Abstract

We report on the fabrication, modeling, and experimental verification of the emission of fiber lenses fabricated on multimode fibers in different media. Concave fiber lenses with a radius of 150 μm were fabricated onto a multimode silica fiber (100 μm core) by grinding and polishing against a ruby sphere template. In our theoretical model we assume that the fiber guides light from a Lambertian light source and that the emission cone is governed solely by the range of permitted emission angles. We investigate concave and convex lenses at 532 nm with different radii and in a variety of surrounding media from air (n0=1.00) to sapphire (n0=1.77). It was found that noticeable focusing or defocusing effects of a silica fiber lens in ethanol (n0=1.36) and dimethyl sulfoxide (DMSO) (n0=1.48) are only observed when the fiber lens radius was less than the fiber diameter.

© 2013 Optical Society of America

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  1. D. Kato, “Light coupling from a stripe-geometry GaAs diode laser into an optical fiber with spherical end,” J. Appl. Phys. 44, 2756–2758 (1973).
    [CrossRef]
  2. U. C. Paek and A. L. Weaver, “Formation of a spherical lens at optical fiber ends with a CO2-laser,” Appl. Opt. 14, 294–298 (1975).
    [CrossRef]
  3. A. Hokkanen and S. Tammela, “Hemispherically ended optical fiber lenses,” Phys. Scr. T69, 159–162 (1997).
    [CrossRef]
  4. H. P. Loock, “Ring-down absorption spectroscopy for analytical microdevices,” TrAC Trends Anal. Chem. 25, 655–664 (2006).
    [CrossRef]
  5. H. Waechter, D. Munzke, A. Jang, and H. P. Loock, “Simultaneous and continuous multiple wavelength absorption spectroscopy on nanoliter volumes based on frequency-division multiplexing fiber-loop cavity ring-down spectroscopy,” Anal. Chem. 83, 2719–2725 (2011).
    [CrossRef]
  6. S. Yakunin and J. Heitz, “Microgrinding of lensed fibers by means of a scanning-probe microscope setup,” Appl. Opt. 48, 6172–6177 (2009).
    [CrossRef]
  7. D. R. Rivera, C. M. Brown, D. G. Ouzounov, W. W. Webb, and C. Xu, “Use of a lensed fiber for a large-field-of-view, high-resolution, fiber-scanning microendoscope,” Opt. Lett. 37, 881–883 (2012).
    [CrossRef]
  8. S. Cabrini, C. Liberale, D. Cojoc, A. Carpentiero, M. Prasciolu, S. Mora, V. Degiorgio, F. De Angelis, and E. Di Fabrizio, “Axicon lens on optical fiber forming optical tweezers, made by focused ion beam milling,” Microelectron. Eng. 83, 804–807 (2006).
    [CrossRef]
  9. F. Schiappelli, R. Kumar, M. Prasciolu, D. Cojoc, S. Cabrini, M. De Vittorio, G. Visimberga, A. Gerardino, V. Degiorgio, and E. Di Fabrizio, “Efficient fiber-to-waveguide coupling by a lens on the end of the optical fiber fabricated by focused ion beam milling,” Microelectron. Eng. 73–74, 397–404 (2004).
    [CrossRef]
  10. J. K. Kim, J. Kim, K. Oh, I. B. Sohn, W. Shin, H. Y. Choi, and B. Lee, “Fabrication of micro Fresnel zone plate lens on a mode-expanded hybrid optical fiber using a femtosecond laser ablation system,” IEEE Photonics Technol. Lett. 21, 21–23 (2009).
    [CrossRef]
  11. Y. L. Yu, L. Lui, H. Tam, and W. Chung, “Fiber-laser-based wavelength-division multiplexed fiber Bragg grating sensor system,” IEEE Photonics Technol. Lett. 13, 702–704 (2001).
    [CrossRef]
  12. D. Hunger, C. Deutsch, R. J. Barbour, R. J. Warburton, and J. Reichel, “Laser micro-fabrication of concave, low-roughness features in silica,” AIP Adv. 2, 012119 (2012).
    [CrossRef]
  13. D. M. B. Kunert, T. P. Meyrath, and H. Giessen, “Fabrication of a fiber-based microcavity with spherical concave fiber tips,” Appl. Phys. B 98, 707–710 (2010).
    [CrossRef]
  14. M. Mayeh and F. Farahi, “Tailoring Gaussian laser beam shape through controlled etching of single-mode and multimode fibers: simulation and experimental studies,” IEEE Sens. J. 12, 168–173 (2012).
    [CrossRef]
  15. J. Mervis, A. H. Bloom, G. Bravo, L. Mills, F. Zarinetchi, M. Prentiss, and S. P. Smith, “Aligning and attaching a lens to an optical fiber using light pressure force,” Opt. Lett. 18, 325–327 (1993).
    [CrossRef]
  16. M. Mirkhalaf, V. M. Murukeshan, S. B. Tor, V. K. Shinoj, and K. Sathiyamoorthy, “Characteristics of stand-alone microlenses in fiber-based fluorescence imaging applications,” Rev. Sci. Instrum. 82, 043110 (2011).
  17. A. Mori, T. Horiuchi, M. Mizumachi, S. Seino, T. Nakagawa, and K. Suzuki, “Formation of micro lens by laser polymerization,” Electron. Commun. Jpn. 95, 59–67 (2012).
    [CrossRef]
  18. W. R. Cox, T. Chen, D. Ussery, D. J. Hayes, J. A. Tatum, and D. L. MacFarlane, “Microjetted lenslet triplet fibers,” Opt. Commun. 123, 492–496 (1996).
    [CrossRef]
  19. D. M. Hartmann, D. J. Reiley, and S. C. Esener, “Microlenses self-aligned to optical fibers fabricated using the hydrophobic effect,” IEEE Photonics Technol. Lett. 13, 1088–1090 (2001).
    [CrossRef]
  20. C. A. Brackett, “Efficiency of coupling light from stripe-geometry GaAs lasers into multimode optical fibers,” J. Appl. Phys. 45, 2636–2637 (1974).
    [CrossRef]
  21. H. Omrani, J. A. Barnes, A. E. Dudelzak, H.-P. Loock, and H. Waechter, “Fluorescence excitation–emission matrix (EEM) spectroscopy and cavity ring-down (CRD) absorption spectroscopy of oil-contaminated jet fuel using fiber-optic probes,” Analyst 137, 2782–2790 (2012).
    [CrossRef]
  22. D. Munzke, J. Saunders, H. Omrani, O. Reich, and H.-P. Loock, “Modeling of fiber-optic fluorescence probes for strongly absorbing samples,” Appl. Opt. 51, 6343–6351 (2012).
    [CrossRef]
  23. G. He and F. W. Cuomo, “A light-intensity function suitable for multimode fiberoptic sensors,” J. Lightwave Technol. 9, 545–551 (1991).
    [CrossRef]

