Abstract

Dense photonic integration promises to revolutionize optical computing and communications. However, efforts towards this goal face unacceptable attenuation of light caused by surface roughness in microscopic devices. Here we address this problem by introducing Surface Nanoscale Axial Photonics (SNAP). The SNAP platform is based on whispering gallery modes circulating around the optical fiber surface and undergoing slow axial propagation readily described by the one-dimensional Schrödinger equation. These modes can be steered with dramatically small nanoscale variation of the fiber radius, which is quite simple to introduce in practice. Extremely low loss of SNAP devices is achieved due to the low surface roughness inherent in a drawn fiber surface. In excellent agreement with the developed theory, we experimentally demonstrate localization of light in quantum wells, halting light by a point source, tunneling through potential barriers, dark states, etc. This demonstration has intriguing potential applications in filtering, switching, slowing light, and sensing.

© 2011 OSA

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2011

2010

M. Notomi, “Manipulating light with strongly modulated photonic crystals,” Rep. Prog. Phys. 73(9), 096501 (2010).
[CrossRef]

U. K. Khankhoje, S.-H. Kim, B. C. Richards, J. Hendrickson, J. Sweet, J. D. Olitzky, G. Khitrova, H. M. Gibbs, and A. Scherer, “Modelling and fabrication of GaAs photonic-crystal cavities for cavity quantum electrodynamics,” Nanotechnology 21(6), 065202 (2010).
[CrossRef] [PubMed]

W. Bogaerts, S. K. Selvaraja, P. Dumon, J. Brouckaert, K. De Vos, D. Van Thourhout, and R. Baets, “Silicon-on-insulator spectral filters fabricated with CMOS technology,” IEEE J. Sel. Top. Quantum Electron. 16(1), 33–44 (2010).
[CrossRef]

A. Melloni, A. Canciamilla, C. Ferrari, F. Morichetti, L. O'Faolain, T. F. Krauss, R. De La Rue, A. Samarelli, and M. Sorel, “Tunable delay lines in silicon photonics: coupled resonators and photonic crystals, a comparison,” IEEE Photonics J. 2(2), 181–194 (2010).
[CrossRef]

M. Sumetsky, “Mode localization and the Q-factor of a cylindrical microresonator,” Opt. Lett. 35(14), 2385–2387 (2010).
[CrossRef] [PubMed]

M. Sumetsky and Y. Dulashko, “Radius variation of optical fibers with angstrom accuracy,” Opt. Lett. 35(23), 4006–4008 (2010).
[CrossRef] [PubMed]

2009

2008

Y. Vlasov, W. M. J. Green, and F. Xia, “High-throughput silicon nanophotonic wavelength-insensitive switch for on-chip optical networks,” Nat. Photonics 2(4), 242–246 (2008).
[CrossRef]

M. Notomi, E. Kuramochi, and T. Tanabe, “Large-scale arrays of ultrahigh-Q coupled nanocavities,” Nat. Photonics 2(12), 741–747 (2008).
[CrossRef]

T. Baba, “Slow light in photonic crystals,” Nat. Photonics 2(8), 465–473 (2008).
[CrossRef]

2007

F. N. Xia, L. Sekaric, and Y. Vlasov, “Ultracompact optical buffers on a silicon chip,” Nat. Photonics 1(1), 65–71 (2007).
[CrossRef]

2006

2004

A. D. Yablon, M. F. Yan, P. Wisk, F. V. DiMarcello, J. W. Fleming, W. A. Reed, E. M. Monberg, D. J. DiGiovanni, J. Jasapara, and M. E. Lines, “Refractive index perturbations in optical fibers resulting from frozen-in viscoelasticity,” Appl. Phys. Lett. 84(1), 19–21 (2004).
[CrossRef]

M. Sumetsky, “Whispering-gallery-bottle microcavities: the three-dimensional etalon,” Opt. Lett. 29(1), 8–10 (2004).
[CrossRef] [PubMed]

2003

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

2002

A. N. Oraevsky, “Whispering-gallery waves,” Quantum Electron. 32(5), 377–400 (2002).
[CrossRef]

2000

Y. Xu, Y. Li, R. K. Lee, and A. Yariv, “Scattering-theory analysis of waveguide-resonator coupling,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 62(55 Pt B), 7389–7404 (2000).
[CrossRef] [PubMed]

T. A. Birks, J. C. Knight, and T. E. Dimmick, “High-resolution measurement of the fiber diameter variations using whispering gallery modes and no optical alignment,” IEEE Photon. Technol. Lett. 12(2), 182–183 (2000).
[CrossRef]

1999

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, M. Khan, C. Manolatou, and H. Haus, “Theoretical analysis of channel drop tunneling processes,” Phys. Rev. B 59(24), 15882–15892 (1999).
[CrossRef]

1997

1947

A. Q. Tool, L. W. Tilton, and J. B. Saunders, “Changes caused in the refractivity and density of glass by annealing,” J Res Natl Bur Stand (1934) 38(5), 519–526 (1947).
[PubMed]

1910

L. Rayleigh, “The problem of the whispering gallery,” Philos. Mag. 20, 1001–1004 (1910).

Baba, T.

T. Baba, “Slow light in photonic crystals,” Nat. Photonics 2(8), 465–473 (2008).
[CrossRef]

Baets, R.

