Abstract

Single photon emitters coupled to optical fibers are becoming important as sources of non-classical light and nano-scale sensors. At present it is not possible to efficiently interface single photon emitters with the optical fiber platform, and there are particular challenges associated with the need to ensure highly efficient collection and delivery of emitted photons. To model single particle emission, we have considered the coupling of a dipole to an optical fiber mode as a function of orientation and position with respect to the core-cladding interface. Our model shows that it is possible to significantly enhance the collection efficiency into the guided modes as a result of modifications to the dipole emission pattern and power resulting from the surrounding fiber environment. For certain geometries the fiber-dipole coupling can result in a factor of 2.6 increase in the power emitted by the dipole.

© 2011 OSA

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  1. I. Aharonovich, S. Castelletto, D. A. Simpson, C.-H. Su, A. D. Greentree, and S. Prawer, “Diamond based single photon emitters,” Rep. Prog. Phys. 74, 076501 (2011).
    [CrossRef]
  2. S. Afshar V., S. C. Warren-Smith, and T. M. Monro, “Enhancement of fluorescence-based sensing using microstructured optical fibres,” Opt. Express 15, 17891–17901 (2007).
    [CrossRef]
  3. E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69, 681 (1946).
  4. W. Żakowicz and M. Janowicz, “Spontaneous emission in the presence of a dielectric cylinder,” Phys. Rev. A 62, 013820 (2000).
    [CrossRef]
  5. T. Søndergaard and B. Tromborg, “General theory for spontaneous emission in active dielectric microstructures: example of a fiber amplifier,” Phys. Rev. A 64, 033812 (2001).
    [CrossRef]
  6. J.-P. Hermier, M. Dahan, X. Brokmann, and L. Coolen, “Emission properties of single CdSe/ZnS quantum dots close to a dielectric interface,” Chem. Phys. 318, 91–98 (2005).
    [CrossRef]
  7. P. Anger, P. Bharadwaj, and L. Novotny, “Enhancement and quenching of single-molecule fluorescence,” Phys. Rev. Lett. 96, 113002 (2006).
    [CrossRef] [PubMed]
  8. I.-K. Hwang, S.-K. Kim, J.-K. Yang, S.-H. Kim, S. H. Lee, and Y.-H. Lee, “Curved-microfiber photon coupling for photonic crystal light emitter,” Appl. Phys. Lett. 87, 131107 (2005).
    [CrossRef]
  9. K.-M. C. Fu, P. E. Barclay, C. Santori, A. Faraon, and R. G. Beausoleil, “Low-temperature tapered-fiber probing of diamond nitrogen-vacancy ensembles coupled to GaP microcavities,” New J. Phys. 13, 055023 (2011).
    [CrossRef]
  10. D. D. Awschalom, R. Epstein, and R. Hanson, “The diamond age of spintronics,” Sci. Am. 297, 84–91 (2007).
    [CrossRef] [PubMed]
  11. H. Benisty, H. De Neve, and C. Weisbuch, “Impact of planar microcavity effects on light extraction — part I: basic concepts and analytical trends,” IEEE J. Quantum Electron. 34, 1612–1631 (1998).
    [CrossRef]
  12. M. R. Henderson, B. C. Gibson, H. Ebendorff-Heidepriem, K. Kuan, S. Afshar V., J. O. Orwa, I. Aharonovich, S. Tomljenovic-Hanic, A. D. Greentree, S. Prawer, and T. M. Monro, “Diamond in tellurite glass: a new medium for quantum information,” Adv. Mater. 23, 2806–2810 (2011).
    [CrossRef] [PubMed]
  13. T. M. Babinec, B. J. M. Hausmann, M. Khan, Y. Zhang, J. R. Maze, P. R. Hemmer, and M. Loncar, “A diamond nanowire single-photon source,” Nat. Nanotechnol. 5, 195–199 (2010).
    [CrossRef] [PubMed]
  14. A. Faraon, P. E. Barclay, C. Santori, K.-M. C. Fu, and R. G. Beausoleil, “Resonant enhancement of the zero-phonon emission from a colour centre in a diamond cavity,” Nat. Photonics 5, 301–305 (2011).