2012 (6)

D. R. Rivera, C. M. Brown, D. G. Ouzounov, W. W. Webb, and C. Xu, “Use of a lensed fiber for a large-field-of-view, high-resolution, fiber-scanning microendoscope,” Opt. Lett. 37, 881–883 (2012).
[CrossRef]

D. Hunger, C. Deutsch, R. J. Barbour, R. J. Warburton, and J. Reichel, “Laser micro-fabrication of concave, low-roughness features in silica,” AIP Adv. 2, 012119 (2012).
[CrossRef]

M. Mayeh and F. Farahi, “Tailoring Gaussian laser beam shape through controlled etching of single-mode and multimode fibers: simulation and experimental studies,” IEEE Sens. J. 12, 168–173 (2012).
[CrossRef]

A. Mori, T. Horiuchi, M. Mizumachi, S. Seino, T. Nakagawa, and K. Suzuki, “Formation of micro lens by laser polymerization,” Electron. Commun. Jpn. 95, 59–67 (2012).
[CrossRef]

H. Omrani, J. A. Barnes, A. E. Dudelzak, H.-P. Loock, and H. Waechter, “Fluorescence excitation–emission matrix (EEM) spectroscopy and cavity ring-down (CRD) absorption spectroscopy of oil-contaminated jet fuel using fiber-optic probes,” Analyst 137, 2782–2790 (2012).
[CrossRef]

D. Munzke, J. Saunders, H. Omrani, O. Reich, and H.-P. Loock, “Modeling of fiber-optic fluorescence probes for strongly absorbing samples,” Appl. Opt. 51, 6343–6351 (2012).
[CrossRef]

2011 (2)

M. Mirkhalaf, V. M. Murukeshan, S. B. Tor, V. K. Shinoj, and K. Sathiyamoorthy, “Characteristics of stand-alone microlenses in fiber-based fluorescence imaging applications,” Rev. Sci. Instrum. 82, 043110 (2011).

