Abstract

For the adiabatically deformed optical fiber the intermode transmission amplitudes and loss vanish exponentially with the characteristic length of the fiber’s nonuniformity. For this reason smoothly deformed optical fiber tapers can have very small losses. However, losses dramatically increase with a thinning of the microfiber down to a diameter much smaller than the radiation wavelength. The theory of nonadiabatic intermode transitions is briefly discussed and, by using this theory, the problem of the smallest diameter of a microfiber that can transmit evanescent radiation is studied. It is shown that even for an extremely high uniformity of microfiber the ability of light transmission does not leave much space for microfiber thinning: the propagating mode vanishes at a threshold value of the microfiber’s diameter, that is smaller than the radiation wavelength by only an order of magnitude.

© 2006 Optical Society of America

Full Article  |  PDF Article

Corrections

M. Sumetsky, "How thin can a microfiber be and still guide light? Errata," Opt. Lett. 31, 3577-3578 (2006)
https://www.osapublishing.org/ol/abstract.cfm?uri=ol-31-24-3577

References

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2005 (3)

2004 (2)

V. I. Balykin, K. Hakuta, F. Le Kien, J. Q. Liang, and M. Morinaga, Phys. Rev. A 70, 011401(R) (2004).
[CrossRef]

G. Brambilla, V. Finazzi, and D. J. Richardson, Opt. Express 12, 2258 (2004).
[CrossRef] [PubMed]

2003 (2)

V. P. Krainov, J. Phys. B 36, L169 (2003).
[CrossRef]

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

1991 (1)

J. D. Love, W. M. Henry, W. J. Stewart, R. J. Black, S. Lacroix, and F. Gonthier, IEE Proc. J: Optoelectron. 138, 343 (1991).
[CrossRef]

1984 (1)

1976 (1)

J. P. Davis and P. Pechukas, J. Chem. Phys. 64, 3129 (1976).
[CrossRef]

1963 (1)

A. V. Chaplik, Sov. Phys. JETP 18, 1046 (1963).

1962 (1)

A. M. Dykhne, Sov. Phys. JETP 14, 941 (1962).

Ashcom, J. B.

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

Balykin, V. I.

V. I. Balykin, K. Hakuta, F. Le Kien, J. Q. Liang, and M. Morinaga, Phys. Rev. A 70, 011401(R) (2004).
[CrossRef]

Birks, T. A.

P. J. Roberts, F. Couny, H. Sabert, B. J. Mangan, T. A. Birks, J. C. Knight, and P. St. J. Russell, Opt. Express 13, 7779 (2005).
[CrossRef] [PubMed]

T. A. Birks, S. G. Leon-Saval, W. J. Wadsworth, and P. St. J. Russell, 'Optical micro- and nano-structures using fiber tapers,' in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science and Photonic Applications, Systems and Technologies 2005 (Optical Society of America, 2005), paper CMD1.
[PubMed]

Black, R. J.

J. D. Love, W. M. Henry, W. J. Stewart, R. J. Black, S. Lacroix, and F. Gonthier, IEE Proc. J: Optoelectron. 138, 343 (1991).
[CrossRef]

Brambilla, G.

Chaplik, A. V.

A. V. Chaplik, Sov. Phys. JETP 18, 1046 (1963).

Couny, F.

Davis, J. P.

J. P. Davis and P. Pechukas, J. Chem. Phys. 64, 3129 (1976).
[CrossRef]

Dulashko, Y.

M. Sumetsky, Y. Dulashko, J. M. Fini, and A. Hale, Appl. Phys. Lett. 86, 161108 (2005).
[CrossRef]

Dykhne, A. M.

A. M. Dykhne, Sov. Phys. JETP 14, 941 (1962).

Finazzi, V.

Fini, J. M.

M. Sumetsky, Y. Dulashko, J. M. Fini, and A. Hale, Appl. Phys. Lett. 86, 161108 (2005).
[CrossRef]

Gattass, R. R.

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

Gonthier, F.

J. D. Love, W. M. Henry, W. J. Stewart, R. J. Black, S. Lacroix, and F. Gonthier, IEE Proc. J: Optoelectron. 138, 343 (1991).
[CrossRef]

Hagedorn, G. A.