    [CrossRef]
  15. P. Siyushev, F. Kaiser, V. Jacques, I. Gerhardt, S. Bischof, H. Fedder, J. Dodson, M. Markham, D. Twitchen, F. Jelezko, and J. Wrachtrup, “Monolithic diamond optics for single photon detection,” Appl. Phys. Lett. 97, 241902 (2010).
    [CrossRef]
  16. T. Schröder, F. Gädeke, M. J. Banholzer, and O. Benson, “Ultra-bright and efficient single photon generation based on n-v centres in nanodiamonds on a solid immersion lens,” New J. Phys. 13, 055017 (2011).
    [CrossRef]
  17. L. Marseglia, J. P. Hadden, A. C. Stanley-Clarke, J. P. Harrison, B. Patton, Y.-L. D. Ho, B. Naydenov, F. Jelezko, J. Meijer, P. R. Dolan, J. M. Smith, J. G. Rarity, and J. L. O’Brien, “Nano-fabricated solid immersion lenses registered to single emitters in diamond,” Appl. Phys. Lett. 98, 189902 (2011).
  18. P. E. Barclay, C. Santori, K.-M. Fu, R. G. Beausoleil, and O. Painter, “Coherent interference effects in a nano-assembled diamond NV center cavity-QED system,” Opt. Express 17, 8081–8097 (2009).
    [CrossRef] [PubMed]
  19. D. Englund, B. Shields, K. Rivoire, F. Hatami, J. Vučković, H. Park, and M. D. Lukin, “Deterministic coupling of a single nitrogen vacancy center to a photonic crystal cavity,” Nano Lett. 10, 3922–3926 (2010).
    [CrossRef] [PubMed]
  20. Y.-S. Park, A. K. Cook, and H. Wang, “Cavity QED with diamond nanocrystals and silica microspheres,” Nano Lett. 6, 2075–2079 (2006).
    [CrossRef] [PubMed]
  21. J. Rabeau, S. Huntington, A. Greentree, and S. Prawer, “Diamond chemical-vapor deposition on optical fibers for fluorescence waveguiding,” Appl. Phys. Lett. 86, 134104 (2005).
    [CrossRef]
  22. S. Kuhn, C. Hettich, C. Schmitt, J. Poizat, and V. Sandoghdar, “Diamond colour centres as a nanoscopic light source for scanning near-field optical microscopy,” J. Microsc. 202, 2–6 (2001).
    [CrossRef] [PubMed]
  23. E. Ampem-Lassen, D. A. Simpson, B. C. Gibson, S. Trpkovski, F. M. Hossain, S. T. Huntington, K. Ganesan, L. C. Hollenberg, and S. Prawer, “Nano-manipulation of diamond-based single photon sources,” Opt. Express 17, 11287–11293 (2009).
    [CrossRef] [PubMed]
  24. T. Schroder, A. W. Schell, G. Kewes, T. Aichele, and O. Benson, “Fiber-integrated diamond-based single photon source,” Nano Lett. 11, 198–202 (2011).
    [CrossRef]
  25. I. Aharonovich, A. D. Greentree, and S. Prawer, “Diamond photonics,” Nat. Photonics 5, 397–405 (2011).
    [CrossRef]
  26. M. R. Oermann, H. Ebendorff-Heidepriem, Y. Li, T.-C. Foo, and T. M. Monro, “Index matching between passive and active tellurite glasses for use in microstructured fiber lasers: erbium doped lanthanum-tellurite glass,” Opt. Express 17, 15578–15584 (2009).
    [CrossRef] [PubMed]
  27. T. M. Monro, S. Warren-Smith, E. P. Schartner, A. François, S. Heng, H. Ebendorff-Heidepriem, and S. Afshar V., “Sensing with suspended-core optical fibers,” Opt. Fiber Technol. 16, 343–356 (2010).
    [CrossRef]
  28. A. Snyder and J. Love, Optical Waveguide Theory (Springer, 1983).
  29. A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: a flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
    [CrossRef]

2011

K.-M. C. Fu, P. E. Barclay, C. Santori, A. Faraon, and R. G. Beausoleil, “Low-temperature tapered-fiber probing of diamond nitrogen-vacancy ensembles coupled to GaP microcavities,” New J. Phys. 13, 055023 (2011).
[CrossRef]

M. R. Henderson, B. C. Gibson, H. Ebendorff-Heidepriem, K. Kuan, S. Afshar V., J. O. Orwa, I. Aharonovich, S. Tomljenovic-Hanic, A. D. Greentree, S. Prawer, and T. M. Monro, “Diamond in tellurite glass: a new medium for quantum information,” Adv. Mater. 23, 2806–2810 (2011).
[CrossRef] [PubMed]

