Abstract

Fiber tapers provide a way to rapidly measure the spectra of many types of optical microcavities. Proper fabrication of the taper ensures that its width varies sufficiently slowly (adiabatically) along the length of the taper so as to maintain single spatial mode propagation. This is usually accomplished by monitoring the spectral transmission through the taper. In addition to this characterization method it is also helpful to know the taper width versus length. By developing a model of optical backscattering within the fiber taper, it is possible to use backscatter measurements to characterize the taper width versus length. The model uses the concept of a local taper numerical aperture to accurately account for varying backscatter collection along the length of the taper. In addition to taper profile information, the backscatter reflectometry method delineates locations along the taper where fluctuations in fiber core refractive index, cladding refractive index, and taper surface roughness each provide the dominant source of backscattering. Rayleigh backscattering coefficients are also extracted by fitting the data with the model and are consistent with the fiber manufacturer’s datasheet. The optical backscattering reflectometer is also used to observe defects resulting from microcracks and surface contamination. All of this information can be obtained before the taper is removed from its fabrication apparatus. The backscattering method should also be prove useful for characterization of nanofibers.

© 2017 Optical Society of America

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2017 (3)

2016 (2)

F. Monifi, J. Zhang, Ş. K. Özdemir, B. Peng, Y. X. Liu, F. Bo, F. Nori, and L. Yang, “Optomechanically induced stochastic resonance and chaos transfer between optical fields,” Nat. Photon. 10(6), 399–405 (2016).
[Crossref]

V. Brasch, M. Geiselmann, T. Herr, G. Lihachev, M. H. P. Pfeiffer, M. L. Gorodetsky, and T. J. Kippenberg, “Photonic chip-based optical frequency comb using soliton Cherenkov radiation,” Science 351(6271), 357–360 (2016).
[Crossref] [PubMed]

2015 (2)

2014 (2)

B. Peng, Ş. K. Özdemir, 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(6207) 328–332 (2014).
[Crossref] [PubMed]

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, “Temporal solitons in optical microresonators,” Nat. Photon. 8(2), 145–152 (2014).
[Crossref]

2013 (3)

J. Li, H. Lee, and K. J. Vahala, “Microwave synthesizer using an on-chip Brillouin oscillator,” Nat. Commun. 4, 2097 (2013).
[Crossref] [PubMed]

B. J. Eggleton, C. G. Poulton, and R. Pant, “Inducing and harnessing stimulated Brillouin scattering in photonic integrated circuits,” Adv. Opt. Photon. 5(4), 536–587 (2013).
[Crossref]

H. Lee, M. G. Suh, T. Chen, J. Li, S. A. Diddams, and K. J. Vahala, “Spiral resonators for on-chip laser frequency stabilization,” Nat. Commun. 4, 2468 (2013).
[Crossref] [PubMed]

2012 (3)

F. Vollmer and L. Yang, “Label-free detection with high-Q microcavities: a review of biosensing mechanisms for integrated devices,” Nanophotonics 1(3–4), 267–291 (2012).
[Crossref] [PubMed]

G. Bahl, M. Tomes, F. Marquardt, and T. Carmon, “Observation of spontaneous Brillouin cooling,” Nat. Phys. 8(3), 203–207 (2012).
[Crossref]

A. Goban, K. S. Choi, D. J. Alton, D. Ding, C. Lacroûte, M. Pototschnig, T. Thiele, N. P. Stern, and H. J. Kimble, “Demonstration of a state-insensitive, compensated nanofiber trap,” Phys. Rev. Lett. 109(3), 033603 (2012).
[Crossref] [PubMed]

2011 (4)

J. Chan, T. P. Mayer Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Gröblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478(7367), 89–92 (2011).
[Crossref] [PubMed]

T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, “Microresonator-based optical frequency combs,” Science 332(6029), 555–559 (2011).
[Crossref] [PubMed]