W. Bogaerts, S. K. Selvaraja, P. Dumon, J. Brouckaert, K. De Vos, D. Van Thourhout, and R. Baets, “Silicon-on-insulator spectral filters fabricated with CMOS technology,” IEEE J. Sel. Top. Quantum Electron. 16(1), 33–44 (2010).
[CrossRef]

Birks, T. A.

T. A. Birks, J. C. Knight, and T. E. Dimmick, “High-resolution measurement of the fiber diameter variations using whispering gallery modes and no optical alignment,” IEEE Photon. Technol. Lett. 12(2), 182–183 (2000).
[CrossRef]

J. C. Knight, G. Cheung, F. Jacques, and T. A. Birks, “Phase-matched excitation of whispering-gallery-mode resonances by a fiber taper,” Opt. Lett. 22(15), 1129–1131 (1997).
[CrossRef] [PubMed]

Bogaerts, W.

W. Bogaerts, S. K. Selvaraja, P. Dumon, J. Brouckaert, K. De Vos, D. Van Thourhout, and R. Baets, “Silicon-on-insulator spectral filters fabricated with CMOS technology,” IEEE J. Sel. Top. Quantum Electron. 16(1), 33–44 (2010).
[CrossRef]

Brouckaert, J.

W. Bogaerts, S. K. Selvaraja, P. Dumon, J. Brouckaert, K. De Vos, D. Van Thourhout, and R. Baets, “Silicon-on-insulator spectral filters fabricated with CMOS technology,” IEEE J. Sel. Top. Quantum Electron. 16(1), 33–44 (2010).
[CrossRef]

Canciamilla, A.

A. Melloni, A. Canciamilla, C. Ferrari, F. Morichetti, L. O'Faolain, T. F. Krauss, R. De La Rue, A. Samarelli, and M. Sorel, “Tunable delay lines in silicon photonics: coupled resonators and photonic crystals, a comparison,” IEEE Photonics J. 2(2), 181–194 (2010).
[CrossRef]

Cheung, G.

De La Rue, R.

A. Melloni, A. Canciamilla, C. Ferrari, F. Morichetti, L. O'Faolain, T. F. Krauss, R. De La Rue, A. Samarelli, and M. Sorel, “Tunable delay lines in silicon photonics: coupled resonators and photonic crystals, a comparison,” IEEE Photonics J. 2(2), 181–194 (2010).
[CrossRef]

De Vos, K.

W. Bogaerts, S. K. Selvaraja, P. Dumon, J. Brouckaert, K. De Vos, D. Van Thourhout, and R. Baets, “Silicon-on-insulator spectral filters fabricated with CMOS technology,” IEEE J. Sel. Top. Quantum Electron. 16(1), 33–44 (2010).
[CrossRef]

DiGiovanni, D. J.

A. D. Yablon, M. F. Yan, P. Wisk, F. V. DiMarcello, J. W. Fleming, W. A. Reed, E. M. Monberg, D. J. DiGiovanni, J. Jasapara, and M. E. Lines, “Refractive index perturbations in optical fibers resulting from frozen-in viscoelasticity,” Appl. Phys. Lett. 84(1), 19–21 (2004).
[CrossRef]

M. Sumetsky, D. J. DiGiovanni, Y. Dulashko, J. M. Fini, X. Liu, E. M. Monberg, and T. F. Taunay, “Surface nanoscale axial photonics: robust fabrication of high quality factor microresonators,” Opt. Lett. (to be published).

DiMarcello, F. V.

A. D. Yablon, M. F. Yan, P. Wisk, F. V. DiMarcello, J. W. Fleming, W. A. Reed, E. M. Monberg, D. J. DiGiovanni, J. Jasapara, and M. E. Lines, “Refractive index perturbations in optical fibers resulting from frozen-in viscoelasticity,” Appl. Phys. Lett. 84(1), 19–21 (2004).
[CrossRef]

Dimmick, T. E.

T. A. Birks, J. C. Knight, and T. E. Dimmick, “High-resolution measurement of the fiber diameter variations using whispering gallery modes and no optical alignment,” IEEE Photon. Technol. Lett. 12(2), 182–183 (2000).
[CrossRef]

Doerr, C. R.

Dulashko, Y.

M. Sumetsky and Y. Dulashko, “Radius variation of optical fibers with angstrom accuracy,” Opt. Lett. 35(23), 4006–4008 (2010).
[CrossRef] [PubMed]

M. Sumetsky, D. J. DiGiovanni, Y. Dulashko, J. M. Fini, X. Liu, E. M. Monberg, and T. F. Taunay, “Surface nanoscale axial photonics: robust fabrication of high quality factor microresonators,” Opt. Lett. (to be published).

Dumon, P.

W. Bogaerts, S. K. Selvaraja, P. Dumon, J. Brouckaert, K. De Vos, D. Van Thourhout, and R. Baets, “Silicon-on-insulator spectral filters fabricated with CMOS technology,” IEEE J. Sel. Top. Quantum Electron. 16(1), 33–44 (2010).
[CrossRef]

Fan, S.

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, M. Khan, C. Manolatou, and H. Haus, “Theoretical analysis of channel drop tunneling processes,” Phys. Rev. B 59(24), 15882–15892 (1999).
[CrossRef]

Ferrari, C.

A. Melloni, A. Canciamilla, C. Ferrari, F. Morichetti, L. O'Faolain, T. F. Krauss, R. De La Rue, A. Samarelli, and M. Sorel, “Tunable delay lines in silicon photonics: coupled resonators and photonic crystals, a comparison,” IEEE Photonics J. 2(2), 181–194 (2010).
[CrossRef]

Fini, J. M.