A. Faraon, P. E. Barclay, C. Santori, K.-M. C. Fu, and R. G. Beausoleil, “Resonant enhancement of the zero-phonon emission from a colour centre in a diamond cavity,” Nat. Photonics 5, 301–305 (2011).
[CrossRef]

I. Aharonovich, S. Castelletto, D. A. Simpson, C.-H. Su, A. D. Greentree, and S. Prawer, “Diamond based single photon emitters,” Rep. Prog. Phys. 74, 076501 (2011).
[CrossRef]

T. Schroder, A. W. Schell, G. Kewes, T. Aichele, and O. Benson, “Fiber-integrated diamond-based single photon source,” Nano Lett. 11, 198–202 (2011).
[CrossRef]

I. Aharonovich, A. D. Greentree, and S. Prawer, “Diamond photonics,” Nat. Photonics 5, 397–405 (2011).
[CrossRef]

T. Schröder, F. Gädeke, M. J. Banholzer, and O. Benson, “Ultra-bright and efficient single photon generation based on n-v centres in nanodiamonds on a solid immersion lens,” New J. Phys. 13, 055017 (2011).
[CrossRef]

2010

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: a flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[CrossRef]

T. M. Monro, S. Warren-Smith, E. P. Schartner, A. François, S. Heng, H. Ebendorff-Heidepriem, and S. Afshar V., “Sensing with suspended-core optical fibers,” Opt. Fiber Technol. 16, 343–356 (2010).
[CrossRef]

P. Siyushev, F. Kaiser, V. Jacques, I. Gerhardt, S. Bischof, H. Fedder, J. Dodson, M. Markham, D. Twitchen, F. Jelezko, and J. Wrachtrup, “Monolithic diamond optics for single photon detection,” Appl. Phys. Lett. 97, 241902 (2010).
[CrossRef]

T. M. Babinec, B. J. M. Hausmann, M. Khan, Y. Zhang, J. R. Maze, P. R. Hemmer, and M. Loncar, “A diamond nanowire single-photon source,” Nat. Nanotechnol. 5, 195–199 (2010).
[CrossRef] [PubMed]

D. Englund, B. Shields, K. Rivoire, F. Hatami, J. Vučković, H. Park, and M. D. Lukin, “Deterministic coupling of a single nitrogen vacancy center to a photonic crystal cavity,” Nano Lett. 10, 3922–3926 (2010).
[CrossRef] [PubMed]

2009

2007

2006

P. Anger, P. Bharadwaj, and L. Novotny, “Enhancement and quenching of single-molecule fluorescence,” Phys. Rev. Lett. 96, 113002 (2006).
[CrossRef] [PubMed]

Y.-S. Park, A. K. Cook, and H. Wang, “Cavity QED with diamond nanocrystals and silica microspheres,” Nano Lett. 6, 2075–2079 (2006).
[CrossRef] [PubMed]

2005

J. Rabeau, S. Huntington, A. Greentree, and S. Prawer, “Diamond chemical-vapor deposition on optical fibers for fluorescence waveguiding,” Appl. Phys. Lett. 86, 134104 (2005).
[CrossRef]

I.-K. Hwang, S.-K. Kim, J.-K. Yang, S.-H. Kim, S. H. Lee, and Y.-H. Lee, “Curved-microfiber photon coupling for photonic crystal light emitter,” Appl. Phys. Lett. 87, 131107 (2005).
[CrossRef]

J.-P. Hermier, M. Dahan, X. Brokmann, and L. Coolen, “Emission properties of single CdSe/ZnS quantum dots close to a dielectric interface,” Chem. Phys. 318, 91–98 (2005).
[CrossRef]

2001

T. Søndergaard and B. Tromborg, “General theory for spontaneous emission in active dielectric microstructures: example of a fiber amplifier,” Phys. Rev. A 64, 033812 (2001).
[CrossRef]

S. Kuhn, C. Hettich, C. Schmitt, J. Poizat, and V. Sandoghdar, “Diamond colour centres as a nanoscopic light source for scanning near-field optical microscopy,” J. Microsc. 202, 2–6 (2001).
[CrossRef] [PubMed]

2000

W. Żakowicz and M. Janowicz, “Spontaneous emission in the presence of a dielectric cylinder,” Phys. Rev. A 62, 013820 (2000).
[CrossRef]

1998

H. Benisty, H. De Neve, and C. Weisbuch, “Impact of planar microcavity effects on light extraction — part I: basic concepts and analytical trends,” IEEE J. Quantum Electron. 34, 1612–1631 (1998).
[CrossRef]

1983

A. Snyder and J. Love, Optical Waveguide Theory (Springer, 1983).

1946

E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69, 681 (1946).