T. Lu, H. Lee, T. Chen, S. Herchak, J.-H. Kim, S. E. Fraser, R. C. Flagan, and K. J. Vahala, “High sensitivity nanoparticle detection using optical microcavities,” Proc. Natl. Acad. Sci. 108, 5976–5979 (2011).
[Crossref] [PubMed]

J. Alnis, A. Schliesser, C. Y. Wang, J. Hofer, T. J. Kippenberg, and T. W. Hänsch, “Thermal-noise-limited crystalline whispering-gallery-mode resonator for laser stabilization,” Phys. Rev. A 84(1), 011804 (2011).
[Crossref]

2010 (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 microresonator,” Nat. Photon. 4(1), 46–49 (2010).
[Crossref]

I. S. Grudinin, H. Lee, O. Painter, and K. J. Vahala, “Phonon laser action in a tunable two-level system,” Phys. Rev. Lett. 104(8), 083901 (2010).
[Crossref] [PubMed]

E. Vetsch, D. Reitz, G. Sagué, R. Schmidt, S. T. Dawkins, and A. Rauschenbeutel, “Optical interface created by laser-cooled atoms trapped in the evanescent field surrounding an optical nanofiber,” Phys. Rev. Lett. 104(20), 203603 (2010).
[Crossref] [PubMed]

L. Ding, C. Belacel, S. Ducci, G. Leo, and I. Favero, “Ultralow loss single-mode silica tapers manufactured by a microheater,” Appl. Opt. 49(13), 2441–2445 (2010).
[Crossref]

2009 (4)

P. Lu, L. Men, K. Sooley, and Q. Chen, “Tapered fiber Mach-Zehnder interferometer for simultaneous measurement of refractive index and temperature,” Appl. Phys. Lett. 94(13), 131110 (2009).
[Crossref]

M. Eichenfield, J. Chan, R. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462(7269), 78–82 (2009).
[Crossref] [PubMed]

M. Tomes and T. Carmon, “Photonic micro-electromechanical systems vibrating at X-band (11-GHz) rates,” Phys. Rev. Lett. 102(11), 113601 (2009).
[Crossref] [PubMed]

I. S. Grudinin, A. B. Matsko, and L. Maleki, “Brillouin lasing with a CaF2 whispering gallery mode resonator,” Phys. Rev. Lett. 102(4), 043902 (2009).
[Crossref] [PubMed]

2008 (2)

T. J. Kippenberg and K. J. Vahala, “Cavity optomechanics: back-action at the mesoscale,” Science 321(5893), 1172–1176 (2008).
[Crossref] [PubMed]

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 (4)

K. Srinivasan and O. Painter, “Linear and nonlinear optical spectroscopy of a strongly coupled microdisk-quantum dot system,” Nature 450(7171), 862–865 (2007).
[Crossref] [PubMed]

T. Carmon and K. J. Vahala, “Visible continuous emission from a silica microphotonic device by third-harmonic generation,” Nat. Phys. 3(6), 430–435 (2007).
[Crossref]

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450(7173), 1214–1217 (2007).
[Crossref]

O. Frazão, P. Caldas, F. M. Araújo, L. A. Ferreira, and J. L. Santos, “Optical flowmeter using a modal interferometer based on a single nonadiabatic fiber taper,” Opt. Lett. 32(14), 1974–1976 (2007).
[Crossref] [PubMed]

2006 (2)

A. B. Matsko and V. S. Ilchenko, “Optical resonators with whispering gallery modes I: Basics,” IEEE J. Sel. Top. Quant. Electron. 12(1), 3–14 (2006).
[Crossref]

T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala, and H. J. Kimble, “Observation of strong coupling between one atom and a monolithic microresonator,” Nature 443(7112), 671–674 (2006).
[Crossref] [PubMed]

2005 (3)

2003 (3)

K. Saito, M. Yamaguchi, H. Kakiuchida, A. J. Ikushima, K. Ohsono, and Y. Kurosawa, “Limit of the Rayleigh scattering loss in silica fiber,” Appl. Phys. Lett. 83(25), 5175–5177 (2003).
[Crossref]

