Abstract

Sensing with optical whispering gallery modes (WGMs) is a rapidly developing detection method in modern microfluidics research. This method explores the perturbations of spectra of WGMs propagating along the wall of an optical microcapillary to characterize the liquid medium inside it. Here we show that WGMs in a silica microcapillary can be fully localized (rather than perturbed) by evanescent coupling to a water droplet and, thus, form a high-quality-factor microresonator. The spectra of this resonator, measured with a microfiber translated along the capillary, present a hierarchy of resonances that allow us to determine the size of the droplet and variation of its length due to the evaporation. The resolution of our measurements of this variation equal to 4.5 nm is only limited by the resolution of the optical spectrum analyzer used. The discovered phenomenon of complete localization of light in liquid-filled optical microcapillaries suggests a new type of microfluidic photonic device as well as an ultraprecise method for microfluidic characterization.

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References

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2017 (6)

F. X. Gu, F. M. Xie, X. Lin, S. Y. Linghu, W. Fang, H. Zeng, L. Tong, and S. Zhuang, “Single whispering-gallery-mode lasing in polymer bottle microresonators via spatial pump engineering,” Light Sci. Appl. 6, e17061 (2017).
[Crossref]

M. Humar, A. Dobravec, X. Zhao, and S. H. Yun, “Biomaterial microlasers implantable in the cornea, skin, and blood,” Optica 4, 1080–1085 (2017).
[Crossref]

E. Kim, M. D. Baaske, and F. Vollmer, “Towards next-generation label-free biosensors: recent advances in whispering gallery mode sensors,” Lab Chip 17, 1190–1205 (2017).
[Crossref]

T. Reynolds, N. Riesen, A. Meldrum, X. Fan, J. M. M. Hall, T. M. Monro, and A. Francois, “Fluorescent and lasing whispering gallery mode microresonators for sensing applications,” Laser Photon. Rev. 11, 1600265 (2017).
[Crossref]

M. Sumetsky, “Lasing microbottles,” Light Sci. Appl. 6, e171022017 (2017).
[Crossref]

T. Hamidfar, A. Dmitriev, B. Mangan, P. Bianucci, and M. Sumetsky, “Surface nanoscale axial photonics at a capillary fiber,” Opt. Lett. 42, 3060–3063 (2017).
[Crossref]

2016 (6)

N. A. Toropov and M. Sumetsky, “Permanent matching of coupled optical bottle resonators with better than 0.16  GHz precision,” Opt. Lett. 41, 2278–2281 (2016).
[Crossref]

A. V. Dmitriev and M. Sumetsky, “Tunable photonic elements at the surface of an optical fiber with piezoelectric core,” Opt. Lett. 41, 2165–2168 (2016).
[Crossref]

M. D. Baaske and F. Vollmer, “Optical observation of single atomic ions interacting with plasmonic nanorods in aqueous solution,” Nat. Photonics 10, 733–739 (2016).
[Crossref]

R. Dahan, L. L. Martin, and T. Carmon, “Droplet optomechanics,” Optica 3, 175–178 (2016).
[Crossref]

J. M. Ward, Y. Yang, and S. Nic Chormaic, “Glass-on-glass fabrication of bottle-shaped tunable microlasers and their applications,” Sci. Rep. 6, 25152 (2016).
[Crossref]

O. Björneholm, M. H. Hansen, A. Hodgson, L. M. Liu, D. T. Limmer, A. Michaelides, P. Pedevilla, J. Rossmeisl, H. Shen, G. Tocci, E. Tyrode, M. M. Walz, J. Werner, and H. Bluhm, “Water at interfaces,” Chem. Rev. 116, 7698–7726 (2016).
[Crossref]

2015 (4)

C. Hao, J. Li, Y. Liu, X. Zhou, Y. Liu, R. Liu, L. Che, W. Zhou, D. Sun, L. Li, L. Xu, and Z. Wang, “Superhydrophobic-like tunable droplet bouncing on slippery liquid interfaces,” Nat. Commun. 6, 7986 (2015).
[Crossref]