G. A. Hagedorn and A. Joye, 'Recent results on non-adiabatic transitions in quantum mechanics,' preprint, http://www-fourier.ujf-grenoble.fr/~joye/simon2005.pdf.

Hakuta, K.

V. I. Balykin, K. Hakuta, F. Le Kien, J. Q. Liang, and M. Morinaga, Phys. Rev. A 70, 011401(R) (2004).
[CrossRef]

Hale, A.

M. Sumetsky, Y. Dulashko, J. M. Fini, and A. Hale, Appl. Phys. Lett. 86, 161108 (2005).
[CrossRef]

He, S.

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

Henry, W. M.

J. D. Love, W. M. Henry, W. J. Stewart, R. J. Black, S. Lacroix, and F. Gonthier, IEE Proc. J: Optoelectron. 138, 343 (1991).
[CrossRef]

Joye, A.

G. A. Hagedorn and A. Joye, 'Recent results on non-adiabatic transitions in quantum mechanics,' preprint, http://www-fourier.ujf-grenoble.fr/~joye/simon2005.pdf.

Knight, J. C.

Krainov, V. P.

V. P. Krainov, J. Phys. B 36, L169 (2003).
[CrossRef]

Lacroix, S.

J. D. Love, W. M. Henry, W. J. Stewart, R. J. Black, S. Lacroix, and F. Gonthier, IEE Proc. J: Optoelectron. 138, 343 (1991).
[CrossRef]

Landau, L. D.

L. D. Landau and E. M. Lifshitz, Quantum Mechanics, 2nd ed. (Pergamon, 1965).

Le Kien, F.

V. I. Balykin, K. Hakuta, F. Le Kien, J. Q. Liang, and M. Morinaga, Phys. Rev. A 70, 011401(R) (2004).
[CrossRef]

Leon-Saval, S. G.

T. A. Birks, S. G. Leon-Saval, W. J. Wadsworth, and P. St. J. Russell, 'Optical micro- and nano-structures using fiber tapers,' in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science and Photonic Applications, Systems and Technologies 2005 (Optical Society of America, 2005), paper CMD1.
[PubMed]

Liang, J. Q.

V. I. Balykin, K. Hakuta, F. Le Kien, J. Q. Liang, and M. Morinaga, Phys. Rev. A 70, 011401(R) (2004).
[CrossRef]

Lifshitz, E. M.

L. D. Landau and E. M. Lifshitz, Quantum Mechanics, 2nd ed. (Pergamon, 1965).

Lou, J.

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

Love, J. D.

J. D. Love, W. M. Henry, W. J. Stewart, R. J. Black, S. Lacroix, and F. Gonthier, IEE Proc. J: Optoelectron. 138, 343 (1991).
[CrossRef]

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

Mangan, B. J.

Mansuripur, M.

Marcuse, D.

Maxwell, I.

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

Mazur, E.

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

Migdal, A. B.

A. B. Migdal, Qualitative Methods in Quantum Theory (Benjamin, 1977).

Morinaga, M.

V. I. Balykin, K. Hakuta, F. Le Kien, J. Q. Liang, and M. Morinaga, Phys. Rev. A 70, 011401(R) (2004).
[CrossRef]

Pechukas, P.

J. P. Davis and P. Pechukas, J. Chem. Phys. 64, 3129 (1976).
[CrossRef]

Peyghambarian, N.

Polynkin, A.

Polynkin, P.

Richardson, D. J.

Roberts, P. J.

Russell, P. St. J.

P. J. Roberts, F. Couny, H. Sabert, B. J. Mangan, T. A. Birks, J. C. Knight, and P. St. J. Russell, Opt. Express 13, 7779 (2005).
[CrossRef] [PubMed]

T. A. Birks, S. G. Leon-Saval, W. J. Wadsworth, and P. St. J. Russell, 'Optical micro- and nano-structures using fiber tapers,' in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science and Photonic Applications, Systems and Technologies 2005 (Optical Society of America, 2005), paper CMD1.
[PubMed]

Sabert, H.

