms for integrated devices,” Nanophotonics 1, 267–291 (2012).
    [Crossref]
  27. J. Yang, H. Giessen, and P. Lalanne, “Simple analytical expression for the peak-frequency shifts of plasmonic resonances for sensing,” Nano Lett. 15, 3439–3444 (2015).
    [Crossref]
  28. S. El Andaloussi, I. Mäger, X. O. Breakefield, and M. J. A. Wood, “Extracellular vesicles: biology and emerging therapeutic opportunities,” Nat. Rev. Drug Discovery 12, 347–357 (2013).
    [Crossref]
  29. C. Théry, M. Ostrowski, and E. Segura, “Membrane vesicles as conveyors of immune responses,” Nat. Rev. Immunol. 9, 581–593 (2009).
    [Crossref]
  30. M. Eigen and M. Rigler, “Sorting single molecules: application to diagnostics and evolutionary biotechnology,” Proc. Natl. Acad. Sci. USA 91, 5740–5747 (1994).
    [Crossref]
  31. B. J. Berne and R. Pecora, Dynamic Light Scattering: With Applications to Chemistry, Biology, and Physics (Wiley, 1976).

2016 (3)

M. Tardif, J.-B. Jager, P. R. Marcoux, K. Uchiyamada, E. Picard, E. Hadji, and D. Peyrade, “Single-cell bacterium identification with a SOI optical microcavity,” Appl. Phys. Lett. 109, 133510 (2016).
[Crossref]

X. Zhou, L. Zhang, and W. Pang, “Performance and noise analysis of optical microresonator-based biochemical sensors using intensity detection,” Opt. Express 24, 18197–18208 (2016).
[Crossref]

J. Dong, J. Huang, T. Li, and L. Liu, “Observation of fundamental thermal noise in optical fibers down to infrasonic frequencies,” Appl. Phys. Lett. 108, 021108 (2016).
[Crossref]

2015 (2)

S. Rosenblum, Y. Lovsky, L. Arazi, F. Vollmer, and B. Dayan, “Cavity ring-up spectroscopy for ultrafast sensing with optical microresonators,” Nat. Commun. 6, 6788 (2015).
[Crossref]

J. Yang, H. Giessen, and P. Lalanne, “Simple analytical expression for the peak-frequency shifts of plasmonic resonances for sensing,” Nano Lett. 15, 3439–3444 (2015).
[Crossref]

2014 (1)

F. Priolo, T. Gregorkiewicz, M. Galli, and T. F. Krauss, “Silicon nanostructures for photonics and photovoltaics,” Nat. Nanotechnol. 9, 19–32 (2014).
[Crossref]

2013 (3)

M. G. Scullion, T. F. Krauss, and A. Di Falco, “Slotted photonic crystal sensors,” Sensors 13, 3675–3710 (2013).
[Crossref]

J. Knittel, J. D. Swaim, D. L. McAuslan, G. A. Brawley, and W. P. Bowen, “Back-scatter based whispering gallery mode sensing,” Sci. Rep. 3, 2974 (2013).
[Crossref]

S. El Andaloussi, I. Mäger, X. O. Breakefield, and M. J. A. Wood, “Extracellular vesicles: biology and emerging therapeutic opportunities,” Nat. Rev. Drug Discovery 12, 347–357 (2013).
[Crossref]

2012 (4)

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

G. A. Cranch and S. Foster, “Comment on probing the ultimate limit of fiber-optic strain sensing,” Science 335, 286 (2012).
[Crossref]

G. Gagliardi, M. Salza, S. Avino, P. Ferraro, and P. De Natale, “Response to comment on probing the ultimate limit of fiber-optic strain sensing,” Science 335, 286 (2012).
[Crossref]

J. Komma, C. Schwarz, G. Hofmann, D. Heinert, and R. Nawrodta, “Thermo-optic coefficient of silicon at 1550  nm and cryogenic temperatures,” Appl. Phys. Lett. 101, 041905 (2012).
[Crossref]

2010 (1)

G. Gagliardi, M. Salza, S. Avino, P. Ferraro, and P. De Natale, “Probing the ultimate limit of fiber-optic strain sensing,” Science 330, 1081–1084 (2010).
[Crossref]

2009 (2)

J. Hu, X. Sun, A. Agarwal, and L. C. Kimerling, “Design guidelines for optical resonator biochemical sensors,” J. Opt. Soc. Am. B 26, 1032–1041 (2009).
[Crossref]

