Abstract

We present the theory and first experimental demonstration, to the best of our knowledge, of a sensing platform based on surface nanoscale axial photonics (SNAP) at a capillary fiber. The platform explores optical whispering gallery modes, which circulate inside the wall of a capillary and slowly propagate along its axis. Due to the small thickness of the capillary wall, these modes are sensitive to spatial and temporal variations of the refractive index of the media adjacent to the internal capillary surface. In particular, the developed theory allows us to determine the internal effective radius variation of the capillary from the measured mode spectra. Experimentally, a SNAP resonator is created by local annealing of the capillary with a focused CO2 laser followed by internal etching with hydrofluoric acid. The comparison of the spectra of this resonator in the cases when it is empty and filled with water allows us to determine the internal surface nonuniformity introduced by etching. The results obtained pave the way for a novel advanced approach in sensing of media adjacent to the internal capillary surface and, in particular, in microfluidic sensing.

Published by The Optical Society under the terms of the Creative Commons Attribution 4.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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Corrections

T. Hamidfar, A. Dmitriev, B. Mangan, P. Bianucci, and M. Sumetsky, "Surface nanoscale axial photonics at a capillary fiber: publisher’s note," Opt. Lett. 42, 4828-4828 (2017)
http://proxy.osapublishing.org/ol/abstract.cfm?uri=ol-42-23-4828

26 October 2017: A typographical correction was made to the author listing.


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References

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  1. M. Sumetsky, D. J. DiGiovanni, Y. Dulashko, J. M. Fini, X. Liu, E. M. Monberg, and T. F. Taunay, Opt. Lett. 36, 4824 (2011).
    [Crossref]
  2. M. Sumetsky, Nanophotonics 2, 393 (2013).
    [Crossref]
  3. M. Sumetsky, Phys. Rev. Lett. 111, 163901 (2013).
    [Crossref]
  4. M. Sumetsky, Opt. Lett. 39, 5578 (2014).
    [Crossref]
  5. I. M. White, H. Oveys, and X. Fan, Opt. Lett. 31, 1319 (2006).
    [Crossref]
  6. X. Fan and I. M. White, Nat. Photonics 5, 591 (2011).
    [Crossref]
  7. T. Reynolds, N. Riesen, A. Meldrum, X. Fan, J. M. M. Hall, T. M. Monro, and A. Francois, Laser Photon. Rev. 11, 1600265 (2017).
    [Crossref]
  8. The fact that the cutoff wavelengths of the WGMs with very large azimuthal quantum numbers m correspond to the zero propagation constant, β=0, does not contradict to the well-known relation kmpnext<β<kmpncap for small m (see, e.g., [9]).
  9. A. W. Snyder and J. Love, Optical Waveguide Theory (Chapman and Hall, 1983).
  10. For the case kmpncapr0≈m≫1 and kmpnextr0<m considered, the Bessel function Jm(kmpnextρ) exponentially decays with the growth of ρ for 0<kmpnext(ρ−r0)≪m.
  11. M. Sumetsky and J. M. Fini, Opt. Express 19, 26470 (2011).
    [Crossref]
  12. Y. Li, F. Abolmaali, K. W. Allen, N. I. Limberopoulos, A. Urbas, Y. Rakovich, A. V. Maslov, and V. N. Astratov, Laser Photon. Rev. 11, 1600278 (2017).
    [Crossref]

2017 (2)

T. Reynolds, N. Riesen, A. Meldrum, X. Fan, J. M. M. Hall, T. M. Monro, and A. Francois, Laser Photon. Rev. 11, 1600265 (2017).
[Crossref]

Y. Li, F. Abolmaali, K. W. Allen, N. I. Limberopoulos, A. Urbas, Y. Rakovich, A. V. Maslov, and V. N. Astratov, Laser Photon. Rev. 11, 1600278 (2017).
[Crossref]

2014 (1)

2013 (2)

M. Sumetsky, Nanophotonics 2, 393 (2013).
[Crossref]

M. Sumetsky, Phys. Rev. Lett. 111, 163901 (2013).
[Crossref]

2011 (3)

2006 (1)

Abolmaali, F.

Y. Li, F. Abolmaali, K. W. Allen, N. I. Limberopoulos, A. Urbas, Y. Rakovich, A. V. Maslov, and V. N. Astratov, Laser Photon. Rev. 11, 1600278 (2017).
[Crossref]

Allen, K. W.