H. Waechter, D. Munzke, A. Jang, and H. P. Loock, “Simultaneous and continuous multiple wavelength absorption spectroscopy on nanoliter volumes based on frequency-division multiplexing fiber-loop cavity ring-down spectroscopy,” Anal. Chem. 83, 2719–2725 (2011).
[CrossRef]

2010 (1)

D. M. B. Kunert, T. P. Meyrath, and H. Giessen, “Fabrication of a fiber-based microcavity with spherical concave fiber tips,” Appl. Phys. B 98, 707–710 (2010).
[CrossRef]

2009 (2)

J. K. Kim, J. Kim, K. Oh, I. B. Sohn, W. Shin, H. Y. Choi, and B. Lee, “Fabrication of micro Fresnel zone plate lens on a mode-expanded hybrid optical fiber using a femtosecond laser ablation system,” IEEE Photonics Technol. Lett. 21, 21–23 (2009).
[CrossRef]

S. Yakunin and J. Heitz, “Microgrinding of lensed fibers by means of a scanning-probe microscope setup,” Appl. Opt. 48, 6172–6177 (2009).
[CrossRef]

2006 (2)

S. Cabrini, C. Liberale, D. Cojoc, A. Carpentiero, M. Prasciolu, S. Mora, V. Degiorgio, F. De Angelis, and E. Di Fabrizio, “Axicon lens on optical fiber forming optical tweezers, made by focused ion beam milling,” Microelectron. Eng. 83, 804–807 (2006).
[CrossRef]

H. P. Loock, “Ring-down absorption spectroscopy for analytical microdevices,” TrAC Trends Anal. Chem. 25, 655–664 (2006).
[CrossRef]

2004 (1)

F. Schiappelli, R. Kumar, M. Prasciolu, D. Cojoc, S. Cabrini, M. De Vittorio, G. Visimberga, A. Gerardino, V. Degiorgio, and E. Di Fabrizio, “Efficient fiber-to-waveguide coupling by a lens on the end of the optical fiber fabricated by focused ion beam milling,” Microelectron. Eng. 73–74, 397–404 (2004).
[CrossRef]

2001 (2)

Y. L. Yu, L. Lui, H. Tam, and W. Chung, “Fiber-laser-based wavelength-division multiplexed fiber Bragg grating sensor system,” IEEE Photonics Technol. Lett. 13, 702–704 (2001).
[CrossRef]

D. M. Hartmann, D. J. Reiley, and S. C. Esener, “Microlenses self-aligned to optical fibers fabricated using the hydrophobic effect,” IEEE Photonics Technol. Lett. 13, 1088–1090 (2001).
[CrossRef]

1997 (1)

A. Hokkanen and S. Tammela, “Hemispherically ended optical fiber lenses,” Phys. Scr. T69, 159–162 (1997).
[CrossRef]

1996 (1)

W. R. Cox, T. Chen, D. Ussery, D. J. Hayes, J. A. Tatum, and D. L. MacFarlane, “Microjetted lenslet triplet fibers,” Opt. Commun. 123, 492–496 (1996).
[CrossRef]

1993 (1)

J. Mervis, A. H. Bloom, G. Bravo, L. Mills, F. Zarinetchi, M. Prentiss, and S. P. Smith, “Aligning and attaching a lens to an optical fiber using light pressure force,” Opt. Lett. 18, 325–327 (1993).
[CrossRef]

1991 (1)

G. He and F. W. Cuomo, “A light-intensity function suitable for multimode fiberoptic sensors,” J. Lightwave Technol. 9, 545–551 (1991).
[CrossRef]

1975 (1)

U. C. Paek and A. L. Weaver, “Formation of a spherical lens at optical fiber ends with a CO2-laser,” Appl. Opt. 14, 294–298 (1975).
[CrossRef]

1974 (1)

C. A. Brackett, “Efficiency of coupling light from stripe-geometry GaAs lasers into multimode optical fibers,” J. Appl. Phys. 45, 2636–2637 (1974).
[CrossRef]

1973 (1)

D. Kato, “Light coupling from a stripe-geometry GaAs diode laser into an optical fiber with spherical end,” J. Appl. Phys. 44, 2756–2758 (1973).
[CrossRef]

Barbour, R. J.

D. Hunger, C. Deutsch, R. J. Barbour, R. J. Warburton, and J. Reichel, “Laser micro-fabrication of concave, low-roughness features in silica,” AIP Adv. 2, 012119 (2012).
[CrossRef]

Barnes, J. A.

H. Omrani, J. A. Barnes, A. E. Dudelzak, H.-P. Loock, and H. Waechter, “Fluorescence excitation–emission matrix (EEM) spectroscopy and cavity ring-down (CRD) absorption spectroscopy of oil-contaminated jet fuel using fiber-optic probes,” Analyst 137, 2782–2790 (2012).
[CrossRef]

Bloom, A. H.