1899

L. Marseglia, J. P. Hadden, A. C. Stanley-Clarke, J. P. Harrison, B. Patton, Y.-L. D. Ho, B. Naydenov, F. Jelezko, J. Meijer, P. R. Dolan, J. M. Smith, J. G. Rarity, and J. L. O’Brien, “Nano-fabricated solid immersion lenses registered to single emitters in diamond,” Appl. Phys. Lett. 98, 189902 (2011).

Afshar V., S.

M. R. Henderson, B. C. Gibson, H. Ebendorff-Heidepriem, K. Kuan, S. Afshar V., J. O. Orwa, I. Aharonovich, S. Tomljenovic-Hanic, A. D. Greentree, S. Prawer, and T. M. Monro, “Diamond in tellurite glass: a new medium for quantum information,” Adv. Mater. 23, 2806–2810 (2011).
[CrossRef] [PubMed]

T. M. Monro, S. Warren-Smith, E. P. Schartner, A. François, S. Heng, H. Ebendorff-Heidepriem, and S. Afshar V., “Sensing with suspended-core optical fibers,” Opt. Fiber Technol. 16, 343–356 (2010).
[CrossRef]

S. Afshar V., S. C. Warren-Smith, and T. M. Monro, “Enhancement of fluorescence-based sensing using microstructured optical fibres,” Opt. Express 15, 17891–17901 (2007).
[CrossRef]

Aharonovich, I.

I. Aharonovich, S. Castelletto, D. A. Simpson, C.-H. Su, A. D. Greentree, and S. Prawer, “Diamond based single photon emitters,” Rep. Prog. Phys. 74, 076501 (2011).
[CrossRef]

M. R. Henderson, B. C. Gibson, H. Ebendorff-Heidepriem, K. Kuan, S. Afshar V., J. O. Orwa, I. Aharonovich, S. Tomljenovic-Hanic, A. D. Greentree, S. Prawer, and T. M. Monro, “Diamond in tellurite glass: a new medium for quantum information,” Adv. Mater. 23, 2806–2810 (2011).
[CrossRef] [PubMed]

I. Aharonovich, A. D. Greentree, and S. Prawer, “Diamond photonics,” Nat. Photonics 5, 397–405 (2011).
[CrossRef]

Aichele, T.

T. Schroder, A. W. Schell, G. Kewes, T. Aichele, and O. Benson, “Fiber-integrated diamond-based single photon source,” Nano Lett. 11, 198–202 (2011).
[CrossRef]

Ampem-Lassen, E.

Anger, P.

P. Anger, P. Bharadwaj, and L. Novotny, “Enhancement and quenching of single-molecule fluorescence,” Phys. Rev. Lett. 96, 113002 (2006).
[CrossRef] [PubMed]

Awschalom, D. D.

D. D. Awschalom, R. Epstein, and R. Hanson, “The diamond age of spintronics,” Sci. Am. 297, 84–91 (2007).
[CrossRef] [PubMed]

Babinec, T. M.

T. M. Babinec, B. J. M. Hausmann, M. Khan, Y. Zhang, J. R. Maze, P. R. Hemmer, and M. Loncar, “A diamond nanowire single-photon source,” Nat. Nanotechnol. 5, 195–199 (2010).
[CrossRef] [PubMed]

Banholzer, M. J.

T. Schröder, F. Gädeke, M. J. Banholzer, and O. Benson, “Ultra-bright and efficient single photon generation based on n-v centres in nanodiamonds on a solid immersion lens,” New J. Phys. 13, 055017 (2011).
[CrossRef]

Barclay, P. E.