M. Sumetsky, D. J. DiGiovanni, Y. Dulashko, J. M. Fini, X. Liu, E. M. Monberg, and T. F. Taunay, “Surface nanoscale axial photonics: robust fabrication of high quality factor microresonators,” Opt. Lett. (to be published).

Fleming, J. W.

A. D. Yablon, M. F. Yan, P. Wisk, F. V. DiMarcello, J. W. Fleming, W. A. Reed, E. M. Monberg, D. J. DiGiovanni, J. Jasapara, and M. E. Lines, “Refractive index perturbations in optical fibers resulting from frozen-in viscoelasticity,” Appl. Phys. Lett. 84(1), 19–21 (2004).
[CrossRef]

Gibbs, H. M.

U. K. Khankhoje, S.-H. Kim, B. C. Richards, J. Hendrickson, J. Sweet, J. D. Olitzky, G. Khitrova, H. M. Gibbs, and A. Scherer, “Modelling and fabrication of GaAs photonic-crystal cavities for cavity quantum electrodynamics,” Nanotechnology 21(6), 065202 (2010).
[CrossRef] [PubMed]

Green, W. M. J.

Y. Vlasov, W. M. J. Green, and F. Xia, “High-throughput silicon nanophotonic wavelength-insensitive switch for on-chip optical networks,” Nat. Photonics 2(4), 242–246 (2008).
[CrossRef]

Grudinin, I. S.

Haus, H.

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, M. Khan, C. Manolatou, and H. Haus, “Theoretical analysis of channel drop tunneling processes,” Phys. Rev. B 59(24), 15882–15892 (1999).
[CrossRef]

Hendrickson, J.

U. K. Khankhoje, S.-H. Kim, B. C. Richards, J. Hendrickson, J. Sweet, J. D. Olitzky, G. Khitrova, H. M. Gibbs, and A. Scherer, “Modelling and fabrication of GaAs photonic-crystal cavities for cavity quantum electrodynamics,” Nanotechnology 21(6), 065202 (2010).
[CrossRef] [PubMed]

Ilchenko, V. S.

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

A. A. Savchenkov, I. S. Grudinin, A. B. Matsko, D. Strekalov, M. Mohageg, V. S. Ilchenko, and L. Maleki, “Morphology-dependent photonic circuit elements,” Opt. Lett. 31(9), 1313–1315 (2006).
[CrossRef] [PubMed]

Jacques, F.

Jasapara, J.

A. D. Yablon, M. F. Yan, P. Wisk, F. V. DiMarcello, J. W. Fleming, W. A. Reed, E. M. Monberg, D. J. DiGiovanni, J. Jasapara, and M. E. Lines, “Refractive index perturbations in optical fibers resulting from frozen-in viscoelasticity,” Appl. Phys. Lett. 84(1), 19–21 (2004).
[CrossRef]

Joannopoulos, J. D.

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, M. Khan, C. Manolatou, and H. Haus, “Theoretical analysis of channel drop tunneling processes,” Phys. Rev. B 59(24), 15882–15892 (1999).
[CrossRef]

Khan, M.

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, M. Khan, C. Manolatou, and H. Haus, “Theoretical analysis of channel drop tunneling processes,” Phys. Rev. B 59(24), 15882–15892 (1999).
[CrossRef]

Khankhoje, U. K.

U. K. Khankhoje, S.-H. Kim, B. C. Richards, J. Hendrickson, J. Sweet, J. D. Olitzky, G. Khitrova, H. M. Gibbs, and A. Scherer, “Modelling and fabrication of GaAs photonic-crystal cavities for cavity quantum electrodynamics,” Nanotechnology 21(6), 065202 (2010).
[CrossRef] [PubMed]

Khitrova, G.

U. K. Khankhoje, S.-H. Kim, B. C. Richards, J. Hendrickson, J. Sweet, J. D. Olitzky, G. Khitrova, H. M. Gibbs, and A. Scherer, “Modelling and fabrication of GaAs photonic-crystal cavities for cavity quantum electrodynamics,” Nanotechnology 21(6), 065202 (2010).
[CrossRef] [PubMed]

Kim, S.-H.

U. K. Khankhoje, S.-H. Kim, B. C. Richards, J. Hendrickson, J. Sweet, J. D. Olitzky, G. Khitrova, H. M. Gibbs, and A. Scherer, “Modelling and fabrication of GaAs photonic-crystal cavities for cavity quantum electrodynamics,” Nanotechnology 21(6), 065202 (2010).
[CrossRef] [PubMed]

Knight, J. C.

T. A. Birks, J. C. Knight, and T. E. Dimmick, “High-resolution measurement of the fiber diameter variations using whispering gallery modes and no optical alignment,” IEEE Photon. Technol. Lett. 12(2), 182–183 (2000).
[CrossRef]

J. C. Knight, G. Cheung, F. Jacques, and T. A. Birks, “Phase-matched excitation of whispering-gallery-mode resonances by a fiber taper,” Opt. Lett. 22(15), 1129–1131 (1997).
[CrossRef] [PubMed]

Krauss, T. F.

A. Melloni, A. Canciamilla, C. Ferrari, F. Morichetti, L. O'Faolain, T. F. Krauss, R. De La Rue, A. Samarelli, and M. Sorel, “Tunable delay lines in silicon photonics: coupled resonators and photonic crystals, a comparison,” IEEE Photonics J. 2(2), 181–194 (2010).
[CrossRef]

Kuramochi, E.