J. Mervis, A. H. Bloom, G. Bravo, L. Mills, F. Zarinetchi, M. Prentiss, and S. P. Smith, “Aligning and attaching a lens to an optical fiber using light pressure force,” Opt. Lett. 18, 325–327 (1993).
[CrossRef]

Brackett, C. A.

C. A. Brackett, “Efficiency of coupling light from stripe-geometry GaAs lasers into multimode optical fibers,” J. Appl. Phys. 45, 2636–2637 (1974).
[CrossRef]

Bravo, G.

J. Mervis, A. H. Bloom, G. Bravo, L. Mills, F. Zarinetchi, M. Prentiss, and S. P. Smith, “Aligning and attaching a lens to an optical fiber using light pressure force,” Opt. Lett. 18, 325–327 (1993).
[CrossRef]

Brown, C. M.

D. R. Rivera, C. M. Brown, D. G. Ouzounov, W. W. Webb, and C. Xu, “Use of a lensed fiber for a large-field-of-view, high-resolution, fiber-scanning microendoscope,” Opt. Lett. 37, 881–883 (2012).
[CrossRef]

Cabrini, S.

S. Cabrini, C. Liberale, D. Cojoc, A. Carpentiero, M. Prasciolu, S. Mora, V. Degiorgio, F. De Angelis, and E. Di Fabrizio, “Axicon lens on optical fiber forming optical tweezers, made by focused ion beam milling,” Microelectron. Eng. 83, 804–807 (2006).
[CrossRef]

F. Schiappelli, R. Kumar, M. Prasciolu, D. Cojoc, S. Cabrini, M. De Vittorio, G. Visimberga, A. Gerardino, V. Degiorgio, and E. Di Fabrizio, “Efficient fiber-to-waveguide coupling by a lens on the end of the optical fiber fabricated by focused ion beam milling,” Microelectron. Eng. 73–74, 397–404 (2004).
[CrossRef]

Carpentiero, A.

S. Cabrini, C. Liberale, D. Cojoc, A. Carpentiero, M. Prasciolu, S. Mora, V. Degiorgio, F. De Angelis, and E. Di Fabrizio, “Axicon lens on optical fiber forming optical tweezers, made by focused ion beam milling,” Microelectron. Eng. 83, 804–807 (2006).
[CrossRef]

Chen, T.

W. R. Cox, T. Chen, D. Ussery, D. J. Hayes, J. A. Tatum, and D. L. MacFarlane, “Microjetted lenslet triplet fibers,” Opt. Commun. 123, 492–496 (1996).
[CrossRef]

Choi, H. Y.

J. K. Kim, J. Kim, K. Oh, I. B. Sohn, W. Shin, H. Y. Choi, and B. Lee, “Fabrication of micro Fresnel zone plate lens on a mode-expanded hybrid optical fiber using a femtosecond laser ablation system,” IEEE Photonics Technol. Lett. 21, 21–23 (2009).
[CrossRef]

Chung, W.

Y. L. Yu, L. Lui, H. Tam, and W. Chung, “Fiber-laser-based wavelength-division multiplexed fiber Bragg grating sensor system,” IEEE Photonics Technol. Lett. 13, 702–704 (2001).
[CrossRef]

Cojoc, D.

S. Cabrini, C. Liberale, D. Cojoc, A. Carpentiero, M. Prasciolu, S. Mora, V. Degiorgio, F. De Angelis, and E. Di Fabrizio, “Axicon lens on optical fiber forming optical tweezers, made by focused ion beam milling,” Microelectron. Eng. 83, 804–807 (2006).
[CrossRef]

F. Schiappelli, R. Kumar, M. Prasciolu, D. Cojoc, S. Cabrini, M. De Vittorio, G. Visimberga, A. Gerardino, V. Degiorgio, and E. Di Fabrizio, “Efficient fiber-to-waveguide coupling by a lens on the end of the optical fiber fabricated by focused ion beam milling,” Microelectron. Eng. 73–74, 397–404 (2004).
[CrossRef]

Cox, W. R.

W. R. Cox, T. Chen, D. Ussery, D. J. Hayes, J. A. Tatum, and D. L. MacFarlane, “Microjetted lenslet triplet fibers,” Opt. Commun. 123, 492–496 (1996).
[CrossRef]

Cuomo, F. W.

G. He and F. W. Cuomo, “A light-intensity function suitable for multimode fiberoptic sensors,” J. Lightwave Technol. 9, 545–551 (1991).
[CrossRef]

De Angelis, F.