C. Théry, M. Ostrowski, and E. Segura, “Membrane vesicles as conveyors of immune responses,” Nat. Rev. Immunol. 9, 581–593 (2009).
[Crossref]

2008 (1)

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]

2007 (1)

D. Keng, S. McAnanama, I. Teraoka, and S. Arnold, “Resonance fluctuations of a whispering gallery mode biosensor by particles undergoing Brownian motion,” Appl. Phys. Lett. 91, 103902 (2007).
[Crossref]

2005 (1)

2004 (1)

2003 (2)

Y. Akahane, T. Asano, B.-S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944–947 (2003).
[Crossref]

K. J. Vahala, “Optical microcavities,” Nature 424, 839–846 (2003).
[Crossref]

1994 (1)

M. Eigen and M. Rigler, “Sorting single molecules: application to diagnostics and evolutionary biotechnology,” Proc. Natl. Acad. Sci. USA 91, 5740–5747 (1994).
[Crossref]

Agarwal, A.

Akahane, Y.

Y. Akahane, T. Asano, B.-S. Song, and S. Noda, “Fine-tuned high-Q photonic-crystal nanocavity,” Opt. Express 13, 1202–1214 (2005).
[Crossref]

Y. Akahane, T. Asano, B.-S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944–947 (2003).
[Crossref]

Arazi, L.

S. Rosenblum, Y. Lovsky, L. Arazi, F. Vollmer, and B. Dayan, “Cavity ring-up spectroscopy for ultrafast sensing with optical microresonators,” Nat. Commun. 6, 6788 (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]

D. Keng, S. McAnanama, I. Teraoka, and S. Arnold, “Resonance fluctuations of a whispering gallery mode biosensor by particles undergoing Brownian motion,” Appl. Phys. Lett. 91, 103902 (2007).
[Crossref]

Asano, T.

Y. Akahane, T. Asano, B.-S. Song, and S. Noda, “Fine-tuned high-Q photonic-crystal nanocavity,” Opt. Express 13, 1202–1214 (2005).
[Crossref]

Y. Akahane, T. Asano, B.-S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944–947 (2003).
[Crossref]

Avino, S.

G. Gagliardi, M. Salza, S. Avino, P. Ferraro, and P. De Natale, “Response to comment on probing the ultimate limit of fiber-optic strain sensing,” Science 335, 286 (2012).
[Crossref]

G. Gagliardi, M. Salza, S. Avino, P. Ferraro, and P. De Natale, “Probing the ultimate limit of fiber-optic strain sensing,” Science 330, 1081–1084 (2010).
[Crossref]

Berne, B. J.

B. J. Berne and R. Pecora, Dynamic Light Scattering: With Applications to Chemistry, Biology, and Physics (Wiley, 1976).

Bowen, W. P.

J. Knittel, J. D. Swaim, D. L. McAuslan, G. A. Brawley, and W. P. Bowen, “Back-scatter based whispering gallery mode sensing,” Sci. Rep. 3, 2974 (2013).
[Crossref]

Brawley, G. A.

J. Knittel, J. D. Swaim, D. L. McAuslan, G. A. Brawley, and W. P. Bowen, “Back-scatter based whispering gallery mode sensing,” Sci. Rep. 3, 2974 (2013).
[Crossref]

Breakefield, X. O.

S. El Andaloussi, I. Mäger, X. O. Breakefield, and M. J. A. Wood, “Extracellular vesicles: biology and emerging therapeutic opportunities,” Nat. Rev. Drug Discovery 12, 347–357 (2013).
[Crossref]

Cranch, G. A.

G. A. Cranch and S. Foster, “Comment on probing the ultimate limit of fiber-optic strain sensing,” Science 335, 286 (2012).
[Crossref]

Dayan, B.

S. Rosenblum, Y. Lovsky, L. Arazi, F. Vollmer, and B. Dayan, “Cavity ring-up spectroscopy for ultrafast sensing with optical microresonators,” Nat. Commun. 6, 6788 (2015).
[Crossref]

De Natale, P.

G. Gagliardi, M. Salza, S. Avino, P. Ferraro, and P. De Natale, “Response to comment on probing the ultimate limit of fiber-optic strain sensing,” Science 335, 286 (2012).
[Crossref]

G. Gagliardi, M. Salza, S. Avino, P. Ferraro, and P. De Natale, “Probing the ultimate limit of fiber-optic strain sensing,” Science 330, 1081–1084 (2010).
[Crossref]

Di Falco, A.

