Abstract

We have theoretically predicted and experimentally demonstrated mode conversion in fiber tapers subject to large adiabatic bending. The far field intensity distribution of the taper mode is imaged in part by cleaving the taper at the position of minimum diameter.

© 2007 Optical Society of America

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References

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  1. J. C. Knight, G. Cheung, F. Jacques, and T. A. Birks, "Phase-matched excitationof whispering-gallery-mode resonances by a fibertaper," Opt. Lett. 22, 1129-1131 (1997).
    [CrossRef] [PubMed]
  2. V. S. Ilchenko, X. S. Yao and L. Maleki, "Pigtailing the high-Q microsphere cavity: a simple fiber coupler for optical whispering-gallery-modes," Opt. Lett. 24, 723-725 (1999).
    [CrossRef]
  3. M. Cai and K. J. Vahala, "Highly efficient hybrid fiber taper coupled microsphere laser," Opt. Lett. 26, 114-116 (2001).
    [CrossRef]
  4. D. Marcuse, "Mode conversion in optical fibers with monotonically increasing core radius," J. Lightwave Technol. LT-5, 125-133 (1987).
    [CrossRef]
  5. P. N. Moar, S. T. Huntington, J. Katsifolis, L. W. Cahill, A. Roberts, and K. A. Nugent, J. Appl. Phys. 85, 3395 (1999).
    [CrossRef]
  6. M. L. Gorodetsky, A. A. Savchenkov, and V. S. Ilchenko, "Ultimate Q of optical microsphere resonators," Opt. Lett. 21, 453-455 (1996).
    [CrossRef] [PubMed]
  7. For example, J. D. Jackson, Classical Electrodynamics, 3rd ed., (John Wiley & Sons, 1998) Ch. 8.
  8. V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, and L. Maleki, "Dispersion compensation in whispering-gallery modes," J. Opt. Soc. Am. A 20, 157-162 (2003).
    [CrossRef]
  9. E. A. J. Mercatili, "Bends in Optical Dielectric Guides," Bell Syst. Tech. J. 48, 2103 (1969).
  10. M. Sumetsky, Y. Dulashko, and A. Hale, "Fabrication and study of bent and coiled free silica nanowires: Self-coupling microloop optical interferometer," Opt. Express 12, 3521-3531 (2004).
    [CrossRef] [PubMed]
  11. A. B. Matsko, A. A. Savchenkov, D. Strekalov, and L. Maleki, "Whispering Gallery Resonators for studying Orbital Angular Momentum of a Photon," Phys. Rev. Lett. 95, 143904 (2005).
    [CrossRef] [PubMed]

2005 (1)

A. B. Matsko, A. A. Savchenkov, D. Strekalov, and L. Maleki, "Whispering Gallery Resonators for studying Orbital Angular Momentum of a Photon," Phys. Rev. Lett. 95, 143904 (2005).
[CrossRef] [PubMed]

2004 (1)

2003 (1)

2001 (1)

M. Cai and K. J. Vahala, "Highly efficient hybrid fiber taper coupled microsphere laser," Opt. Lett. 26, 114-116 (2001).
[CrossRef]

1999 (2)

P. N. Moar, S. T. Huntington, J. Katsifolis, L. W. Cahill, A. Roberts, and K. A. Nugent, J. Appl. Phys. 85, 3395 (1999).
[CrossRef]

V. S. Ilchenko, X. S. Yao and L. Maleki, "Pigtailing the high-Q microsphere cavity: a simple fiber coupler for optical whispering-gallery-modes," Opt. Lett. 24, 723-725 (1999).
[CrossRef]

1997 (1)

1996 (1)

1987 (1)

D. Marcuse, "Mode conversion in optical fibers with monotonically increasing core radius," J. Lightwave Technol. LT-5, 125-133 (1987).
[CrossRef]

1969 (1)

E. A. J. Mercatili, "Bends in Optical Dielectric Guides," Bell Syst. Tech. J. 48, 2103 (1969).

Birks, T. A.

Cahill, L. W.