S. M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Vahala, “Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics,” Phys. Rev. Lett. 91(4), 043902 (2003).
[Crossref] [PubMed]

K. J. Vahala, “Optical microcavities,” Nature 424(6950), 839–846 (2003).
[Crossref] [PubMed]

2002 (2)

2000 (3)

1998 (1)

1997 (1)

1993 (1)

U. Glombitza and E. Brinkmeyer, “Coherent frequency-domain reflectometry for characterization of single-mode integrated-optical waveguides,” J. Lightwave Tech. 11(8), 1377–1384 (1993).
[Crossref]

1992 (2)

M. Ohashi, K. Shiraki, and K. Tajima, “Optical loss property of silica-based single-mode fibers,” J. Lightwave Tech. 10(5), 539–543 (1992).
[Crossref]

T. A. Birks and Y. W. Li, “The shape of fiber tapers,” J. Lightwave Tech. 10(4), 432–438 (1992).
[Crossref]

1989 (1)

H. Barfuss and E. Brinkmeyer, “Modified optical frequency domain reflectometry with high spatial resolution for components of integrated optic systems,” J. Lightwave Tech. 7(1), 3–10, (1989).
[Crossref]

1984 (2)

A. H. Hartog and M. P. Gold, “On the theory of backscattering in single-mode optical fibers,” J. Lightwave Tech. 2(2), 76–82 (1984).
[Crossref]

M. E. Lines, “Scattering losses in optic fiber materials, I. A new parametrization, II. Numerical estimates,” J. Appl. Phys. 55(11), 4052–4063 (1984).
[Crossref]

1983 (1)

1981 (1)

W. Eickhoff and R. Ulrich, “Optical frequency domain reflectometry in single-mode fiber,” Appl. Phys. Lett. 39(9), 693–695 (1981).
[Crossref]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics, 4th Ed. (Academic Press, 2006).

Alnis, J.

J. Alnis, A. Schliesser, C. Y. Wang, J. Hofer, T. J. Kippenberg, and T. W. Hänsch, “Thermal-noise-limited crystalline whispering-gallery-mode resonator for laser stabilization,” Phys. Rev. A 84(1), 011804 (2011).
[Crossref]

Alton, D. J.

A. Goban, K. S. Choi, D. J. Alton, D. Ding, C. Lacroûte, M. Pototschnig, T. Thiele, N. P. Stern, and H. J. Kimble, “Demonstration of a state-insensitive, compensated nanofiber trap,” Phys. Rev. Lett. 109(3), 033603 (2012).
[Crossref] [PubMed]

D. J. Alton, “Interacting single atoms with nanophotonics for chip-integrated quantum networks,” PhD thesis, California Institute of Technology, Chap. 7 (2013).

Aoki, T.

T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala, and H. J. Kimble, “Observation of strong coupling between one atom and a monolithic microresonator,” Nature 443(7112), 671–674 (2006).
[Crossref] [PubMed]

Araújo, F. M.

Arcizet, O.

P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450(7173), 1214–1217 (2007).
[Crossref]

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]

Aspelmeyer, M.

J. Chan, T. P. Mayer Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Gröblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478(7367), 89–92 (2011).
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S. M. Spillane, T. J. Kippenberg, and K. J. Vahala, “Ultralow-threshold Raman laser using a spherical dielectric microcavity,” Nature 415(6872), 621–623 (2002).
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K. J. Vahala, “Optical microcavities,” Nature 424(6950), 839–846 (2003).
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P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature 450(7173), 1214–1217 (2007).
[Crossref]

T. Aoki, B. Dayan, E. Wilcut, W. P. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala, and H. J. Kimble, “Observation of strong coupling between one atom and a monolithic microresonator,” Nature 443(7112), 671–674 (2006).
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K. Srinivasan and O. Painter, “Linear and nonlinear optical spectroscopy of a strongly coupled microdisk-quantum dot system,” Nature 450(7171), 862–865 (2007).
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[Crossref]