M. G. Scullion, T. F. Krauss, and A. Di Falco, “Slotted photonic crystal sensors,” Sensors 13, 3675–3710 (2013).
[Crossref]

Dong, J.

J. Dong, J. Huang, T. Li, and L. Liu, “Observation of fundamental thermal noise in optical fibers down to infrasonic frequencies,” Appl. Phys. Lett. 108, 021108 (2016).
[Crossref]

Eigen, M.

M. Eigen and M. Rigler, “Sorting single molecules: application to diagnostics and evolutionary biotechnology,” Proc. Natl. Acad. Sci. USA 91, 5740–5747 (1994).
[Crossref]

El Andaloussi, S.

S. El Andaloussi, I. Mäger, X. O. Breakefield, and M. J. A. Wood, “Extracellular vesicles: biology and emerging therapeutic opportunities,” Nat. Rev. Drug Discovery 12, 347–357 (2013).
[Crossref]

Ferraro, P.

G. Gagliardi, M. Salza, S. Avino, P. Ferraro, and P. De Natale, “Response to comment on probing the ultimate limit of fiber-optic strain sensing,” Science 335, 286 (2012).
[Crossref]

G. Gagliardi, M. Salza, S. Avino, P. Ferraro, and P. De Natale, “Probing the ultimate limit of fiber-optic strain sensing,” Science 330, 1081–1084 (2010).
[Crossref]

Foster, S.

G. A. Cranch and S. Foster, “Comment on probing the ultimate limit of fiber-optic strain sensing,” Science 335, 286 (2012).
[Crossref]

Gagliardi, G.

G. Gagliardi, M. Salza, S. Avino, P. Ferraro, and P. De Natale, “Response to comment on probing the ultimate limit of fiber-optic strain sensing,” Science 335, 286 (2012).
[Crossref]

G. Gagliardi, M. Salza, S. Avino, P. Ferraro, and P. De Natale, “Probing the ultimate limit of fiber-optic strain sensing,” Science 330, 1081–1084 (2010).
[Crossref]

Galli, M.

F. Priolo, T. Gregorkiewicz, M. Galli, and T. F. Krauss, “Silicon nanostructures for photonics and photovoltaics,” Nat. Nanotechnol. 9, 19–32 (2014).
[Crossref]

Giessen, H.

J. Yang, H. Giessen, and P. Lalanne, “Simple analytical expression for the peak-frequency shifts of plasmonic resonances for sensing,” Nano Lett. 15, 3439–3444 (2015).
[Crossref]

Gorodetsky, M. L.

Gregorkiewicz, T.

F. Priolo, T. Gregorkiewicz, M. Galli, and T. F. Krauss, “Silicon nanostructures for photonics and photovoltaics,” Nat. Nanotechnol. 9, 19–32 (2014).
[Crossref]

Grudinin, I. S.

Hadji, E.

M. Tardif, J.-B. Jager, P. R. Marcoux, K. Uchiyamada, E. Picard, E. Hadji, and D. Peyrade, “Single-cell bacterium identification with a SOI optical microcavity,” Appl. Phys. Lett. 109, 133510 (2016).
[Crossref]

Heinert, D.

J. Komma, C. Schwarz, G. Hofmann, D. Heinert, and R. Nawrodta, “Thermo-optic coefficient of silicon at 1550  nm and cryogenic temperatures,” Appl. Phys. Lett. 101, 041905 (2012).
[Crossref]

Hofmann, G.

J. Komma, C. Schwarz, G. Hofmann, D. Heinert, and R. Nawrodta, “Thermo-optic coefficient of silicon at 1550  nm and cryogenic temperatures,” Appl. Phys. Lett. 101, 041905 (2012).
[Crossref]

Hu, J.

Huang, J.

J. Dong, J. Huang, T. Li, and L. Liu, “Observation of fundamental thermal noise in optical fibers down to infrasonic frequencies,” Appl. Phys. Lett. 108, 021108 (2016).
[Crossref]

Jager, J.-B.