K.-M. C. Fu, P. E. Barclay, C. Santori, A. Faraon, and R. G. Beausoleil, “Low-temperature tapered-fiber probing of diamond nitrogen-vacancy ensembles coupled to GaP microcavities,” New J. Phys. 13, 055023 (2011).
[CrossRef]

A. Faraon, P. E. Barclay, C. Santori, K.-M. C. Fu, and R. G. Beausoleil, “Resonant enhancement of the zero-phonon emission from a colour centre in a diamond cavity,” Nat. Photonics 5, 301–305 (2011).
[CrossRef]

P. E. Barclay, C. Santori, K.-M. Fu, R. G. Beausoleil, and O. Painter, “Coherent interference effects in a nano-assembled diamond NV center cavity-QED system,” Opt. Express 17, 8081–8097 (2009).
[CrossRef] [PubMed]

Beausoleil, R. G.

A. Faraon, P. E. Barclay, C. Santori, K.-M. C. Fu, and R. G. Beausoleil, “Resonant enhancement of the zero-phonon emission from a colour centre in a diamond cavity,” Nat. Photonics 5, 301–305 (2011).
[CrossRef]

K.-M. C. Fu, P. E. Barclay, C. Santori, A. Faraon, and R. G. Beausoleil, “Low-temperature tapered-fiber probing of diamond nitrogen-vacancy ensembles coupled to GaP microcavities,” New J. Phys. 13, 055023 (2011).
[CrossRef]

P. E. Barclay, C. Santori, K.-M. Fu, R. G. Beausoleil, and O. Painter, “Coherent interference effects in a nano-assembled diamond NV center cavity-QED system,” Opt. Express 17, 8081–8097 (2009).
[CrossRef] [PubMed]

Benisty, H.

H. Benisty, H. De Neve, and C. Weisbuch, “Impact of planar microcavity effects on light extraction — part I: basic concepts and analytical trends,” IEEE J. Quantum Electron. 34, 1612–1631 (1998).
[CrossRef]

Benson, O.

T. Schroder, A. W. Schell, G. Kewes, T. Aichele, and O. Benson, “Fiber-integrated diamond-based single photon source,” Nano Lett. 11, 198–202 (2011).
[CrossRef]

T. Schröder, F. Gädeke, M. J. Banholzer, and O. Benson, “Ultra-bright and efficient single photon generation based on n-v centres in nanodiamonds on a solid immersion lens,” New J. Phys. 13, 055017 (2011).
[CrossRef]

Bermel, P.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: a flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181, 687–702 (2010).
[CrossRef]

Bharadwaj, P.

P. Anger, P. Bharadwaj, and L. Novotny, “Enhancement and quenching of single-molecule fluorescence,” Phys. Rev. Lett. 96, 113002 (2006).
[CrossRef] [PubMed]

Bischof, S.

P. Siyushev, F. Kaiser, V. Jacques, I. Gerhardt, S. Bischof, H. Fedder, J. Dodson, M. Markham, D. Twitchen, F. Jelezko, and J. Wrachtrup, “Monolithic diamond optics for single photon detection,” Appl. Phys. Lett. 97, 241902 (2010).
[CrossRef]

Brokmann, X.

J.-P. Hermier, M. Dahan, X. Brokmann, and L. Coolen, “Emission properties of single CdSe/ZnS quantum dots close to a dielectric interface,” Chem. Phys. 318, 91–98 (2005).
[CrossRef]

Castelletto, S.

I. Aharonovich, S. Castelletto, D. A. Simpson, C.-H. Su, A. D. Greentree, and S. Prawer, “Diamond based single photon emitters,” Rep. Prog. Phys. 74, 076501 (2011).
[CrossRef]

Cook, A. K.

Y.-S. Park, A. K. Cook, and H. Wang, “Cavity QED with diamond nanocrystals and silica microspheres,” Nano Lett. 6, 2075–2079 (2006).
[CrossRef] [PubMed]

Coolen, L.

J.-P. Hermier, M. Dahan, X. Brokmann, and L. Coolen, “Emission properties of single CdSe/ZnS quantum dots close to a dielectric interface,” Chem. Phys. 318, 91–98 (2005).
[CrossRef]

Dahan, M.

J.-P. Hermier, M. Dahan, X. Brokmann, and L. Coolen, “Emission properties of single CdSe/ZnS quantum dots close to a dielectric interface,” Chem. Phys. 318, 91–98 (2005).
[CrossRef]

De Neve, H.

H. Benisty, H. De Neve, and C. Weisbuch, “Impact of planar microcavity effects on light extraction — part I: basic concepts and analytical trends,” IEEE J. Quantum Electron. 34, 1612–1631 (1998).
[CrossRef]

Dodson, J.