S. Yakunin, L. Protesescu, F. Krieg, M. I. Bodnarchuk, G. Nedelcu, M. Humer, G. De Luca, M. Fiebig, W. Heiss, and M. V. Kovalenko, “Low-threshold amplified spontaneous emission and lasing from colloidal nanocrystals of caesium lead halide perovskites,” Nat. Commun. 6, 8056 (2015).
[Crossref]

W. Liang, D. Eliyahu, V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, D. Seidel, and L. Maleki, “High spectral purity Kerr frequency comb radio frequency photonic oscillator,” Nat. Commun. 6, 7957 (2015).
[Crossref]

A. Reiserer, “Cavity-based quantum networks with single atoms and optical photons,” Rev. Mod. Phys. 87, 1379–1418 (2015).
[Crossref]

2014 (5)

J. Volz, M. Scheucher, C. Junge, and A. Rauschenbeutel, “Nonlinear π phase shift for single fiber-guided photons interacting with a single resonator-enhanced atom,” Nat. Photonics 8, 965–970 (2014).
[Crossref]

M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, “Cavity optomechanics,” Rev. Mod. Phys. 86, 1391–1452 (2014).
[Crossref]

B. Peng, K. Ozdemir, S. Rotter, H. Yilmaz, M. Liertzer, F. Monifi, C. M. Bender, F. Nori, and L. Yang, “Loss-induced suppression and revival of lasing,” Science 346, 328–332 (2014).
[Crossref]

M. Sumetsky, “Slow light optofluidics: a proposal,” Opt. Lett. 39, 5578–5581 (2014).
[Crossref]

D. Lis, E. H. G. Backus, J. Hunger, S. H. Parekh, and M. Bonn, “Liquid flow along a solid surface reversibly alters interfacial chemistry,” Science 344, 1138–1142 (2014).
[Crossref]

2013 (3)

M. Sumetsky, “Nanophotonics of optical fibers,” Nanophotonics 2, 393–406 (2013).
[Crossref]

G. Bahl, K. H. Kim, W. Lee, J. Liu, X. Fan, and T. Carmon, “Cavity optomechanics on a microfluidic resonator with water and viscous liquids,” Nat. Commun. 4, 1994 (2013).
[Crossref]

M. Sumetsky, “Delay of light in an optical bottle resonator with nanoscale radius variation: dispersionless, broadband, and low loss,” Phys. Rev. Lett. 111, 163901 (2013).
[Crossref]

2012 (1)

2011 (4)

L. P. Santos, T. R. D. Ducati, L. B. S. Balestrin, and F. Galembeck, “Water with excess electric charge,” J. Phys. Chem. C 115, 11226–11232 (2011).
[Crossref]

M. Sumetsky and J. M. Fini, “Surface nanoscale axial photonics,” Opt. Express 19, 26470–26485 (2011).
[Crossref]

G. C. Righini, Y. Dumeige, P. Féron, M. Ferrari, G. Nunzi Conti, D. Ristic, and S. Soria, “Whispering gallery mode microresonators: fundamentals and applications,” Riv. Nuovo Cimento Soc. Ital. Fis. 34, 435–488 (2011).
[Crossref]

X. Fan and I. M. White, “Optofluidic microsystems for chemical and biological analysis,” Nat. Photonics 5, 591–597 (2011).
[Crossref]

2008 (1)

H. J. Kimble, “The quantum internet,” Nature 453, 1023–1030 (2008).
[Crossref]

2007 (2)

2006 (1)

2003 (2)

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

J. D. Tice, H. Song, A. D. Lyon, and R. F. Ismagilov, “Formation of droplets and mixing in multiphase microfluidics at low values of the Reynolds and the capillary numbers,” Langmuir 19, 9127–9133 (2003).
[Crossref]

2001 (1)

S. H. Behrens and D. G. Grier, “The charge of glass and silica surfaces,” J. Chem. Phys. 115, 6716–6721 (2001).
[Crossref]

2000 (2)

1994 (2)

N. Mukherjee, R. A. Myers, and S. R. J. Brueck, “Dynamics of second-harmonic generation in fused silica,” J. Opt. Soc. Am. B 11, 665–669 (1994).
[Crossref]

A. Liu, M. Digonnet, and G. Kino, “DC Kerr coefficient in silica: theory and experiment,” Proc. SPIE 3542, 102–107 (1994).
[Crossref]

1912 (1)

L. Rayleigh, “The problem of the whispering gallery,” Sci. Pap. 5, 617–620 (1912).

Andrés, M. V.