Shen, M.

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

Snyder, A. W.

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

Stewart, W. J.

J. D. Love, W. M. Henry, W. J. Stewart, R. J. Black, S. Lacroix, and F. Gonthier, IEE Proc. J: Optoelectron. 138, 343 (1991).
[CrossRef]

Sumetsky, M.

M. Sumetsky, Y. Dulashko, J. M. Fini, and A. Hale, Appl. Phys. Lett. 86, 161108 (2005).
[CrossRef]

Tong, L.

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

Wadsworth, W. J.

T. A. Birks, S. G. Leon-Saval, W. J. Wadsworth, and P. St. J. Russell, 'Optical micro- and nano-structures using fiber tapers,' in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science and Photonic Applications, Systems and Technologies 2005 (Optical Society of America, 2005), paper CMD1.
[PubMed]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

M. Sumetsky, Y. Dulashko, J. M. Fini, and A. Hale, Appl. Phys. Lett. 86, 161108 (2005).
[CrossRef]

IEE Proc. J: Optoelectron. (1)

J. D. Love, W. M. Henry, W. J. Stewart, R. J. Black, S. Lacroix, and F. Gonthier, IEE Proc. J: Optoelectron. 138, 343 (1991).
[CrossRef]

J. Chem. Phys. (1)

J. P. Davis and P. Pechukas, J. Chem. Phys. 64, 3129 (1976).
[CrossRef]

J. Phys. B (1)

V. P. Krainov, J. Phys. B 36, L169 (2003).
[CrossRef]

Nature (1)

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

Opt. Express (2)

Opt. Lett. (1)

Phys. Rev. A (1)

V. I. Balykin, K. Hakuta, F. Le Kien, J. Q. Liang, and M. Morinaga, Phys. Rev. A 70, 011401(R) (2004).
[CrossRef]

Sov. Phys. JETP (2)

A. M. Dykhne, Sov. Phys. JETP 14, 941 (1962).

A. V. Chaplik, Sov. Phys. JETP 18, 1046 (1963).

Other (6)

A. B. Migdal, Qualitative Methods in Quantum Theory (Benjamin, 1977).

Ref. , page 563.

L. D. Landau and E. M. Lifshitz, Quantum Mechanics, 2nd ed. (Pergamon, 1965).

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

T. A. Birks, S. G. Leon-Saval, W. J. Wadsworth, and P. St. J. Russell, 'Optical micro- and nano-structures using fiber tapers,' in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science and Photonic Applications, Systems and Technologies 2005 (Optical Society of America, 2005), paper CMD1.
[PubMed]

G. A. Hagedorn and A. Joye, 'Recent results on non-adiabatic transitions in quantum mechanics,' preprint, http://www-fourier.ujf-grenoble.fr/~joye/simon2005.pdf.

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Figures (2)

Fig. 1
Fig. 1

Refractive index distribution for (a1) a W-type optical fiber and (b1) a subwavelength optical fiber; (a2) behavior of the L P 01 and L P 02 propagation constants, β 1 and β 2 , respectively, for a W-type fiber taper in the neighborhood of the taper diameter d 0 , where β 1 and β 2 approach each other; (b2) behavior of the H E 11 propagation constant β 1 for the optical microfiber with a subwavelength diameter; (a3) and (b3) profiles of the biconical fiber tapers with characteristic diameters much greater and much smaller that the wavelength, respectively; (a4) and (b4) dependences Δ β 12 ( z ) for the fiber tapers shown in (a3) and (b3), respectively.

Fig. 2
Fig. 2

Transmission loss as a function of the microfiber diameter d 0 calculated with Eq. (3) for different characteristic lengths of the microfiber diameter variation L (curves 1, 2, and 3) and d = 1 μ m , and experimentally measured in Ref. [2] (curve 4).

Equations (3)

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A 12 = exp [ i z r z * d z Δ β 12 ( z ) ] , P 12 = A 12 2 .
P 12 = exp ( π 2 Δ β 0 L ) .
P exp [ 0.687 L d 0 1 2 ( d d 0 ) 1 2 exp ( 0.27 λ 2 d 0 2 ) ] .

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