Y. Li, F. Abolmaali, K. W. Allen, N. I. Limberopoulos, A. Urbas, Y. Rakovich, A. V. Maslov, and V. N. Astratov, Laser Photon. Rev. 11, 1600278 (2017).
[Crossref]

Astratov, V. N.

Y. Li, F. Abolmaali, K. W. Allen, N. I. Limberopoulos, A. Urbas, Y. Rakovich, A. V. Maslov, and V. N. Astratov, Laser Photon. Rev. 11, 1600278 (2017).
[Crossref]

DiGiovanni, D. J.

Dulashko, Y.

Fan, X.

T. Reynolds, N. Riesen, A. Meldrum, X. Fan, J. M. M. Hall, T. M. Monro, and A. Francois, Laser Photon. Rev. 11, 1600265 (2017).
[Crossref]

X. Fan and I. M. White, Nat. Photonics 5, 591 (2011).
[Crossref]

I. M. White, H. Oveys, and X. Fan, Opt. Lett. 31, 1319 (2006).
[Crossref]

Fini, J. M.

Francois, A.

T. Reynolds, N. Riesen, A. Meldrum, X. Fan, J. M. M. Hall, T. M. Monro, and A. Francois, Laser Photon. Rev. 11, 1600265 (2017).
[Crossref]

Hall, J. M. M.

T. Reynolds, N. Riesen, A. Meldrum, X. Fan, J. M. M. Hall, T. M. Monro, and A. Francois, Laser Photon. Rev. 11, 1600265 (2017).
[Crossref]

Li, Y.

Y. Li, F. Abolmaali, K. W. Allen, N. I. Limberopoulos, A. Urbas, Y. Rakovich, A. V. Maslov, and V. N. Astratov, Laser Photon. Rev. 11, 1600278 (2017).
[Crossref]

Limberopoulos, N. I.

Y. Li, F. Abolmaali, K. W. Allen, N. I. Limberopoulos, A. Urbas, Y. Rakovich, A. V. Maslov, and V. N. Astratov, Laser Photon. Rev. 11, 1600278 (2017).
[Crossref]

Liu, X.

Love, J.

A. W. Snyder and J. Love, Optical Waveguide Theory (Chapman and Hall, 1983).

Maslov, A. V.

Y. Li, F. Abolmaali, K. W. Allen, N. I. Limberopoulos, A. Urbas, Y. Rakovich, A. V. Maslov, and V. N. Astratov, Laser Photon. Rev. 11, 1600278 (2017).
[Crossref]

Meldrum, A.

T. Reynolds, N. Riesen, A. Meldrum, X. Fan, J. M. M. Hall, T. M. Monro, and A. Francois, Laser Photon. Rev. 11, 1600265 (2017).
[Crossref]

Monberg, E. M.

Monro, T. M.

T. Reynolds, N. Riesen, A. Meldrum, X. Fan, J. M. M. Hall, T. M. Monro, and A. Francois, Laser Photon. Rev. 11, 1600265 (2017).
[Crossref]

Oveys, H.

Rakovich, Y.

Y. Li, F. Abolmaali, K. W. Allen, N. I. Limberopoulos, A. Urbas, Y. Rakovich, A. V. Maslov, and V. N. Astratov, Laser Photon. Rev. 11, 1600278 (2017).
[Crossref]

Reynolds, T.

T. Reynolds, N. Riesen, A. Meldrum, X. Fan, J. M. M. Hall, T. M. Monro, and A. Francois, Laser Photon. Rev. 11, 1600265 (2017).
[Crossref]

Riesen, N.

T. Reynolds, N. Riesen, A. Meldrum, X. Fan, J. M. M. Hall, T. M. Monro, and A. Francois, Laser Photon. Rev. 11, 1600265 (2017).
[Crossref]

Snyder, A. W.

A. W. Snyder and J. Love, Optical Waveguide Theory (Chapman and Hall, 1983).

Sumetsky, M.

Taunay, T. F.

Urbas, A.

Y. Li, F. Abolmaali, K. W. Allen, N. I. Limberopoulos, A. Urbas, Y. Rakovich, A. V. Maslov, and V. N. Astratov, Laser Photon. Rev. 11, 1600278 (2017).
[Crossref]

White, I. M.