Aspelmeyer, M.

M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, “Cavity optomechanics,” Rev. Mod. Phys. 86, 1391–1452 (2014).
[Crossref]

Baaske, M. D.

E. Kim, M. D. Baaske, and F. Vollmer, “Towards next-generation label-free biosensors: recent advances in whispering gallery mode sensors,” Lab Chip 17, 1190–1205 (2017).
[Crossref]

M. D. Baaske and F. Vollmer, “Optical observation of single atomic ions interacting with plasmonic nanorods in aqueous solution,” Nat. Photonics 10, 733–739 (2016).
[Crossref]

Backus, E. H. G.

D. Lis, E. H. G. Backus, J. Hunger, S. H. Parekh, and M. Bonn, “Liquid flow along a solid surface reversibly alters interfacial chemistry,” Science 344, 1138–1142 (2014).
[Crossref]

Bahl, G.

G. Bahl, K. H. Kim, W. Lee, J. Liu, X. Fan, and T. Carmon, “Cavity optomechanics on a microfluidic resonator with water and viscous liquids,” Nat. Commun. 4, 1994 (2013).
[Crossref]

Balestrin, L. B. S.

L. P. Santos, T. R. D. Ducati, L. B. S. Balestrin, and F. Galembeck, “Water with excess electric charge,” J. Phys. Chem. C 115, 11226–11232 (2011).
[Crossref]

Behrens, S. H.

S. H. Behrens and D. G. Grier, “The charge of glass and silica surfaces,” J. Chem. Phys. 115, 6716–6721 (2001).
[Crossref]

Bender, C. M.

B. Peng, K. Ozdemir, S. Rotter, H. Yilmaz, M. Liertzer, F. Monifi, C. M. Bender, F. Nori, and L. Yang, “Loss-induced suppression and revival of lasing,” Science 346, 328–332 (2014).
[Crossref]

Berg, J. C.

J. C. Berg, An Introduction to Interfaces and Colloids: The Bridge to Nanoscience (World Scientific, 2009).

Bianucci, P.

Björneholm, O.

O. Björneholm, M. H. Hansen, A. Hodgson, L. M. Liu, D. T. Limmer, A. Michaelides, P. Pedevilla, J. Rossmeisl, H. Shen, G. Tocci, E. Tyrode, M. M. Walz, J. Werner, and H. Bluhm, “Water at interfaces,” Chem. Rev. 116, 7698–7726 (2016).
[Crossref]

Bluhm, H.

O. Björneholm, M. H. Hansen, A. Hodgson, L. M. Liu, D. T. Limmer, A. Michaelides, P. Pedevilla, J. Rossmeisl, H. Shen, G. Tocci, E. Tyrode, M. M. Walz, J. Werner, and H. Bluhm, “Water at interfaces,” Chem. Rev. 116, 7698–7726 (2016).
[Crossref]

Bodnarchuk, M. I.

S. Yakunin, L. Protesescu, F. Krieg, M. I. Bodnarchuk, G. Nedelcu, M. Humer, G. De Luca, M. Fiebig, W. Heiss, and M. V. Kovalenko, “Low-threshold amplified spontaneous emission and lasing from colloidal nanocrystals of caesium lead halide perovskites,” Nat. Commun. 6, 8056 (2015).
[Crossref]

Bonn, M.

D. Lis, E. H. G. Backus, J. Hunger, S. H. Parekh, and M. Bonn, “Liquid flow along a solid surface reversibly alters interfacial chemistry,” Science 344, 1138–1142 (2014).
[Crossref]

Brueck, S. R. J.

Cai, M.

Carmon, T.