P. Siyushev, F. Kaiser, V. Jacques, I. Gerhardt, S. Bischof, H. Fedder, J. Dodson, M. Markham, D. Twitchen, F. Jelezko, and J. Wrachtrup, “Monolithic diamond optics for single photon detection,” Appl. Phys. Lett. 97, 241902 (2010).
[CrossRef]

Dolan, P. R.

L. Marseglia, J. P. Hadden, A. C. Stanley-Clarke, J. P. Harrison, B. Patton, Y.-L. D. Ho, B. Naydenov, F. Jelezko, J. Meijer, P. R. Dolan, J. M. Smith, J. G. Rarity, and J. L. O’Brien, “Nano-fabricated solid immersion lenses registered to single emitters in diamond,” Appl. Phys. Lett. 98, 189902 (2011).

Ebendorff-Heidepriem, H.

M. R. Henderson, B. C. Gibson, H. Ebendorff-Heidepriem, K. Kuan, S. Afshar V., J. O. Orwa, I. Aharonovich, S. Tomljenovic-Hanic, A. D. Greentree, S. Prawer, and T. M. Monro, “Diamond in tellurite glass: a new medium for quantum information,” Adv. Mater. 23, 2806–2810 (2011).
[CrossRef] [PubMed]

T. M. Monro, S. Warren-Smith, E. P. Schartner, A. François, S. Heng, H. Ebendorff-Heidepriem, and S. Afshar V., “Sensing with suspended-core optical fibers,” Opt. Fiber Technol. 16, 343–356 (2010).
[CrossRef]

M. R. Oermann, H. Ebendorff-Heidepriem, Y. Li, T.-C. Foo, and T. M. Monro, “Index matching between passive and active tellurite glasses for use in microstructured fiber lasers: erbium doped lanthanum-tellurite glass,” Opt. Express 17, 15578–15584 (2009).
[CrossRef] [PubMed]

Englund, D.

D. Englund, B. Shields, K. Rivoire, F. Hatami, J. Vučković, H. Park, and M. D. Lukin, “Deterministic coupling of a single nitrogen vacancy center to a photonic crystal cavity,” Nano Lett. 10, 3922–3926 (2010).
[CrossRef] [PubMed]

Epstein, R.

D. D. Awschalom, R. Epstein, and R. Hanson, “The diamond age of spintronics,” Sci. Am. 297, 84–91 (2007).
[CrossRef] [PubMed]

Faraon, A.

K.-M. C. Fu, P. E. Barclay, C. Santori, A. Faraon, and R. G. Beausoleil, “Low-temperature tapered-fiber probing of diamond nitrogen-vacancy ensembles coupled to GaP microcavities,” New J. Phys. 13, 055023 (2011).
[CrossRef]

A. Faraon, P. E. Barclay, C. Santori, K.-M. C. Fu, and R. G. Beausoleil, “Resonant enhancement of the zero-phonon emission from a colour centre in a diamond cavity,” Nat. Photonics 5, 301–305 (2011).
[CrossRef]

Fedder, H.

P. Siyushev, F. Kaiser, V. Jacques, I. Gerhardt, S. Bischof, H. Fedder, J. Dodson, M. Markham, D. Twitchen, F. Jelezko, and J. Wrachtrup, “Monolithic diamond optics for single photon detection,” Appl. Phys. Lett. 97, 241902 (2010).
[CrossRef]

Foo, T.-C.

François, A.

T. M. Monro, S. Warren-Smith, E. P. Schartner, A. François, S. Heng, H. Ebendorff-Heidepriem, and S. Afshar V., “Sensing with suspended-core optical fibers,” Opt. Fiber Technol. 16, 343–356 (2010).
[CrossRef]

Fu, K.-M.

Fu, K.-M. C.

A. Faraon, P. E. Barclay, C. Santori, K.-M. C. Fu, and R. G. Beausoleil, “Resonant enhancement of the zero-phonon emission from a colour centre in a diamond cavity,” Nat. Photonics 5, 301–305 (2011).
[CrossRef]

K.-M. C. Fu, P. E. Barclay, C. Santori, A. Faraon, and R. G. Beausoleil, “Low-temperature tapered-fiber probing of diamond nitrogen-vacancy ensembles coupled to GaP microcavities,” New J. Phys. 13, 055023 (2011).
[CrossRef]

Gädeke, F.