P. N. Moar, S. T. Huntington, J. Katsifolis, L. W. Cahill, A. Roberts, and K. A. Nugent, J. Appl. Phys. 85, 3395 (1999).
[CrossRef]

Cai, M.

M. Cai and K. J. Vahala, "Highly efficient hybrid fiber taper coupled microsphere laser," Opt. Lett. 26, 114-116 (2001).
[CrossRef]

Cheung, G.

Dulashko, Y.

Gorodetsky, M. L.

Hale, A.

Huntington, S. T.

P. N. Moar, S. T. Huntington, J. Katsifolis, L. W. Cahill, A. Roberts, and K. A. Nugent, J. Appl. Phys. 85, 3395 (1999).
[CrossRef]

Ilchenko, V. S.

Jacques, F.

Katsifolis, J.

P. N. Moar, S. T. Huntington, J. Katsifolis, L. W. Cahill, A. Roberts, and K. A. Nugent, J. Appl. Phys. 85, 3395 (1999).
[CrossRef]

Knight, J. C.

Maleki, L.

A. B. Matsko, A. A. Savchenkov, D. Strekalov, and L. Maleki, "Whispering Gallery Resonators for studying Orbital Angular Momentum of a Photon," Phys. Rev. Lett. 95, 143904 (2005).
[CrossRef] [PubMed]

V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, and L. Maleki, "Dispersion compensation in whispering-gallery modes," J. Opt. Soc. Am. A 20, 157-162 (2003).
[CrossRef]

V. S. Ilchenko, X. S. Yao and L. Maleki, "Pigtailing the high-Q microsphere cavity: a simple fiber coupler for optical whispering-gallery-modes," Opt. Lett. 24, 723-725 (1999).
[CrossRef]

Marcuse, D.

D. Marcuse, "Mode conversion in optical fibers with monotonically increasing core radius," J. Lightwave Technol. LT-5, 125-133 (1987).
[CrossRef]

Matsko, A. B.

A. B. Matsko, A. A. Savchenkov, D. Strekalov, and L. Maleki, "Whispering Gallery Resonators for studying Orbital Angular Momentum of a Photon," Phys. Rev. Lett. 95, 143904 (2005).
[CrossRef] [PubMed]

V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, and L. Maleki, "Dispersion compensation in whispering-gallery modes," J. Opt. Soc. Am. A 20, 157-162 (2003).
[CrossRef]

Mercatili, E. A. J.

E. A. J. Mercatili, "Bends in Optical Dielectric Guides," Bell Syst. Tech. J. 48, 2103 (1969).

Moar, P. N.

P. N. Moar, S. T. Huntington, J. Katsifolis, L. W. Cahill, A. Roberts, and K. A. Nugent, J. Appl. Phys. 85, 3395 (1999).
[CrossRef]

Nugent, K. A.

P. N. Moar, S. T. Huntington, J. Katsifolis, L. W. Cahill, A. Roberts, and K. A. Nugent, J. Appl. Phys. 85, 3395 (1999).
[CrossRef]

Roberts, A.

P. N. Moar, S. T. Huntington, J. Katsifolis, L. W. Cahill, A. Roberts, and K. A. Nugent, J. Appl. Phys. 85, 3395 (1999).
[CrossRef]

Savchenkov, A. A.

Strekalov, D.

A. B. Matsko, A. A. Savchenkov, D. Strekalov, and L. Maleki, "Whispering Gallery Resonators for studying Orbital Angular Momentum of a Photon," Phys. Rev. Lett. 95, 143904 (2005).
[CrossRef] [PubMed]

Sumetsky, M.

Vahala, K. J.

M. Cai and K. J. Vahala, "Highly efficient hybrid fiber taper coupled microsphere laser," Opt. Lett. 26, 114-116 (2001).
[CrossRef]

Yao, X. S.