R. Dahan, L. L. Martin, and T. Carmon, “Droplet optomechanics,” Optica 3, 175–178 (2016).
[Crossref]

G. Bahl, K. H. Kim, W. Lee, J. Liu, X. Fan, and T. Carmon, “Cavity optomechanics on a microfluidic resonator with water and viscous liquids,” Nat. Commun. 4, 1994 (2013).
[Crossref]

Che, L.

C. Hao, J. Li, Y. Liu, X. Zhou, Y. Liu, R. Liu, L. Che, W. Zhou, D. Sun, L. Li, L. Xu, and Z. Wang, “Superhydrophobic-like tunable droplet bouncing on slippery liquid interfaces,” Nat. Commun. 6, 7986 (2015).
[Crossref]

Dahan, R.

De Luca, G.

S. Yakunin, L. Protesescu, F. Krieg, M. I. Bodnarchuk, G. Nedelcu, M. Humer, G. De Luca, M. Fiebig, W. Heiss, and M. V. Kovalenko, “Low-threshold amplified spontaneous emission and lasing from colloidal nanocrystals of caesium lead halide perovskites,” Nat. Commun. 6, 8056 (2015).
[Crossref]

Díez, A.

Digonnet, M.

A. Liu, M. Digonnet, and G. Kino, “DC Kerr coefficient in silica: theory and experiment,” Proc. SPIE 3542, 102–107 (1994).
[Crossref]

Dmitriev, A.

Dmitriev, A. V.

Dobravec, A.

Ducati, T. R. D.

L. P. Santos, T. R. D. Ducati, L. B. S. Balestrin, and F. Galembeck, “Water with excess electric charge,” J. Phys. Chem. C 115, 11226–11232 (2011).
[Crossref]

Dumeige, Y.

G. C. Righini, Y. Dumeige, P. Féron, M. Ferrari, G. Nunzi Conti, D. Ristic, and S. Soria, “Whispering gallery mode microresonators: fundamentals and applications,” Riv. Nuovo Cimento Soc. Ital. Fis. 34, 435–488 (2011).
[Crossref]

Eliyahu, D.

W. Liang, D. Eliyahu, V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, D. Seidel, and L. Maleki, “High spectral purity Kerr frequency comb radio frequency photonic oscillator,” Nat. Commun. 6, 7957 (2015).
[Crossref]

Fan, X.

T. Reynolds, N. Riesen, A. Meldrum, X. Fan, J. M. M. Hall, T. M. Monro, and A. Francois, “Fluorescent and lasing whispering gallery mode microresonators for sensing applications,” Laser Photon. Rev. 11, 1600265 (2017).
[Crossref]

G. Bahl, K. H. Kim, W. Lee, J. Liu, X. Fan, and T. Carmon, “Cavity optomechanics on a microfluidic resonator with water and viscous liquids,” Nat. Commun. 4, 1994 (2013).
[Crossref]

X. Fan and I. M. White, “Optofluidic microsystems for chemical and biological analysis,” Nat. Photonics 5, 591–597 (2011).
[Crossref]

I. M. White, H. Oveys, and X. Fan, “Liquid-core optical ring-resonator sensors,” Opt. Lett. 31, 1319–1321 (2006).
[Crossref]

Fang, W.

F. X. Gu, F. M. Xie, X. Lin, S. Y. Linghu, W. Fang, H. Zeng, L. Tong, and S. Zhuang, “Single whispering-gallery-mode lasing in polymer bottle microresonators via spatial pump engineering,” Light Sci. Appl. 6, e17061 (2017).
[Crossref]

Féron, P.

G. C. Righini, Y. Dumeige, P. Féron, M. Ferrari, G. Nunzi Conti, D. Ristic, and S. Soria, “Whispering gallery mode microresonators: fundamentals and applications,” Riv. Nuovo Cimento Soc. Ital. Fis. 34, 435–488 (2011).
[Crossref]

Ferrari, M.

G. C. Righini, Y. Dumeige, P. Féron, M. Ferrari, G. Nunzi Conti, D. Ristic, and S. Soria, “Whispering gallery mode microresonators: fundamentals and applications,” Riv. Nuovo Cimento Soc. Ital. Fis. 34, 435–488 (2011).
[Crossref]

Fiebig, M.