M. Tardif, J.-B. Jager, P. R. Marcoux, K. Uchiyamada, E. Picard, E. Hadji, and D. Peyrade, “Single-cell bacterium identification with a SOI optical microcavity,” Appl. Phys. Lett. 109, 133510 (2016).
[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]

D. Keng, S. McAnanama, I. Teraoka, and S. Arnold, “Resonance fluctuations of a whispering gallery mode biosensor by particles undergoing Brownian motion,” Appl. Phys. Lett. 91, 103902 (2007).
[Crossref]

Kimerling, L. C.

Knittel, J.

J. Knittel, J. D. Swaim, D. L. McAuslan, G. A. Brawley, and W. P. Bowen, “Back-scatter based whispering gallery mode sensing,” Sci. Rep. 3, 2974 (2013).
[Crossref]

Komma, J.

J. Komma, C. Schwarz, G. Hofmann, D. Heinert, and R. Nawrodta, “Thermo-optic coefficient of silicon at 1550  nm and cryogenic temperatures,” Appl. Phys. Lett. 101, 041905 (2012).
[Crossref]

Krauss, T. F.

F. Priolo, T. Gregorkiewicz, M. Galli, and T. F. Krauss, “Silicon nanostructures for photonics and photovoltaics,” Nat. Nanotechnol. 9, 19–32 (2014).
[Crossref]

M. G. Scullion, T. F. Krauss, and A. Di Falco, “Slotted photonic crystal sensors,” Sensors 13, 3675–3710 (2013).
[Crossref]

Lalanne, P.

J. Yang, H. Giessen, and P. Lalanne, “Simple analytical expression for the peak-frequency shifts of plasmonic resonances for sensing,” Nano Lett. 15, 3439–3444 (2015).
[Crossref]

Landau, L. D.

L. D. Landau and E. M. Lifshitz, Statistical Physics, Part 1, 3rd ed. (Pergamon, 1980), § 114.

Li, T.

J. Dong, J. Huang, T. Li, and L. Liu, “Observation of fundamental thermal noise in optical fibers down to infrasonic frequencies,” Appl. Phys. Lett. 108, 021108 (2016).
[Crossref]

Lifshitz, E. M.

L. D. Landau and E. M. Lifshitz, Statistical Physics, Part 1, 3rd ed. (Pergamon, 1980), § 114.

Liu, L.

J. Dong, J. Huang, T. Li, and L. Liu, “Observation of fundamental thermal noise in optical fibers down to infrasonic frequencies,” Appl. Phys. Lett. 108, 021108 (2016).
[Crossref]

Lovsky, Y.

S. Rosenblum, Y. Lovsky, L. Arazi, F. Vollmer, and B. Dayan, “Cavity ring-up spectroscopy for ultrafast sensing with optical microresonators,” Nat. Commun. 6, 6788 (2015).
[Crossref]

Mäger, I.

S. El Andaloussi, I. Mäger, X. O. Breakefield, and M. J. A. Wood, “Extracellular vesicles: biology and emerging therapeutic opportunities,” Nat. Rev. Drug Discovery 12, 347–357 (2013).
[Crossref]

Marcoux, P. R.

M. Tardif, J.-B. Jager, P. R. Marcoux, K. Uchiyamada, E. Picard, E. Hadji, and D. Peyrade, “Single-cell bacterium identification with a SOI optical microcavity,” Appl. Phys. Lett. 109, 133510 (2016).
[Crossref]

McAnanama, S.

D. Keng, S. McAnanama, I. Teraoka, and S. Arnold, “Resonance fluctuations of a whispering gallery mode biosensor by particles undergoing Brownian motion,” Appl. Phys. Lett. 91, 103902 (2007).
[Crossref]

McAuslan, D. L.

J. Knittel, J. D. Swaim, D. L. McAuslan, G. A. Brawley, and W. P. Bowen, “Back-scatter based whispering gallery mode sensing,” Sci. Rep. 3, 2974 (2013).
[Crossref]

Nawrodta, R.

J. Komma, C. Schwarz, G. Hofmann, D. Heinert, and R. Nawrodta, “Thermo-optic coefficient of silicon at 1550  nm and cryogenic temperatures,” Appl. Phys. Lett. 101, 041905 (2012).
[Crossref]

Noda, S.

Y. Akahane, T. Asano, B.-S. Song, and S. Noda, “Fine-tuned high-Q photonic-crystal nanocavity,” Opt. Express 13, 1202–1214 (2005).
[Crossref]

Y. Akahane, T. Asano, B.-S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944–947 (2003).
[Crossref]

Ostrowski, M.