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S. M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Vahala, “Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics,” Phys. Rev. Lett. 91(4), 043902 (2003).
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Figures (8)

Fig. 1
Fig. 1

Taper width versus position measurement and OBR measurement. (a) A composite image is presented for a fiber taper. The image was produced by stitching together a series of scanning electron microscope (SEM) images as described in the text. The black vertical lines in the image are 1 mm tick marks on a metal ruler and provide a reference used to construct the image. The scale factors for the vertical and horizontal axes are different and are provided in the legend. (b) Width versus position profiles measured on two different tapers are presented. The tapers were fabricated under the same conditions and measured using the SEM method in panel (a). (c) OBR data for the two tapers in panel (b). The consistency between taper profiles and scattering traces verifies the reproducibility of the fabrication system. (d) Four sets of OBR data taken using one taper illustrate the consistency of the OBR measurement.

Fig. 2
Fig. 2

Illustration showing a fiber taper with a HE11 mode profile superimposed. The blue planes give the energy density profiles associated with the transverse polarization. Initially in region A, light is confined in the core region and the fluctuations in refractive index of the core dominate the scattering process. In region B, the taper width is reduced to tens of microns and a substantial portion of the optical power is propagating within the cladding region. Here, the refractive-index fluctuations of the cladding dominate the scattering process. Region C occurs around the taper waist where the surrounding air functions as the cladding and the taper surface roughness dominates the scattering process.

Fig. 3
Fig. 3

Calculation of the parameters σcore, σclad and η in Eq. (1) versus the taper width w. The calculations used a finite element method solver. The effective index, neff, is also presented. For the narrowest taper widths neff approaches unity, the index of air, while at the largest widths it has the index of the SMF-28 fiber used to prepare the fiber taper. The wavelength assumed is 1566 nm and SMF-28 parameters are: wclad = 125μm, wcore = 8.2μm, ncore = 1.4682, nclad = 1.4631.

Fig. 4
Fig. 4

Flow charts illustrating three distinct taper-related calculations that are possible. (a) Calculation I (blue): a known taper profile is combined with OBR data to determine fitting parameters (αcore, αclad, β). Calculation II (orange): a known taper profile is combined with average fitting parameters ( α ¯ core , α ¯ clad , β ¯ ) to predict an OBR signal. (b) Calculation III: an OBR signal is combined with average fitting parameters ( α ¯ core , α ¯ clad , β ¯ ) to determine a taper profile. This particular measurement is performed in a piecewise fashion on regions where the OBR signal monotonically varies with taper length.

Fig. 5
Fig. 5

Predicted OBR signal is compared with actual OBR data. (a) OBR data from taper 2a in Table 1 is plotted versus taper position relative to the taper waist at one end of the taper. The data are compared with the prediction based on Calculation II using the average parameters in Table 1. Also shown are the contributions from the three scattering mechanisms in Eq. (1). A, B, and C intervals delineated by the dashed vertical lines (see Fig. 2) give regions in which each mechanism provides the dominant contribution to total scattering. (b) Averaged parameters from measurements on the 6 tapers in Table 1 are used to predict the OBR signal measurements (dots) from four tapers (Table I) by using Calculation II (solid curves). Taper waist widths are provided in the legend. Note that for the smallest taper width, 0.49 μm, the model successfully predicts the reduction in the OBR scattering at the taper waist qualitatively. Inset: OBR trace over the full length of taper 4a is compared with the prediction using Calculation II.

Fig. 6
Fig. 6

(a) The position zOBR calculated from Eq. (4) plotted versus position z for tapers 1a, 2a, 5a, 6a in Table 1. Zero on both axes corresponds to the taper center. The calculated OBR position error ranges from 0.13 mm (w0 = 1.74 μm) to 0.57 mm (w0 = 0.49 μm) after 2 mm of light propagation and is caused by the varying effective index along the taper. The legend gives the taper waist width and the black dashed line is the case zOBR = z. (b) The taper width versus position as determined from the OBR signal using Calculation III is plotted for four tapers from Table I (solid curves). The circles are the taper profiles measured using an SEM. The taper waist widths are provided in the legend.