V. S. Ilchenko, X. S. Yao and L. Maleki, "Pigtailing the high-Q microsphere cavity: a simple fiber coupler for optical whispering-gallery-modes," Opt. Lett. 24, 723-725 (1999).
[CrossRef]

Bell Syst. Tech. J. (1)

E. A. J. Mercatili, "Bends in Optical Dielectric Guides," Bell Syst. Tech. J. 48, 2103 (1969).

J. Appl. Phys. (1)

P. N. Moar, S. T. Huntington, J. Katsifolis, L. W. Cahill, A. Roberts, and K. A. Nugent, J. Appl. Phys. 85, 3395 (1999).
[CrossRef]

J. Lightwave Technol. (1)

D. Marcuse, "Mode conversion in optical fibers with monotonically increasing core radius," J. Lightwave Technol. LT-5, 125-133 (1987).
[CrossRef]

J. Opt. Soc. Am. A (1)

Opt. Express (1)

Opt. Lett. (4)

V. S. Ilchenko, X. S. Yao and L. Maleki, "Pigtailing the high-Q microsphere cavity: a simple fiber coupler for optical whispering-gallery-modes," Opt. Lett. 24, 723-725 (1999).
[CrossRef]

M. Cai and K. J. Vahala, "Highly efficient hybrid fiber taper coupled microsphere laser," Opt. Lett. 26, 114-116 (2001).
[CrossRef]

J. C. Knight, G. Cheung, F. Jacques, and T. A. Birks, "Phase-matched excitationof whispering-gallery-mode resonances by a fibertaper," Opt. Lett. 22, 1129-1131 (1997).
[CrossRef] [PubMed]

M. L. Gorodetsky, A. A. Savchenkov, and V. S. Ilchenko, "Ultimate Q of optical microsphere resonators," Opt. Lett. 21, 453-455 (1996).
[CrossRef] [PubMed]

Phys. Rev. Lett. (1)

A. B. Matsko, A. A. Savchenkov, D. Strekalov, and L. Maleki, "Whispering Gallery Resonators for studying Orbital Angular Momentum of a Photon," Phys. Rev. Lett. 95, 143904 (2005).
[CrossRef] [PubMed]

Other (1)

For example, J. D. Jackson, Classical Electrodynamics, 3rd ed., (John Wiley & Sons, 1998) Ch. 8.

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Figures (4)

Fig. 1.
Fig. 1.

(a). Fiber taper before cleaving. The diameter of this taper varies by less than 2% over 300 μm. b) 4 μm diameter cleaved taper. c) 10 μm diameter cleaved taper. The cleaved face is orthogonal to the taper axis. d) A sub-micron diameter taper that is too small to be resolved by our microscope.

Fig. 2.
Fig. 2.

Motivation for the physical model. Region I is an unmodified SMF28 fiber. Region II is a transition to a step index taper of radius b. The optical mode in region II possesses the same spatial symmetry as the single mode in region I. A circular bend of radius A is applied to the taper in region III. In our model, we treat the mode in this region as a WGM associated with a sphere (toroid) of radius A. The eventual mode in region IV is possibly determined by the bend in region III.

Fig. 3.
Fig. 3.

(a). Results of numerical computation of Eq. (1) for the first four TE taper modes. For large diameters, bending couples light to multiple taper modes. For small diameters, the bend couples to a single symmetric mode. For intermediate diameters, bending causes preferential coupling to the TE11 mode. b) Diagram illustrating physical overlap between the bend mode (colored fill) and the taper TE11 mode (blue contour lines) in an 8 μm diameter taper subject to a 300 μm radius bend.

Fig. 4.
Fig. 4.

Results using a 4 μm radius taper. a) Far field at 635 nm, no bend. The mode is spatially symmetric, with some structure that could be attributed to multimode propagation in the SMF28 fiber. b) Far field at 1550 nm, no bend. The mode is spatially symmetric. c) Far field at 635 nm, 90o bend. This is a superposition of many modes, with at least 9 visible peaks. d) Far field at 1550 nm, 90° bend. There are two apparent peaks, consistent with the predictions of Eq. (2).

Equations (1)

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I = d V ψ W G M ( r , θ , φ ) . ψ T A P E R ( r , θ , φ )

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