C. Théry, M. Ostrowski, and E. Segura, “Membrane vesicles as conveyors of immune responses,” Nat. Rev. Immunol. 9, 581–593 (2009).
[Crossref]

Pang, W.

Pecora, R.

B. J. Berne and R. Pecora, Dynamic Light Scattering: With Applications to Chemistry, Biology, and Physics (Wiley, 1976).

Peyrade, D.

M. Tardif, J.-B. Jager, P. R. Marcoux, K. Uchiyamada, E. Picard, E. Hadji, and D. Peyrade, “Single-cell bacterium identification with a SOI optical microcavity,” Appl. Phys. Lett. 109, 133510 (2016).
[Crossref]

Picard, E.

M. Tardif, J.-B. Jager, P. R. Marcoux, K. Uchiyamada, E. Picard, E. Hadji, and D. Peyrade, “Single-cell bacterium identification with a SOI optical microcavity,” Appl. Phys. Lett. 109, 133510 (2016).
[Crossref]

Priolo, F.

F. Priolo, T. Gregorkiewicz, M. Galli, and T. F. Krauss, “Silicon nanostructures for photonics and photovoltaics,” Nat. Nanotechnol. 9, 19–32 (2014).
[Crossref]

Rigler, M.

M. Eigen and M. Rigler, “Sorting single molecules: application to diagnostics and evolutionary biotechnology,” Proc. Natl. Acad. Sci. USA 91, 5740–5747 (1994).
[Crossref]

Rosenblum, S.

S. Rosenblum, Y. Lovsky, L. Arazi, F. Vollmer, and B. Dayan, “Cavity ring-up spectroscopy for ultrafast sensing with optical microresonators,” Nat. Commun. 6, 6788 (2015).
[Crossref]

Salza, M.

G. Gagliardi, M. Salza, S. Avino, P. Ferraro, and P. De Natale, “Response to comment on probing the ultimate limit of fiber-optic strain sensing,” Science 335, 286 (2012).
[Crossref]

G. Gagliardi, M. Salza, S. Avino, P. Ferraro, and P. De Natale, “Probing the ultimate limit of fiber-optic strain sensing,” Science 330, 1081–1084 (2010).
[Crossref]

Schwarz, C.

J. Komma, C. Schwarz, G. Hofmann, D. Heinert, and R. Nawrodta, “Thermo-optic coefficient of silicon at 1550  nm and cryogenic temperatures,” Appl. Phys. Lett. 101, 041905 (2012).
[Crossref]

Scullion, M. G.

M. G. Scullion, T. F. Krauss, and A. Di Falco, “Slotted photonic crystal sensors,” Sensors 13, 3675–3710 (2013).
[Crossref]

Segura, E.

C. Théry, M. Ostrowski, and E. Segura, “Membrane vesicles as conveyors of immune responses,” Nat. Rev. Immunol. 9, 581–593 (2009).
[Crossref]

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Sun, X.

Swaim, J. D.

J. Knittel, J. D. Swaim, D. L. McAuslan, G. A. Brawley, and W. P. Bowen, “Back-scatter based whispering gallery mode sensing,” Sci. Rep. 3, 2974 (2013).
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Tardif, M.

M. Tardif, J.-B. Jager, P. R. Marcoux, K. Uchiyamada, E. Picard, E. Hadji, and D. Peyrade, “Single-cell bacterium identification with a SOI optical microcavity,” Appl. Phys. Lett. 109, 133510 (2016).
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Teraoka, I.

D. Keng, S. McAnanama, I. Teraoka, and S. Arnold, “Resonance fluctuations of a whispering gallery mode biosensor by particles undergoing Brownian motion,” Appl. Phys. Lett. 91, 103902 (2007).
[Crossref]

Théry, C.

