Abstract

The forward scattering of light illuminating a transparent dielectric cylinder, such as a tapered fiber, from the side can be understood as interference of the diffracted, reflected, and transmitted light. Additionally, light can be resonantly coupled into the fiber if a multiple of the wavelength matches the circumference. Using a suitable laser setup with a novel evaluation algorithm allows us to quickly extract the fiber radius from the complex diffraction pattern, obtaining an accuracy of better than 50 nm. We demonstrate experimentally our method, which is noncontact and allows one to simultaneously measure the profile of a several-centimeter-long fiber waist with a diameter near the diffraction limit.

© 2004 Optical Society of America

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2003 (3)

J. Teipel, K. Franke, D. Turke, F. Warken, D. Meiser, M. Leuschner, and H. Giessen, Appl. Phys. B 77, 245 (2003).
[CrossRef]

K. J. Vahala, Nature 424, 839 (2003).
[CrossRef] [PubMed]

L. Tong, R. Gattass, J. Ashcom, S. He, J. Lou, M. Shen, I. Maxwell, and E. Mazur, Nature 426, 816 (2003).
[CrossRef] [PubMed]

2002 (2)

Th. Udem, R. Holzwarth, and T. W. Hänsch, Nature 416, 233 (2002).
[CrossRef] [PubMed]

S. M. Spillane, T. J. Klippenberg, and K. J. Vahala, Nature 415, 621 (2002).
[CrossRef] [PubMed]

2001 (2)

2000 (3)

T. A. Birks, J. C. Knight, and T. E. Dimmick, IEEE Photon. Technol. Lett. 12, 182 (2000).
[CrossRef]

M. Cai, O. Painter, and K. J. Vahala, Phys. Rev. Lett. 85, 74 (2000).
[CrossRef] [PubMed]

T. A. Birks, W. J. Wadsworth, and P. St. J. Russell, Opt. Lett. 25, 1415 (2000).
[CrossRef]

1998 (1)

1997 (1)

1994 (2)

M. B. van der Mark and L. Bosselaar, J. Lightwave Technol. 12, 1 (1994).
[CrossRef]

L. G. Guimaraes and H. M. Nussenzveig, J. Mod. Opt. 41, 625 (1994).
[CrossRef]

1992 (1)

T. A. Birks and Y. W. Li, J. Lightwave Technol. 10, 432 (1992).
[CrossRef]

1991 (1)

R. P. Kenny, T. A. Birks, and K. P. Oakley, Electron. Lett. 27, 1654 (1991).
[CrossRef]

1982 (1)

S. Kozaki, J. Appl. Phys. 53, 7195 (1982).
[CrossRef]

1977 (1)

1974 (1)

Ashcom, J.

L. Tong, R. Gattass, J. Ashcom, S. He, J. Lou, M. Shen, I. Maxwell, and E. Mazur, Nature 426, 816 (2003).
[CrossRef] [PubMed]

Birks, T. A.

T. A. Birks, W. J. Wadsworth, and P. St. J. Russell, Opt. Lett. 25, 1415 (2000).
[CrossRef]

T. A. Birks, J. C. Knight, and T. E. Dimmick, IEEE Photon. Technol. Lett. 12, 182 (2000).
[CrossRef]

J. C. Knight, G. Cheung, F. Jacques, and T. A. Birks, Opt. Lett. 22, 1129 (1997).
[CrossRef] [PubMed]

T. A. Birks and Y. W. Li, J. Lightwave Technol. 10, 432 (1992).
[CrossRef]

R. P. Kenny, T. A. Birks, and K. P. Oakley, Electron. Lett. 27, 1654 (1991).
[CrossRef]

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Bosselaar, L.

M. B. van der Mark and L. Bosselaar, J. Lightwave Technol. 12, 1 (1994).
[CrossRef]

Butler, D. J.

Cai, M.

M. Cai, O. Painter, and K. J. Vahala, Phys. Rev. Lett. 85, 74 (2000).
[CrossRef] [PubMed]

Chang, R. K.

Cheung, G.

Chowdhury, D. Q.

Dimmick, T. E.

T. A. Birks, J. C. Knight, and T. E. Dimmick, IEEE Photon. Technol. Lett. 12, 182 (2000).
[CrossRef]

Féron, P.

Forbes, G. W.

Franke, K.

J. Teipel, K. Franke, D. Turke, F. Warken, D. Meiser, M. Leuschner, and H. Giessen, Appl. Phys. B 77, 245 (2003).
[CrossRef]

Frazee, R. E.

Gattass, R.

L. Tong, R. Gattass, J. Ashcom, S. He, J. Lou, M. Shen, I. Maxwell, and E. Mazur, Nature 426, 816 (2003).
[CrossRef] [PubMed]

Giessen, H.