X. Fan and I. M. White, Nat. Photonics 5, 591 (2011).
[Crossref]

I. M. White, H. Oveys, and X. Fan, Opt. Lett. 31, 1319 (2006).
[Crossref]

Laser Photon. Rev. (2)

T. Reynolds, N. Riesen, A. Meldrum, X. Fan, J. M. M. Hall, T. M. Monro, and A. Francois, Laser Photon. Rev. 11, 1600265 (2017).
[Crossref]

Y. Li, F. Abolmaali, K. W. Allen, N. I. Limberopoulos, A. Urbas, Y. Rakovich, A. V. Maslov, and V. N. Astratov, Laser Photon. Rev. 11, 1600278 (2017).
[Crossref]

Nanophotonics (1)

M. Sumetsky, Nanophotonics 2, 393 (2013).
[Crossref]

Nat. Photonics (1)

X. Fan and I. M. White, Nat. Photonics 5, 591 (2011).
[Crossref]

Opt. Express (1)

Opt. Lett. (3)

Phys. Rev. Lett. (1)

M. Sumetsky, Phys. Rev. Lett. 111, 163901 (2013).
[Crossref]

Other (3)

The fact that the cutoff wavelengths of the WGMs with very large azimuthal quantum numbers m correspond to the zero propagation constant, β=0, does not contradict to the well-known relation kmpnext<β<kmpncap for small m (see, e.g., [9]).

A. W. Snyder and J. Love, Optical Waveguide Theory (Chapman and Hall, 1983).

For the case kmpncapr0≈m≫1 and kmpnextr0<m considered, the Bessel function Jm(kmpnextρ) exponentially decays with the growth of ρ for 0<kmpnext(ρ−r0)≪m.

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Figures (3)

Fig. 1.
Fig. 1. Illustration of a capillary fiber coupled to an input–output microfiber. The capillary was processed with a CO 2 laser beam and, internally, with hydrofluoric acid. Inset: magnified cross section of the capillary wall (not to scale).
Fig. 2.
Fig. 2. Surface plots of spectra of the fabricated SNAP resonator measured with 20 μm resolution along the capillary axis. (a) Before etching, p = 0 . (b) After etching, empty capillary, p = 0 (bottom) and p = 1 (top). (c) After etching, capillary filled with water, p = 0 (bottom) and p = 1 (top). (d) Parabolic approximation of the cutoff wavelength for the empty (black curve) and water-filled (blue curve) capillary. Dashed red curve is the difference of these curves. (f) The restored internal ERV. The solid, dashed, and dotted curves correspond to λ w λ e equal to 0.05 nm, 0.04 nm, and 0.06 nm, respectively.
Fig. 3.
Fig. 3. (a) Cutoff wavelength as a function of internal ERV for the quantum numbers indicated on the plot. (b) Dependencies shown in (a) magnified and shifted along the vertical axis. (c) Cutoff wavelength as a function of internal ERV for the empty and water-filled capillaries for the quantum numbers indicated on the plot. (d) Dependencies shown in (c) magnified and shifted along the vertical axis. Curves shown in (b) and (d) are compared by horizontal translation into the darker rectangles.

Equations (7)

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n ( ρ , z ) = { n int , n cap , n ext , 0 < ρ r int ( z ) , r int ( z ) < ρ r ext ( z ) , r ext ( z ) < ρ .
d 2 Q m p d ρ 2 + 1 ρ d Q m p d ρ + ( ( 2 π n ( ρ , z ) λ ) 2 m 2 ρ 2 β 2 ( z ) ) Q m p = 0 ,
d 2 Ψ m p q d z 2 + β 2 ( z ) Ψ m p q = 0 .
β ( z ) = 2 π n cap λ m p ( cut ) 2 ( λ λ m p ( cut ) ( z ) ) λ m p ( cut )
d 2 Q m p d ρ 2 + 1 ρ d Q m p d ρ + ( ( 2 π n ( ρ , z ) λ m p ( cut ) ) 2 m 2 ρ 2 ) Q m p = 0 .
Q m p ( ρ , z ) = { A J m ( k m p n int ρ ) , B J m ( k m p n cap ρ ) + C Y m ( k m p n cap ρ ) , D J m ( k m p n ext ρ ) , 0 < ρ r int ( z ) , r int ( z ) < ρ r ext ( z ) , r ext ( z ) < ρ .
Δ λ ˜ ( cut ) ( r int + s ) = λ m p q ( cut ) ( r int + s ) | water λ m p q ( cut ) ( r int + s ) | empty ,

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