Fig. 7
Fig. 7

Measured and predicted OBR signals and taper profiles for SMF-28 and SM980 tapers pulled at 1550°C. (a) SMF-28 OBR signal traces (dots) and the Calculation II prediction (solid curve). (b) SMF-28 profiles measured by an SEM (circles) and profiles predicted using Calculation III (solid curves). (c) SM980 OBR signal traces (dots) and the Calculation II prediction (solid curve). (d) SM980 profiles measured by an SEM (circles) and profiles predicted using Calculation III (solid curves). Taper waist widths are given in the legend of each panel.

Fig. 8
Fig. 8

OBR measurements of dust and microcracks. (a) Backscatter traces produced by coupling into the right and left ends of a taper are shown. Evidence of dust or defects on the taper appear as small spikes in the backscatter signal and, as expected, switch sides in the traces relative to the taper center. (b) Lower trace shows an OBR trace without tension. Upper trace shows the scan when tension is increased to induce what is believed to be a microcrack.

Tables (4)

Tables Icon

Table 1 Rayleigh Scattering Coefficients of Different SMF-28 Tapers Pulled at 1660°C

Tables Icon

Table 2 Waist Width Comparison of Tapers Pulled at 1660°C

Tables Icon

Table 3 Rayleigh Scattering Coefficients of Different Taper Types Pulled at 1550°C

Tables Icon

Table 4 Taper Rayleigh Scattering Coefficients Comparison With Optical Fiber

Equations (17)

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1 P in d P OBR ( w ( z ) ) d z = α core σ core ( w ( z ) ) + α clad σ clad ( w ( z ) ) + β η ( w ( z ) )
σ core , clad 3 λ 2 8 π n 2 core , clad | E ( r ) | 4 d S ( all | E ( r ) | 2 d S ) 2
η 3 λ 2 8 π n 2 interface | E ( r ) | 4 d l ( all | E ( r ) | 2 d S ) 2
0 z n eff ( w ( z ) ) d z = n OBR z OBR
d P OBR d z = d P OBR d z OBR d z OBR d z = n corr ( w ) d P OBR d z OBR
n corr ( w ) = n eff ( w ) n OBR
d z OBR d z = n corr ( w ( z OBR ) )
z = 0 z OBR d z OBR n corr ( w ( z OBR ) )
A n = V J E n * d V 2 S E n H n * d S = i ω c V Δ n ( r ) | E n ( r ) | 2 d V all | E n ( r ) | 2 d S
P s = ω 2 c 2 V V | E n ( r ) | 2 Δ n ( r ) Δ n ( r ) | E n ( r ) | 2 d V d V ( all | E n ( r ) | 2 d S ) ( all | E n ( r ) | 2 d S ) P in
Δ n ( r ) Δ n ( r ) Δ n 2 V c δ ( r r )
d P s ( z ) = ω 2 c 2 Δ n 2 V c S | E n ( r ) | 4 d S ( all | E n ( r ) | 2 d S ) 2 P in d z
α = 32 π 3 n 2 3 λ 4 Δ n 2 V c
1 P in d P s ( z ) d z = 3 λ 2 8 π n 2 α S | E n ( r ) | 4 d S ( all | E n ( r ) | 2 d S ) 2
1 P in d P s ( z ) d z = 3 λ 2 8 π n 2 i α i S i | E n ( r ) | 4 d S ( all | E n ( r ) | 2 d S ) 2 i α i σ i
3 λ 2 8 π n 2 α ss ss | E n ( r ) | 4 d S ( all | E n ( r ) | 2 d S ) 2 = 3 λ 2 8 π n 2 α ss Δ t interface | E n ( r ) | 4 d l ( all | E n ( r ) | 2 d S ) 2 β η
β α ss Δ t