J. Teipel, K. Franke, D. Turke, F. Warken, D. Meiser, M. Leuschner, and H. Giessen, Appl. Phys. B 77, 245 (2003).
[CrossRef]

J. Teipel and H. Giessen, in Conference on Lasers and Electro-Optics (CLEO), Postconference Digest, Vol. 88 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2003), p. 58.

Guimaraes, L. G.

L. G. Guimaraes and H. M. Nussenzveig, J. Mod. Opt. 41, 625 (1994).
[CrossRef]

Hänsch, T. W.

Th. Udem, R. Holzwarth, and T. W. Hänsch, Nature 416, 233 (2002).
[CrossRef] [PubMed]

He, S.

L. Tong, R. Gattass, J. Ashcom, S. He, J. Lou, M. Shen, I. Maxwell, and E. Mazur, Nature 426, 816 (2003).
[CrossRef] [PubMed]

Holzwarth, R.

Th. Udem, R. Holzwarth, and T. W. Hänsch, Nature 416, 233 (2002).
[CrossRef] [PubMed]

Huffman, D. R.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Jacques, F.

Kenny, R. P.

R. P. Kenny, T. A. Birks, and K. P. Oakley, Electron. Lett. 27, 1654 (1991).
[CrossRef]

Klippenberg, T. J.

S. M. Spillane, T. J. Klippenberg, and K. J. Vahala, Nature 415, 621 (2002).
[CrossRef] [PubMed]

Knight, J. C.

T. A. Birks, J. C. Knight, and T. E. Dimmick, IEEE Photon. Technol. Lett. 12, 182 (2000).
[CrossRef]

J. C. Knight, G. Cheung, F. Jacques, and T. A. Birks, Opt. Lett. 22, 1129 (1997).
[CrossRef] [PubMed]

Kozaki, S.

S. Kozaki, J. Appl. Phys. 53, 7195 (1982).
[CrossRef]

Leuschner, M.

J. Teipel, K. Franke, D. Turke, F. Warken, D. Meiser, M. Leuschner, and H. Giessen, Appl. Phys. B 77, 245 (2003).
[CrossRef]

Li, Y. W.

T. A. Birks and Y. W. Li, J. Lightwave Technol. 10, 432 (1992).
[CrossRef]

Lissilour, F.

Lou, J.

L. Tong, R. Gattass, J. Ashcom, S. He, J. Lou, M. Shen, I. Maxwell, and E. Mazur, Nature 426, 816 (2003).
[CrossRef] [PubMed]

Maxwell, I.

L. Tong, R. Gattass, J. Ashcom, S. He, J. Lou, M. Shen, I. Maxwell, and E. Mazur, Nature 426, 816 (2003).
[CrossRef] [PubMed]

Mazur, E.

L. Tong, R. Gattass, J. Ashcom, S. He, J. Lou, M. Shen, I. Maxwell, and E. Mazur, Nature 426, 816 (2003).
[CrossRef] [PubMed]

Meiser, D.

J. Teipel, K. Franke, D. Turke, F. Warken, D. Meiser, M. Leuschner, and H. Giessen, Appl. Phys. B 77, 245 (2003).
[CrossRef]

Messager, F. D.

Nussenzveig, H. M.

L. G. Guimaraes and H. M. Nussenzveig, J. Mod. Opt. 41, 625 (1994).
[CrossRef]

Oakley, K. P.

R. P. Kenny, T. A. Birks, and K. P. Oakley, Electron. Lett. 27, 1654 (1991).
[CrossRef]

Painter, O.

M. Cai, O. Painter, and K. J. Vahala, Phys. Rev. Lett. 85, 74 (2000).
[CrossRef] [PubMed]

Poon, A. W.

Russell, P. St. J.

Shen, M.

L. Tong, R. Gattass, J. Ashcom, S. He, J. Lou, M. Shen, I. Maxwell, and E. Mazur, Nature 426, 816 (2003).
[CrossRef] [PubMed]

Smithgall, D. H.

Spillane, S. M.

S. M. Spillane, T. J. Klippenberg, and K. J. Vahala, Nature 415, 621 (2002).
[CrossRef] [PubMed]

Stéphan, G.

Teipel, J.

J. Teipel, K. Franke, D. Turke, F. Warken, D. Meiser, M. Leuschner, and H. Giessen, Appl. Phys. B 77, 245 (2003).
[CrossRef]

J. Teipel and H. Giessen, in Conference on Lasers and Electro-Optics (CLEO), Postconference Digest, Vol. 88 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2003), p. 58.

Tong, L.