M. Notomi, E. Kuramochi, and T. Tanabe, “Large-scale arrays of ultrahigh-Q coupled nanocavities,” Nat. Photonics 2(12), 741–747 (2008).
[CrossRef]

Lee, R. K.

Y. Xu, Y. Li, R. K. Lee, and A. Yariv, “Scattering-theory analysis of waveguide-resonator coupling,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 62(55 Pt B), 7389–7404 (2000).
[CrossRef] [PubMed]

Li, Y.

Y. Xu, Y. Li, R. K. Lee, and A. Yariv, “Scattering-theory analysis of waveguide-resonator coupling,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 62(55 Pt B), 7389–7404 (2000).
[CrossRef] [PubMed]

Lines, M. E.

A. D. Yablon, M. F. Yan, P. Wisk, F. V. DiMarcello, J. W. Fleming, W. A. Reed, E. M. Monberg, D. J. DiGiovanni, J. Jasapara, and M. E. Lines, “Refractive index perturbations in optical fibers resulting from frozen-in viscoelasticity,” Appl. Phys. Lett. 84(1), 19–21 (2004).
[CrossRef]

Liu, X.

M. Sumetsky, D. J. DiGiovanni, Y. Dulashko, J. M. Fini, X. Liu, E. M. Monberg, and T. F. Taunay, “Surface nanoscale axial photonics: robust fabrication of high quality factor microresonators,” Opt. Lett. (to be published).

Maleki, L.

Manolatou, C.

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, M. Khan, C. Manolatou, and H. Haus, “Theoretical analysis of channel drop tunneling processes,” Phys. Rev. B 59(24), 15882–15892 (1999).
[CrossRef]

Matsko, A. B.

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

A. A. Savchenkov, I. S. Grudinin, A. B. Matsko, D. Strekalov, M. Mohageg, V. S. Ilchenko, and L. Maleki, “Morphology-dependent photonic circuit elements,” Opt. Lett. 31(9), 1313–1315 (2006).
[CrossRef] [PubMed]

Melloni, A.

A. Melloni, A. Canciamilla, C. Ferrari, F. Morichetti, L. O'Faolain, T. F. Krauss, R. De La Rue, A. Samarelli, and M. Sorel, “Tunable delay lines in silicon photonics: coupled resonators and photonic crystals, a comparison,” IEEE Photonics J. 2(2), 181–194 (2010).
[CrossRef]

Mohageg, M.

Monberg, E. M.

A. D. Yablon, M. F. Yan, P. Wisk, F. V. DiMarcello, J. W. Fleming, W. A. Reed, E. M. Monberg, D. J. DiGiovanni, J. Jasapara, and M. E. Lines, “Refractive index perturbations in optical fibers resulting from frozen-in viscoelasticity,” Appl. Phys. Lett. 84(1), 19–21 (2004).
[CrossRef]

M. Sumetsky, D. J. DiGiovanni, Y. Dulashko, J. M. Fini, X. Liu, E. M. Monberg, and T. F. Taunay, “Surface nanoscale axial photonics: robust fabrication of high quality factor microresonators,” Opt. Lett. (to be published).

Morichetti, F.

A. Melloni, A. Canciamilla, C. Ferrari, F. Morichetti, L. O'Faolain, T. F. Krauss, R. De La Rue, A. Samarelli, and M. Sorel, “Tunable delay lines in silicon photonics: coupled resonators and photonic crystals, a comparison,” IEEE Photonics J. 2(2), 181–194 (2010).
[CrossRef]

Notomi, M.

M. Notomi, “Manipulating light with strongly modulated photonic crystals,” Rep. Prog. Phys. 73(9), 096501 (2010).
[CrossRef]

M. Notomi, E. Kuramochi, and T. Tanabe, “Large-scale arrays of ultrahigh-Q coupled nanocavities,” Nat. Photonics 2(12), 741–747 (2008).
[CrossRef]

O'Faolain, L.

A. Melloni, A. Canciamilla, C. Ferrari, F. Morichetti, L. O'Faolain, T. F. Krauss, R. De La Rue, A. Samarelli, and M. Sorel, “Tunable delay lines in silicon photonics: coupled resonators and photonic crystals, a comparison,” IEEE Photonics J. 2(2), 181–194 (2010).
[CrossRef]

Okamoto, K.

Olitzky, J. D.

U. K. Khankhoje, S.-H. Kim, B. C. Richards, J. Hendrickson, J. Sweet, J. D. Olitzky, G. Khitrova, H. M. Gibbs, and A. Scherer, “Modelling and fabrication of GaAs photonic-crystal cavities for cavity quantum electrodynamics,” Nanotechnology 21(6), 065202 (2010).
[CrossRef] [PubMed]

Oraevsky, A. N.

A. N. Oraevsky, “Whispering-gallery waves,” Quantum Electron. 32(5), 377–400 (2002).
[CrossRef]

Rayleigh, L.

L. Rayleigh, “The problem of the whispering gallery,” Philos. Mag. 20, 1001–1004 (1910).

Reed, W. A.