C. Théry, M. Ostrowski, and E. Segura, “Membrane vesicles as conveyors of immune responses,” Nat. Rev. Immunol. 9, 581–593 (2009).
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M. Tardif, J.-B. Jager, P. R. Marcoux, K. Uchiyamada, E. Picard, E. Hadji, and D. Peyrade, “Single-cell bacterium identification with a SOI optical microcavity,” Appl. Phys. Lett. 109, 133510 (2016).
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K. J. Vahala, “Optical microcavities,” Nature 424, 839–846 (2003).
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S. Rosenblum, Y. Lovsky, L. Arazi, F. Vollmer, and B. Dayan, “Cavity ring-up spectroscopy for ultrafast sensing with optical microresonators,” Nat. Commun. 6, 6788 (2015).
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F. Vollmer and L. Yang, “Label-free detection with high-Q microcavities: a review of biosensing mechanisms for integrated devices,” Nanophotonics 1, 267–291 (2012).
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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).
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S. El Andaloussi, I. Mäger, X. O. Breakefield, and M. J. A. Wood, “Extracellular vesicles: biology and emerging therapeutic opportunities,” Nat. Rev. Drug Discovery 12, 347–357 (2013).
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J. Yang, H. Giessen, and P. Lalanne, “Simple analytical expression for the peak-frequency shifts of plasmonic resonances for sensing,” Nano Lett. 15, 3439–3444 (2015).
[Crossref]

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Appl. Phys. Lett. (4)

M. Tardif, J.-B. Jager, P. R. Marcoux, K. Uchiyamada, E. Picard, E. Hadji, and D. Peyrade, “Single-cell bacterium identification with a SOI optical microcavity,” Appl. Phys. Lett. 109, 133510 (2016).
[Crossref]

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[Crossref]

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[Crossref]

J. Dong, J. Huang, T. Li, and L. Liu, “Observation of fundamental thermal noise in optical fibers down to infrasonic frequencies,” Appl. Phys. Lett. 108, 021108 (2016).
[Crossref]

J. Opt. Soc. Am. B (2)

Nano Lett. (1)

J. Yang, H. Giessen, and P. Lalanne, “Simple analytical expression for the peak-frequency shifts of plasmonic resonances for sensing,” Nano Lett. 15, 3439–3444 (2015).
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Nanophotonics (1)

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

S. Rosenblum, Y. Lovsky, L. Arazi, F. Vollmer, and B. Dayan, “Cavity ring-up spectroscopy for ultrafast sensing with optical microresonators,” Nat. Commun. 6, 6788 (2015).
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Nat. Rev. Immunol. (1)

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Nature (2)

K. J. Vahala, “Optical microcavities,” Nature 424, 839–846 (2003).
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Proc. Natl. Acad. Sci. USA (2)

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J. Knittel, J. D. Swaim, D. L. McAuslan, G. A. Brawley, and W. P. Bowen, “Back-scatter based whispering gallery mode sensing,” Sci. Rep. 3, 2974 (2013).
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Sensors (1)

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Other (8)

From the local intensity |E|2 of the cavity mode and the dielectric map ε of the photonic structure, the effective volume can be defined as Veff=∫ε|E|2dV/max{ε|E|2}, where the max function takes the maximum value over the entire space. The numerical value Veff=0.06  μm3 has been determined with a finite difference time-domain method.

Note that the current definition of the acquisition time is much more restrictive than the conventional definition of the rise time, which amounts to 6  μs for a load resistance of 1 MΩ with the current photodetector bandwidth of 1.2 GHz at Rload=50  Ω.

L. D. Landau and E. M. Lifshitz, Statistical Physics, Part 1, 3rd ed. (Pergamon, 1980), § 114.

In view of the value of the thermal expansion coefficient of the silicon, the impact of the density fluctuations can be neglected here.

As a first-order approximation, we assume that mode is located within a homogeneous medium whose index equals the effective index of the 215  nm thick silicon slab waveguide. The optical index of the silicon is 3.45.

We have implemented a scanning near-field technique making use of silica nanotips to map the cavity near field, which will be discussed elsewhere.

Note that even if the total quality factor appears as a parameter in Eq. (4), it has no impact on δω/Δω|min, as expected from the normalization by Δω, which confers to this quantity a figure of merit character.

B. J. Berne and R. Pecora, Dynamic Light Scattering: With Applications to Chemistry, Biology, and Physics (Wiley, 1976).

Supplementary Material (1)

NameDescription
» Supplement 1       supplementary materials document to provide intermediate technical steps that have been implemented to determine Eq. (2) and Eq. (5).