L. Tong, R. Gattass, J. Ashcom, S. He, J. Lou, M. Shen, I. Maxwell, and E. Mazur, Nature 426, 816 (2003).
[CrossRef] [PubMed]

Turke, D.

J. Teipel, K. Franke, D. Turke, F. Warken, D. Meiser, M. Leuschner, and H. Giessen, Appl. Phys. B 77, 245 (2003).
[CrossRef]

Udem, Th.

Th. Udem, R. Holzwarth, and T. W. Hänsch, Nature 416, 233 (2002).
[CrossRef] [PubMed]

Vahala, K. J.

K. J. Vahala, Nature 424, 839 (2003).
[CrossRef] [PubMed]

S. M. Spillane, T. J. Klippenberg, and K. J. Vahala, Nature 415, 621 (2002).
[CrossRef] [PubMed]

M. Cai, O. Painter, and K. J. Vahala, Phys. Rev. Lett. 85, 74 (2000).
[CrossRef] [PubMed]

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

van der Mark, M. B.

M. B. van der Mark and L. Bosselaar, J. Lightwave Technol. 12, 1 (1994).
[CrossRef]

Wadsworth, W. J.

Warken, F.

J. Teipel, K. Franke, D. Turke, F. Warken, D. Meiser, M. Leuschner, and H. Giessen, Appl. Phys. B 77, 245 (2003).
[CrossRef]

Watkins, L. S.

Appl. Opt. (2)

Appl. Phys. B (1)

J. Teipel, K. Franke, D. Turke, F. Warken, D. Meiser, M. Leuschner, and H. Giessen, Appl. Phys. B 77, 245 (2003).
[CrossRef]

Electron. Lett. (1)

R. P. Kenny, T. A. Birks, and K. P. Oakley, Electron. Lett. 27, 1654 (1991).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

T. A. Birks, J. C. Knight, and T. E. Dimmick, IEEE Photon. Technol. Lett. 12, 182 (2000).
[CrossRef]

J. Appl. Phys. (1)

S. Kozaki, J. Appl. Phys. 53, 7195 (1982).
[CrossRef]

J. Lightwave Technol. (2)

T. A. Birks and Y. W. Li, J. Lightwave Technol. 10, 432 (1992).
[CrossRef]

M. B. van der Mark and L. Bosselaar, J. Lightwave Technol. 12, 1 (1994).
[CrossRef]

J. Mod. Opt. (1)

L. G. Guimaraes and H. M. Nussenzveig, J. Mod. Opt. 41, 625 (1994).
[CrossRef]

J. Opt. Soc. Am. (1)

Nature (4)

Th. Udem, R. Holzwarth, and T. W. Hänsch, Nature 416, 233 (2002).
[CrossRef] [PubMed]

S. M. Spillane, T. J. Klippenberg, and K. J. Vahala, Nature 415, 621 (2002).
[CrossRef] [PubMed]

K. J. Vahala, Nature 424, 839 (2003).
[CrossRef] [PubMed]

L. Tong, R. Gattass, J. Ashcom, S. He, J. Lou, M. Shen, I. Maxwell, and E. Mazur, Nature 426, 816 (2003).
[CrossRef] [PubMed]

Opt. Lett. (4)

Phys. Rev. Lett. (1)

M. Cai, O. Painter, and K. J. Vahala, Phys. Rev. Lett. 85, 74 (2000).
[CrossRef] [PubMed]

Other (3)

J. Teipel and H. Giessen, in Conference on Lasers and Electro-Optics (CLEO), Postconference Digest, Vol. 88 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2003), p. 58.

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

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Figures (4)

Fig. 1
Fig. 1

Schematic of the experimental setup. A linearly polarized laser beam illuminates a tapered fiber along a line focus. The scattered light pattern (which is actually the one evaluated in Fig. 4) is projected onto a semitransparent Lambertian screen and digitized by a CCD camera.

Fig. 2
Fig. 2

(a) Schematic of the scattering contributions at a transparent cylinder. (b) Typical normalized scattering intensity distribution at λ=532 nm and n=1.46. Note that the minima do not always go down to zero intensity.

Fig. 3
Fig. 3

Radius–angle diagram showing the angle positions of the extremum values of the scattered intensities as a function of the fiber radius. The polarization is varied with respect to the fiber axis.

Fig. 4
Fig. 4

(a) Measured angles of the extremum values of the scattered light as a function of the fiber position. (b) Evaluated fiber radii as a function of the fiber position. This measurement was compared with 30 single-gauged SEM recordings; one of them is shown in the inset.

Equations (1)

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Iθ;r=I0m=0exp-imθimAmw0,k0×Jmk0r-Hm1k0rγmk0,r,n2,

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