A. D. Yablon, M. F. Yan, P. Wisk, F. V. DiMarcello, J. W. Fleming, W. A. Reed, E. M. Monberg, D. J. DiGiovanni, J. Jasapara, and M. E. Lines, “Refractive index perturbations in optical fibers resulting from frozen-in viscoelasticity,” Appl. Phys. Lett. 84(1), 19–21 (2004).
[CrossRef]

Richards, B. C.

U. K. Khankhoje, S.-H. Kim, B. C. Richards, J. Hendrickson, J. Sweet, J. D. Olitzky, G. Khitrova, H. M. Gibbs, and A. Scherer, “Modelling and fabrication of GaAs photonic-crystal cavities for cavity quantum electrodynamics,” Nanotechnology 21(6), 065202 (2010).
[CrossRef] [PubMed]

Samarelli, A.

A. Melloni, A. Canciamilla, C. Ferrari, F. Morichetti, L. O'Faolain, T. F. Krauss, R. De La Rue, A. Samarelli, and M. Sorel, “Tunable delay lines in silicon photonics: coupled resonators and photonic crystals, a comparison,” IEEE Photonics J. 2(2), 181–194 (2010).
[CrossRef]

Saunders, J. B.

A. Q. Tool, L. W. Tilton, and J. B. Saunders, “Changes caused in the refractivity and density of glass by annealing,” J Res Natl Bur Stand (1934) 38(5), 519–526 (1947).
[PubMed]

Savchenkov, A. A.

Scherer, A.

U. K. Khankhoje, S.-H. Kim, B. C. Richards, J. Hendrickson, J. Sweet, J. D. Olitzky, G. Khitrova, H. M. Gibbs, and A. Scherer, “Modelling and fabrication of GaAs photonic-crystal cavities for cavity quantum electrodynamics,” Nanotechnology 21(6), 065202 (2010).
[CrossRef] [PubMed]

Sekaric, L.

F. N. Xia, L. Sekaric, and Y. Vlasov, “Ultracompact optical buffers on a silicon chip,” Nat. Photonics 1(1), 65–71 (2007).
[CrossRef]

Selvaraja, S. K.

W. Bogaerts, S. K. Selvaraja, P. Dumon, J. Brouckaert, K. De Vos, D. Van Thourhout, and R. Baets, “Silicon-on-insulator spectral filters fabricated with CMOS technology,” IEEE J. Sel. Top. Quantum Electron. 16(1), 33–44 (2010).
[CrossRef]

Sorel, M.

A. Melloni, A. Canciamilla, C. Ferrari, F. Morichetti, L. O'Faolain, T. F. Krauss, R. De La Rue, A. Samarelli, and M. Sorel, “Tunable delay lines in silicon photonics: coupled resonators and photonic crystals, a comparison,” IEEE Photonics J. 2(2), 181–194 (2010).
[CrossRef]

Strekalov, D.

Sumetsky, M.

Sweet, J.

U. K. Khankhoje, S.-H. Kim, B. C. Richards, J. Hendrickson, J. Sweet, J. D. Olitzky, G. Khitrova, H. M. Gibbs, and A. Scherer, “Modelling and fabrication of GaAs photonic-crystal cavities for cavity quantum electrodynamics,” Nanotechnology 21(6), 065202 (2010).
[CrossRef] [PubMed]

Tanabe, T.

M. Notomi, E. Kuramochi, and T. Tanabe, “Large-scale arrays of ultrahigh-Q coupled nanocavities,” Nat. Photonics 2(12), 741–747 (2008).
[CrossRef]

Taunay, T. F.

M. Sumetsky, D. J. DiGiovanni, Y. Dulashko, J. M. Fini, X. Liu, E. M. Monberg, and T. F. Taunay, “Surface nanoscale axial photonics: robust fabrication of high quality factor microresonators,” Opt. Lett. (to be published).

Tilton, L. W.

A. Q. Tool, L. W. Tilton, and J. B. Saunders, “Changes caused in the refractivity and density of glass by annealing,” J Res Natl Bur Stand (1934) 38(5), 519–526 (1947).
[PubMed]

Tool, A. Q.

A. Q. Tool, L. W. Tilton, and J. B. Saunders, “Changes caused in the refractivity and density of glass by annealing,” J Res Natl Bur Stand (1934) 38(5), 519–526 (1947).
[PubMed]

Vahala, K. J.

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

Van Thourhout, D.

W. Bogaerts, S. K. Selvaraja, P. Dumon, J. Brouckaert, K. De Vos, D. Van Thourhout, and R. Baets, “Silicon-on-insulator spectral filters fabricated with CMOS technology,” IEEE J. Sel. Top. Quantum Electron. 16(1), 33–44 (2010).
[CrossRef]

Villeneuve, P. R.

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, M. Khan, C. Manolatou, and H. Haus, “Theoretical analysis of channel drop tunneling processes,” Phys. Rev. B 59(24), 15882–15892 (1999).
[CrossRef]

Vlasov, Y.

Y. Vlasov, W. M. J. Green, and F. Xia, “High-throughput silicon nanophotonic wavelength-insensitive switch for on-chip optical networks,” Nat. Photonics 2(4), 242–246 (2008).
[CrossRef]

F. N. Xia, L. Sekaric, and Y. Vlasov, “Ultracompact optical buffers on a silicon chip,” Nat. Photonics 1(1), 65–71 (2007).
[CrossRef]

Wisk, P.