S. Yakunin, L. Protesescu, F. Krieg, M. I. Bodnarchuk, G. Nedelcu, M. Humer, G. De Luca, M. Fiebig, W. Heiss, and M. V. Kovalenko, “Low-threshold amplified spontaneous emission and lasing from colloidal nanocrystals of caesium lead halide perovskites,” Nat. Commun. 6, 8056 (2015).
[Crossref]

Fini, J. M.

Flügge, S.

S. Flügge, Practical Quantum Mechanics (Springer, 1971), vol. 1.

Francois, A.

T. Reynolds, N. Riesen, A. Meldrum, X. Fan, J. M. M. Hall, T. M. Monro, and A. Francois, “Fluorescent and lasing whispering gallery mode microresonators for sensing applications,” Laser Photon. Rev. 11, 1600265 (2017).
[Crossref]

Galembeck, F.

L. P. Santos, T. R. D. Ducati, L. B. S. Balestrin, and F. Galembeck, “Water with excess electric charge,” J. Phys. Chem. C 115, 11226–11232 (2011).
[Crossref]

Gimeno, B.

Goodier, J. N.

S. P. Timoshenko and J. N. Goodier, Theory of Elasticity, 3rd ed. (McGraw-Hill, 1970).

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Supplementary Material (1)

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Figures (3)

Fig. 1.
Fig. 1. (a) The optical microscope image of the cross section of the silica microcapillary used in the experiment. This image was used to determine the radius of the capillary and the thickness of its wall. (b) The optical microscope image of a water droplet inside the capillary. The droplet meniscuses caused by the surface tension are clearly seen. (c) Illustration of the experiment. The input-output taper with a micron-diameter waist (microfiber) is positioned normally to the capillary. The microfiber excites WGMs which propagate along the microcapillary wall and sense the droplet.
Fig. 2.
Fig. 2. Surface plot of the transmission power spectra collected by the input-output microfiber translated along the microcapillary with a droplet inside. The spectral (vertical axis) and spatial (horizontal axis) resolutions of the scan were 1.3 pm and 2 μm, respectively. The central part of the plot indicates the region where the droplet was situated. (b) and (c) Surface plots of the calculated transmission power spectra corresponding to the stationary droplet with the initial (b) and final (c) dimensions which were obtained for a single cutoff wavelength using Eqs. (1)–(3). The initial and final dimensions were taken from the experimental plot (a) at axial coordinates z1 and z2 [Fig. 1(c)] when the measurement of the droplet region started and finished. (d)–(f) Magnified spectral region of the surface plot (a) and the theoretical models of the droplet similar to those shown in (b) and (c) but for a different cutoff wavelength. (g) The resonance of the droplet-induced microresonator measured at the node indicated at the spectral plot (d). (h) Magnified spectral region of the surface plot (a) containing the pathway of resonances with the axial quantum number q=12 which was used for the analysis of the droplet evaporation.
Fig. 3.
Fig. 3. (a) Cutoff wavelengths with the azimuthal quantum number m=364 and radial quantum numbers p=0,1,2,3,4,5 for the silica microcapillary with external radius rext=68  μm as a function of the microcapillary internal radius rint. The solid and dashed curves correspond to the empty and water-filled microcapillary, respectively. (b) The distribution of cutoff wavelengths (dots) for the TE-polarized WGMs having p=0,1,2,3,4,5 in the bandwidth 1540  nm<λ<1550  nm. The corresponding azimuthal quantum numbers m are shown next to each of the dots. (c) A sample surface plot of transmission power spectra calculated using Eqs. (1)–(3) for the water-induced shift of the cutoff wavelength equal to 1 nm and microfiber-capillary coupling parameters indicated in the text.

Equations (5)

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Emp±(z,ρ,ϕ)=exp(±iβmp(λ)z)exp(imϕ)Qmp(ρ).
βmp(a),(w)(λ)=23/2πncap(λmp(a),(w))3/2(λmp(a),(w)λ)1/2,
d2Ψmpdz2+βmp2(λ,z)Ψmp=0,
A(z,λ)=A0i|C|2G(z,z,λ)1+DG(z,z,λ).
ΔL=4ncap2L3q2λmp3Δλ

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