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Figures (5)

Fig. 1.
Fig. 1. (a) Scanning electron micrograph of the top surface of an integrated L3 PhC cavity. The silicon oxide has been removed below the 220 nm thick free-standing slab. The blue arrows indicate the light path of the pump laser beam at a frequency ω p . (b) Experimental optical spectrum of the cavity (dark curve) with the corresponding Lorentzian fit (red dotted curve) whose cavity linewidth is Δ ω = ω 0 / 3800 . The resonant frequency ω 0 corresponds to a wavelength of 1599.3 nm. On the right: Time traces of the photovoltage induced by the collected scattered light I scat for a x = 0 (black trace) and x = 0.29 (blue trace) frequency detuning. Each of the traces is made of 50,000 equidistant data points.
Fig. 2.
Fig. 2. Noise-to-signal ratio δ U / U of the photovoltage U induced by the radiated field from the PhC cavity versus the load resistance R load of the photodetector, and the corresponding acquisition sampling time t acq for pump frequency detunings of x = 0 (dark points) and x = 0.29 (blue points). The error bars correspond to the standard deviation of ten repeated measurements. The black and blue dashed lines correspond to the noise limit imposed by the oscilloscope for x = 0 and x = 0.29 , respectively. The collected powers measured at resonance with R load = 1    for x = 0 and x = 0.29 are 8 μW and 6 μW, respectively. Purple data points: noise-to-signal ratio without any PhC cavity between the laser source and the photodetector for the same collected power, as in the case of x = 0 . The gray area corresponds to a regime limited by the fundamental thermo-optic noise.
Fig. 3.
Fig. 3. (a) and (b) Optical spectra of L3 PhC cavities with Q = 2200 and Q = 16800 , respectively. The red dotted lines are Lorentzian fits. (c) and (d) Near-infrared optical images of the resonant field radiated from the Q = 2200 and Q = 16800 PhC cavities, respectively. (e) Noise-to-signal ratio δ U / U of the photo voltage U versus the quality factor for x = 0 (black dashed line) and x = 0.29 (blue dashed line) with a load resistance of R load = 119    . Black and blue dashed lines are expected variations with the effective mode volume of the Q = 3800 cavity. The blue dotted line is the expected variation with the effective mode volume of the Q = 16800 cavity. The collected power at x = 0 is 0.17 μW.
Fig. 4.
Fig. 4. (a) Square and circle symbols are the minimum relative frequency shift that can be detected versus the load resistance R load , and the corresponding acquisition time t acq for three different quality factors Q with the same input power and the same frequency detuning x = 0.29 . The purple, blue, and red dashed lines are oscilloscope noise limits for the powers of 15, 6, and 1.25 μW that are collected with R load = 1    for each cavity, respectively. Dark dot-dashed line is the oscilloscope noise for an optimal light collection. The purple dot-dashed line pinpoints the saturation level due to the thermal and mechanical noise for Q = 2200 . (b) Minimum relative frequency shift normalized to the quality factor for two load resistances pinpointed by the black and blue arrows in (a). The red dashed line and dotted line are the fundamental thermal noise limits associated with a fundamental mode volume of V eff = 0.060    μm 3 (i.e., for Q = 2200 and Q = 3800 ) and V eff = 0.126    μm 3 (i.e., for Q = 16800 ), respectively.
Fig. 5.
Fig. 5. Relative frequency shift δ ω / Δ ω | T induced by the fundamental thermal noise normalized to Q / V eff versus the effective cavity mode volume V eff . This quantity is proportional to the minimal nanoparticle volume that the sensor can detect when the fundamental thermal noise limit is reached. The arrow pinpoints the value for the standard L3 PhC cavity. V eff is normalized to ( λ / n Si ) 3 where n Si is the index of the silicon material and the wavelength λ = 1.6    μm .

Tables (1)

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Table 1. Settings to Determine the Standard Deviation δ U

Equations (6)

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S ( ω 0 , ω p ) = 1 / 4 Q 2 ( ( ω p ω 0 ) / ω 0 ) 2 + 1 / 4 Q 2 I scat I in ,
δ U / U | δ ω = 1 + 1 + 4 x 2 1 + 4 ( x δ ω / Δ ω 1 + δ ω / Δ ω / Q ) 2 .
δ ω / Δ ω = Q δ ω / ω 0 = Q n ( n T ) k B T 2 ( ρ V ovl ) C V ,
δ ω Δ ω | min = Q + x + Q 1 + ( 2 Q ) 1 [ ( 4 x 2 + 1 ) 1 + δ U / U ] 1 1 .
δ ω ω 0 | pert = 1 2 δ ε ε c + δ ε V part V eff E part 2 E max 2 ,
V part min = 2 ε c + δ ε δ ε E max 2 E part 2 V eff Q δ ω Δ ω | min .

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