A. D. Yablon, M. F. Yan, P. Wisk, F. V. DiMarcello, J. W. Fleming, W. A. Reed, E. M. Monberg, D. J. DiGiovanni, J. Jasapara, and M. E. Lines, “Refractive index perturbations in optical fibers resulting from frozen-in viscoelasticity,” Appl. Phys. Lett. 84(1), 19–21 (2004).
[CrossRef]

Xia, F.

Y. Vlasov, W. M. J. Green, and F. Xia, “High-throughput silicon nanophotonic wavelength-insensitive switch for on-chip optical networks,” Nat. Photonics 2(4), 242–246 (2008).
[CrossRef]

Xia, F. N.

F. N. Xia, L. Sekaric, and Y. Vlasov, “Ultracompact optical buffers on a silicon chip,” Nat. Photonics 1(1), 65–71 (2007).
[CrossRef]

Xu, Y.

Y. Xu, Y. Li, R. K. Lee, and A. Yariv, “Scattering-theory analysis of waveguide-resonator coupling,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 62(55 Pt B), 7389–7404 (2000).
[CrossRef] [PubMed]

Yablon, A. D.

A. D. Yablon, M. F. Yan, P. Wisk, F. V. DiMarcello, J. W. Fleming, W. A. Reed, E. M. Monberg, D. J. DiGiovanni, J. Jasapara, and M. E. Lines, “Refractive index perturbations in optical fibers resulting from frozen-in viscoelasticity,” Appl. Phys. Lett. 84(1), 19–21 (2004).
[CrossRef]

Yan, M. F.

A. D. Yablon, M. F. Yan, P. Wisk, F. V. DiMarcello, J. W. Fleming, W. A. Reed, E. M. Monberg, D. J. DiGiovanni, J. Jasapara, and M. E. Lines, “Refractive index perturbations in optical fibers resulting from frozen-in viscoelasticity,” Appl. Phys. Lett. 84(1), 19–21 (2004).
[CrossRef]

Yariv, A.

Y. Xu, Y. Li, R. K. Lee, and A. Yariv, “Scattering-theory analysis of waveguide-resonator coupling,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 62(55 Pt B), 7389–7404 (2000).
[CrossRef] [PubMed]

Appl. Phys. Lett.

A. D. Yablon, M. F. Yan, P. Wisk, F. V. DiMarcello, J. W. Fleming, W. A. Reed, E. M. Monberg, D. J. DiGiovanni, J. Jasapara, and M. E. Lines, “Refractive index perturbations in optical fibers resulting from frozen-in viscoelasticity,” Appl. Phys. Lett. 84(1), 19–21 (2004).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

W. Bogaerts, S. K. Selvaraja, P. Dumon, J. Brouckaert, K. De Vos, D. Van Thourhout, and R. Baets, “Silicon-on-insulator spectral filters fabricated with CMOS technology,” IEEE J. Sel. Top. Quantum Electron. 16(1), 33–44 (2010).
[CrossRef]

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

IEEE Photon. Technol. Lett.

T. A. Birks, J. C. Knight, and T. E. Dimmick, “High-resolution measurement of the fiber diameter variations using whispering gallery modes and no optical alignment,” IEEE Photon. Technol. Lett. 12(2), 182–183 (2000).
[CrossRef]

IEEE Photonics J.

A. Melloni, A. Canciamilla, C. Ferrari, F. Morichetti, L. O'Faolain, T. F. Krauss, R. De La Rue, A. Samarelli, and M. Sorel, “Tunable delay lines in silicon photonics: coupled resonators and photonic crystals, a comparison,” IEEE Photonics J. 2(2), 181–194 (2010).
[CrossRef]

J Res Natl Bur Stand (1934)

A. Q. Tool, L. W. Tilton, and J. B. Saunders, “Changes caused in the refractivity and density of glass by annealing,” J Res Natl Bur Stand (1934) 38(5), 519–526 (1947).
[PubMed]

J. Lightwave Technol.

Nanotechnology

U. K. Khankhoje, S.-H. Kim, B. C. Richards, J. Hendrickson, J. Sweet, J. D. Olitzky, G. Khitrova, H. M. Gibbs, and A. Scherer, “Modelling and fabrication of GaAs photonic-crystal cavities for cavity quantum electrodynamics,” Nanotechnology 21(6), 065202 (2010).
[CrossRef] [PubMed]

Nat. Photonics

F. N. Xia, L. Sekaric, and Y. Vlasov, “Ultracompact optical buffers on a silicon chip,” Nat. Photonics 1(1), 65–71 (2007).
[CrossRef]

Y. Vlasov, W. M. J. Green, and F. Xia, “High-throughput silicon nanophotonic wavelength-insensitive switch for on-chip optical networks,” Nat. Photonics 2(4), 242–246 (2008).
[CrossRef]

M. Notomi, E. Kuramochi, and T. Tanabe, “Large-scale arrays of ultrahigh-Q coupled nanocavities,” Nat. Photonics 2(12), 741–747 (2008).
[CrossRef]

T. Baba, “Slow light in photonic crystals,” Nat. Photonics 2(8), 465–473 (2008).
[CrossRef]

Nature

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

Opt. Express

Opt. Lett.

Philos. Mag.

L. Rayleigh, “The problem of the whispering gallery,” Philos. Mag. 20, 1001–1004 (1910).

Phys. Rev. B

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, M. Khan, C. Manolatou, and H. Haus, “Theoretical analysis of channel drop tunneling processes,” Phys. Rev. B 59(24), 15882–15892 (1999).
[CrossRef]

Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics

Y. Xu, Y. Li, R. K. Lee, and A. Yariv, “Scattering-theory analysis of waveguide-resonator coupling,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 62(55 Pt B), 7389–7404 (2000).
[CrossRef] [PubMed]

Quantum Electron.