T. Schröder, F. Gädeke, M. J. Banholzer, and O. Benson, “Ultra-bright and efficient single photon generation based on n-v centres in nanodiamonds on a solid immersion lens,” New J. Phys. 13, 055017 (2011).
[CrossRef]

Ganesan, K.

Gerhardt, I.

P. Siyushev, F. Kaiser, V. Jacques, I. Gerhardt, S. Bischof, H. Fedder, J. Dodson, M. Markham, D. Twitchen, F. Jelezko, and J. Wrachtrup, “Monolithic diamond optics for single photon detection,” Appl. Phys. Lett. 97, 241902 (2010).
[CrossRef]

Gibson, B. C.

M. R. Henderson, B. C. Gibson, H. Ebendorff-Heidepriem, K. Kuan, S. Afshar V., J. O. Orwa, I. Aharonovich, S. Tomljenovic-Hanic, A. D. Greentree, S. Prawer, and T. M. Monro, “Diamond in tellurite glass: a new medium for quantum information,” Adv. Mater. 23, 2806–2810 (2011).
[CrossRef] [PubMed]

E. Ampem-Lassen, D. A. Simpson, B. C. Gibson, S. Trpkovski, F. M. Hossain, S. T. Huntington, K. Ganesan, L. C. Hollenberg, and S. Prawer, “Nano-manipulation of diamond-based single photon sources,” Opt. Express 17, 11287–11293 (2009).
[CrossRef] [PubMed]

Greentree, A.

J. Rabeau, S. Huntington, A. Greentree, and S. Prawer, “Diamond chemical-vapor deposition on optical fibers for fluorescence waveguiding,” Appl. Phys. Lett. 86, 134104 (2005).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Schematic of the modelling system.

Fig. 2
Fig. 2

(a) Power emitted by dipole vs. core diameter for a tellurite (n = 2.025) core fiber with an air cladding. A radially oriented dipole emitting at a wavelength of 700nm is located in the core center (red line) and alternately on the cladding side (blue line) of the core-cladding interface. Black dots show the comparison of data calculated using expressions in this paper to that obtained via the finite-difference time domain (FDTD) method. Power has been normalized to the power in a bulk material of the same index. The power oscillates above and below the bulk emitted power from changes in the interference condition due to the varying core diameter. (b) Total power vs. FDTD resolution showing convergence of FDTD solution for 0.4 μm core diameter fiber. Resolution is number of sampling points per wavelength (700 nm).

Fig. 3
Fig. 3

Power captured into the fiber guided modes vs. core diameter for a tellurite core fiber in air cladding with a dipole emitting at a wavelength of 700nm in the core center and also on the cladding side of the core-cladding interface. Power is normalized to the total power emitted by the dipole in a bulk (homogeneous) diamond material. (a) Radially () oriented dipole. (b) Azimuthally ( θ ^ ) oriented dipole. (c) longitudinally () oriented dipole. For most core diameters and dipole orientations the power captured into the guided modes of the fiber is greater than 20% of the power emitted in bulk diamond. For a specific orientation and core diameter (radial dipole at 0.22 μm) the captured power can be greater than the total power emitted in bulk diamond. Note that at the center of the core the radial and azimuthal orientations are equivalent.

Fig. 4
Fig. 4

Power vs. core diameter for an air-clad step index fiber with three different core materials: F2, SF57 and tellurite (n = 1.61, 1.83 and 2.02 respectively at 700 nm). (a) Total power and (b) guided power for a dipole positioned at the core center. (c) Total power and (d) guided power for a dipole positioned on the cladding side of the core-cladding interface. The dipole is radially oriented and emitting at a wavelength of 700nm. Power is normalized to the total power emitted by the dipole in a bulk (homogeneous) diamond material. As might be expected, captured power increases as the core index is increased.

Fig. 5
Fig. 5

Plots for a tellurite core fiber in air cladding with a radially oriented dipole emitting at a wavelength of 700nm. (a) Power captured into the fiber guided modes vs. dipole radial position for a fiber with a core diameter of 0.22 μm. (b) Power captured vs. core diameter, showing the core diameter at which the previous plot was calculated. Power is normalized to the total power emitted by the dipole in a bulk (homogeneous) diamond material. The discontinuity at the core-cladding interface is due to the discontinuity of the radial field.