A. N. Oraevsky, “Whispering-gallery waves,” Quantum Electron. 32(5), 377–400 (2002).
[CrossRef]

Rep. Prog. Phys.

M. Notomi, “Manipulating light with strongly modulated photonic crystals,” Rep. Prog. Phys. 73(9), 096501 (2010).
[CrossRef]

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J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton University Press, 2008).

M. Sumetsky, “Localization of light in an optical fiber with nanoscale radius variation,” in CLEO/Europe and EQEC 2011 Conference Digest, OSA Technical Digest (CD) (Optical Society of America, 2011), Postdeadline Paper PDA_8.

L. D. Landau and E. M. Lifshitz, Quantum Mechanics, (Pergamon Press, 1977).

H. Bach and N. Neuroth eds, The Properties of Optical Glass (Springer Verlag, 1995).

J. W. Fleming, “Sub glass transition relaxation in optical fibers,” in Optical Fiber Communication Conference, Technical Digest (CD) (Optical Society of America, 2004), paper TuB2.

R. P. Feynman and A. R. Hibbs, Quantum Mechanics and Path Integrals (McGraw-Hill, New York, 1965).

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Figures (4)

Fig. 1
Fig. 1

Illustration of a SNAP device. The whispering gallery modes (WGMs) are excited in the SNAP fiber with a transverse microfiber (MF) connected to the light source and detector. The nanoscale variation of the effective radius of this fiber determines the distribution of slow WGMs along the fiber surface and also the spectrum of light transmitted through the MF.

Fig. 2
Fig. 2

Basic elements of a SNAP device. (a) – MF coupling to a bottle microresonator. Slow WGMs excited by the MF can be trapped in the quantum well formed by the nanoscale variation of the effective fiber radius. (b) – MF coupling to the neck of the fiber. In this case, variation of the fiber radius forms a potential barrier. (c) – MF in the region of monotonic variation of the fiber radius. In this case, the WGMs emitted by the MF are reflected from the turning point and, under certain conditions, can be completely halted by the MF source.

Fig. 3
Fig. 3

Experimental characterization of the nanoscale effective radius variation and spectra of the fabricated bottle microresonators with a neck. (a) – Illustration of a bottle microresonator with a neck; (b), (d), and (f) – Resonant transmission spectra measured for the MF positions along the SNAP fiber spaced by 20 μm for the microresonator with multiple, three, and one axial state, respectively; (c), (e), and (g) – radius variation of the SNAP fiber in cases (b), (d), and (f).

Fig. 4
Fig. 4

Experimental demonstration of the effect of full localization of light between a turning point and a point contact of a SNAP fiber with an MF. (a) – Illustration of the localized WGM field distribution excited by MF1 and scanned by MF2. (b) – Experimental resonance spectra along the SNAP fiber for the MF positions spaced by 100 μm (white curves) compared with theoretically found resonance spectra (blue curves). (c) – Radius variation of the SNAP fiber found from spectra in Fig. 4(b); (d) – Resonant transmission spectra measured for the MF2 positions along the SNAP fiber spaced by 20 μm and MF1 positioned at 240 μm from the minimum of the fiber radius; (f) – Surface plot of the theoretically calculated WGM field distribution as a function of the distance along the SNAP fiber and wavelength for the experimental radius variation found from Fig. 4(c).

Equations (46)