Tables (1)

Tables Icon

Table 1 Coefficients Appearing in Eqs. (2) and (3) for ‘TM-like’ (ITM) and ‘TE-like’ (ITE) Radiation Modes *

Equations (26)

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E = j a j ( z ) e j e i β j z + a j ( z ) e j e i β j z + radiation modes
e z = { a ν J ν ( U R ) f ν ( θ ) 0 r < r co [ c ν f J ν ( Q R ) + c ν s H ν ( 1 ) ( Q R ) ] f ν ( θ ) r co r <
h z = { b ν J ν ( U R ) g ν ( θ ) 0 r < r co [ d ν f J ν ( Q R ) + d ν s H ν ( 1 ) ( Q R ) ] g ν ( θ ) r co r <
f ν ( θ ) = { cos ( ν θ ) even modes sin ( ν θ ) odd modes
g ν ( θ ) = { sin ( ν θ ) even modes cos ( ν θ ) odd modes
Q = r co ( k 2 n cl 2 β 2 ) 1 / 2 ,
P ( r ) = j p j e i ω j t δ ( r r j )
J = P t = i ω p 0 e i ω t δ ( r r 0 )
z A F z ^ d A = A F d A
E ¯ = e j e i β j z , H ¯ = h j e i β j z , J ¯ = 0
a j = i ω 4 N j e i ω t e i β j z 0 [ e j * ( r 0 ) p 0 ( r 0 ) ]
N j = 1 2 A ( e × h * ) z ^ d A
A ( e j × h k * ) z ^ d A = A ( e j * × h k ) z ^ d A = 0 for j k
A [ e j ( Q ) × h k * ( Q ) ] . z ^ d A = A [ e j * ( Q ) × h k ( Q ) ] z ^ d A = 0 for all Q if j k , and for Q Q if j = k
P total = j P j + ν P ν ( Q ) d Q
e r = i k 2 n 2 β 2 [ β e z r + ( μ 0 ɛ 0 ) 1 2 k r h z θ ]
e θ = i k 2 n 2 β 2 [ β r e z θ ( μ 0 ɛ 0 ) 1 2 k h z r ]
e r = f ν ( θ ) k 2 n core 2 β 2 i U 2 r co { β a ν [ J ν 1 ( U R ) J ν + 1 ( U R ) ] ( μ 0 ɛ 0 ) 1 2 k b ν [ J ν 1 ( U R ) + J ν + 1 ( U R ) ] }
e θ = g ν ( ϕ ) k 2 n core 2 β 2 i U 2 r co { β a ν [ J ν 1 ( U R ) + J ν + 1 ( U R ) ] ( μ 0 ɛ 0 ) 1 2 k b ν [ J ν 1 ( U R ) J ν + 1 ( U R ) ] }
e r = f ν ( θ ) k 2 n clad 2 β 2 i Q 2 r co ( β { c ν f [ J ν 1 ( Q R ) J ν + 1 ( Q R ) ] + c ν s [ H ν 1 ( 1 ) ( Q R ) H ν + 1 ( 1 ) ( Q R ) ] } k ( μ 0 ɛ 0 ) 1 2 { d ν f [ J ν 1 ( Q R ) + J ν + 1 ( Q R ) ] + d ν s [ H ν 1 ( 1 ) ( Q R ) + H ν + 1 ( 1 ) ( Q R ) ] } )
e θ = g ν ( ϕ ) k 2 n clad 2 β 2 i Q 2 r co ( β { c ν f [ J ν 1 ( Q R ) + J ν + 1 ( Q R ) ] + c ν s [ H ν 1 ( 1 ) ( Q R ) + H ν + 1 ( 1 ) ( Q R ) ] } k ( μ 0 ɛ 0 ) 1 2 { d ν f [ J ν 1 ( Q R ) J ν + 1 ( Q R ) ] + d ν s [ H ν 1 ( 1 ) ( Q R ) H ν + 1 ( 1 ) ( Q R ) ] } )
F ν = J ν ( U ) U J ν ( U ) H ν ( 1 ) ( Q ) Q H ν ( 1 ) ( Q )
G ν = J ν ( U ) U J ν ( U ) n cl 2 n co 2 H ν ( 1 ) ( Q ) Q H ν ( 1 ) ( Q )
A ν = M ν 2 i π n cl 2 n co 2 F ν Q 2 J ν ( Q ) H ν ( 1 ) ( Q )
B ν = M ν 2 i π G ν Q 2 J ν ( Q ) H ν ( 1 ) ( Q )
M ν = ( ν β k n co ) 2 ( V U Q ) 4 F ν G ν

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