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d 2 A d z 2 + β 2 (λ,z)A=0, β 2 (λ,z)=E(λ)V(z), E(λ)=2 β 0 2 ( λ res ) λ λ res i γ res λ res ,V(z)=2 β 0 2 ( λ res )( Δr(z) r 0 + Δ n f (z) n f0 ),
Δ r eff (z)= r 0 Δ n f (z)+ n f0 Δr(z)
Λ(λ, z 1 ,z)=CG(λ, z 1 ,z).
T(λ, z 1 )=1i|C | 2 G(λ, z 1 , z 1 ).
( F 1m (U)+ F 2m (W) )( F 1m (U)+ n 0 2 n f 2 F 2m (W) )= ( mβ k n f ) 2 ( V UW ) 4 ,
F 1m (x)= 1 x J m (x) d J m (x) dx , F 2m (x)= 1 x H m (2) (x) d H m (2) (x) dx
U= r 0 ( k 2 n f 2 β 2 ) 1/2 ,W= r 0 ( k 2 n 0 2 β 2 ) 1/2 ,V=k r 0 ( n f 2 n 0 2 ) 1/2 ,k=2π/λ.
F 1m ( U 0 )+ F 2m ( W 0 )=0 ( TE modes )
F 1m ( U 0 )+ n 0 2 n f 2 F 2m ( W 0 )=0 ( TM modes )
U 0 = n f k r 0 , W 0 = n 0 k r 0 .
λ mp (0),± λ m (0) [ 1+ ζ p 2 1/3 m 2 /3 + n 0 m ( n f 2 n 0 2 ) 1/2 ( n f n 0 ) ±1 ], λ m (0) = 2π n f r 0 m ,
λ m (0) = ( λ m (0) ) 2 2π n f r 0 ,
β 2 =2 ( 2π n f λ res ) 2 [ Δr r 0 + Δ n f n f0 Δλ λ res ].
Ψ c (r)= A m,p,q (z) Ξ m,p (ρ) Φ m (φ)
V c,k = C m,p A m,p,q ( z 1 ), C m,p = Ξ m,p Φ m |V|k.
| Ψ tot =|k+ ( E k H 0 +iε) 1 V| Ψ tot =T|k,
T c,k = V c,k E k E c +i Γ c
Ψ TF (r)= c Ψ tot |c Ψ c (r)= c T c,k Ψ c (r)
Ψ TF (r)= c Ψ tot |c Ψ c (r) = m,p,q C m,p A m,p,q ( z 1 ) A m,p,q (z) E k E c +i Γ c Ξ m,p (ρ) Φ m (φ) = m,p C m,p G m,p (λ,z, z 1 ) Ξ m,p (ρ) Φ m (φ) ,
Ψ TF (r) | λ λ mp C m,p G m,p (λ,z, z 1 ) Ξ m,p (ρ) Φ m (φ)
T(λ, z 1 )=1i c | V c,k | 2 E k E c +i Γ c .
T(λ, z 1 )=1i c | C m,p | 2 G m,p (λ,z, z 1 )
T(λ, z 1 ) | λ λ mp 1i| C m,p | 2 G m,p (λ,z, z 1 ),
G(λ, z 1 , z 2 )= 1 2i β 1/2 (λ, z 1 ) β 1/2 (λ, z 2 ) exp( i z < z > β(λ,z)dz ), z < =min( z 1 , z 2 ), z > =max( z 1 , z 2 ),
T(λ)=1 |C | 2 2β(λ, z 1 )
β(λ,z)= β 0 (λ)=πn (2/ λ res ) 3/2 ( λ res +i γ res λ) 1/2
Λ(λ, z 1 ,z)= C 2i β 0 (λ) exp( i β 0 (λ)|z z 1 | ),
T(λ, z 1 )= T 0 (λ)=1 |C | 2 2 β 0 (λ) .
P(λ, z 1 )=| T 0 (λ) | 2 =1|C | 2 Re( β 0 (λ) 1 ) =1 |C | 2 λ res 3/2 { [ (λ λ res ) 2 + γ res 2 ] 1/2 + λ res λ} 1/2 4π n f [ (λ λ res ) 2 + γ res 2 ] 1/2
G(λ, z 1 ,z)= Cexp( iφ(λ, z t , z 1 ) 3πi 4 ) β 1/2 (λ, z 1 ) β 1/2 (λ,z) { 1 2 exp( |φ(λ, z t ,z)| ), z< z t , cos( φ(λ, z t ,z) π 4 ), z t <z< z 1 1 2 cos( φ(λ, z t , z 1 ) π 4 )exp( iφ(λ, z 1 ,z) ), z> z 1 , ,
φ(λ, z 1 ,z)= z 1 z β(λ,z)dz .
z t z 1 β(λ,z)dz = 3π 4 +πn
T(λ, z 1 )=1i|C | 2 cos(φ(λ, z t1 , z 1 )+ π 4 )cos(φ(λ, z 1 , z t2 )+ π 4 ) 2β(λ, z 1 )cos(φ(λ, z t1 , z t2 )) ,
z t1 z t2 β(λ,z)dz = π 2 +πn.
T(λ, z 1 )=1 i|C | 2 cos 2 (φ(λ, z t1 , z 1 )+ π 4 ) 2β(λ, z 1 )χ(λ, z 1 )[(λ λ n )i γ res ] , χ(λ, z 1 )= z t1 z t2 β(λ, z 1 ) λ | λ= λ n dz.
T(λ, z 1 )= (λ λ n )i( γ p γ c ) (λ λ n )i( γ p + γ c ) ,
γ c = |C | 2 cos 2 (φ(λ, z t1 , z 1 )+ π 4 ) 4β(λ, z 1 )χ(λ, z 1 )
γ c (max) = 2 1/2 n f |C | 2 β 0 5/2 (R r 0 ) 1/4 (n+ 1 2 ) 1/2 .
r eff (z)= r 0 + (z z 0 ) 2 2R ,
G(λ, z 1 , z 2 )= δ z 0 2 3/2 π 1/2 0 dx [sinh(σx)] 1/2 ×exp{ iπ 4 i Δλ ¯ σx+ i 2sinh(σx) [ cosh(σx)( z ¯ 1 2 + z ¯ 2 2 )2 z ¯ 1 z ¯ 2 ] },
z ¯ j = z j /δ z 0 and Δλ ¯ =(λ λ res )/δ λ 0
δ z 0 = ( λ res /2π n eff ) 1/2 ( r 0 R) 1/4 and δ λ 0 = λ res 2 ( r 0 R) 1/2 /2π n eff
Ψ mpq (z,ρ,φ)=exp[ 1 2 ( 2 β 0 2 r 0 R ) 1/2 z 2 ] H q [ ( 2 β 0 2 r 0 R ) 1/4 z ]Ai[ ( 2 β 0 2 r 0 ) 1/3 ( r 0 ρ) t p ]exp(imφ)
Δ r eff ( z 1 )=( λ Turn ( z 1 ) λ res ) r 0 / λ res
Δ r eff ( z 1 )=( λ Peak ( z 1 ) λ res ) r 0 / λ res
Δ r eff ( z 1 )=( λ MainPeak ( z 1 ) λ res ) r 0 / λ res

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