S. Cabrini, C. Liberale, D. Cojoc, A. Carpentiero, M. Prasciolu, S. Mora, V. Degiorgio, F. De Angelis, and E. Di Fabrizio, “Axicon lens on optical fiber forming optical tweezers, made by focused ion beam milling,” Microelectron. Eng. 83, 804–807 (2006).
[CrossRef]

De Vittorio, M.

F. Schiappelli, R. Kumar, M. Prasciolu, D. Cojoc, S. Cabrini, M. De Vittorio, G. Visimberga, A. Gerardino, V. Degiorgio, and E. Di Fabrizio, “Efficient fiber-to-waveguide coupling by a lens on the end of the optical fiber fabricated by focused ion beam milling,” Microelectron. Eng. 73–74, 397–404 (2004).
[CrossRef]

Degiorgio, V.

S. Cabrini, C. Liberale, D. Cojoc, A. Carpentiero, M. Prasciolu, S. Mora, V. Degiorgio, F. De Angelis, and E. Di Fabrizio, “Axicon lens on optical fiber forming optical tweezers, made by focused ion beam milling,” Microelectron. Eng. 83, 804–807 (2006).
[CrossRef]

F. Schiappelli, R. Kumar, M. Prasciolu, D. Cojoc, S. Cabrini, M. De Vittorio, G. Visimberga, A. Gerardino, V. Degiorgio, and E. Di Fabrizio, “Efficient fiber-to-waveguide coupling by a lens on the end of the optical fiber fabricated by focused ion beam milling,” Microelectron. Eng. 73–74, 397–404 (2004).
[CrossRef]

Deutsch, C.

D. Hunger, C. Deutsch, R. J. Barbour, R. J. Warburton, and J. Reichel, “Laser micro-fabrication of concave, low-roughness features in silica,” AIP Adv. 2, 012119 (2012).
[CrossRef]

Di Fabrizio, E.

S. Cabrini, C. Liberale, D. Cojoc, A. Carpentiero, M. Prasciolu, S. Mora, V. Degiorgio, F. De Angelis, and E. Di Fabrizio, “Axicon lens on optical fiber forming optical tweezers, made by focused ion beam milling,” Microelectron. Eng. 83, 804–807 (2006).
[CrossRef]

F. Schiappelli, R. Kumar, M. Prasciolu, D. Cojoc, S. Cabrini, M. De Vittorio, G. Visimberga, A. Gerardino, V. Degiorgio, and E. Di Fabrizio, “Efficient fiber-to-waveguide coupling by a lens on the end of the optical fiber fabricated by focused ion beam milling,” Microelectron. Eng. 73–74, 397–404 (2004).
[CrossRef]

Dudelzak, A. E.

H. Omrani, J. A. Barnes, A. E. Dudelzak, H.-P. Loock, and H. Waechter, “Fluorescence excitation–emission matrix (EEM) spectroscopy and cavity ring-down (CRD) absorption spectroscopy of oil-contaminated jet fuel using fiber-optic probes,” Analyst 137, 2782–2790 (2012).
[CrossRef]

Esener, S. C.

D. M. Hartmann, D. J. Reiley, and S. C. Esener, “Microlenses self-aligned to optical fibers fabricated using the hydrophobic effect,” IEEE Photonics Technol. Lett. 13, 1088–1090 (2001).
[CrossRef]

Farahi, F.

M. Mayeh and F. Farahi, “Tailoring Gaussian laser beam shape through controlled etching of single-mode and multimode fibers: simulation and experimental studies,” IEEE Sens. J. 12, 168–173 (2012).
[CrossRef]

Gerardino, A.

F. Schiappelli, R. Kumar, M. Prasciolu, D. Cojoc, S. Cabrini, M. De Vittorio, G. Visimberga, A. Gerardino, V. Degiorgio, and E. Di Fabrizio, “Efficient fiber-to-waveguide coupling by a lens on the end of the optical fiber fabricated by focused ion beam milling,” Microelectron. Eng. 73–74, 397–404 (2004).
[CrossRef]

Giessen, H.

D. M. B. Kunert, T. P. Meyrath, and H. Giessen, “Fabrication of a fiber-based microcavity with spherical concave fiber tips,” Appl. Phys. B 98, 707–710 (2010).
[CrossRef]

Hartmann, D. M.

D. M. Hartmann, D. J. Reiley, and S. C. Esener, “Microlenses self-aligned to optical fibers fabricated using the hydrophobic effect,” IEEE Photonics Technol. Lett. 13, 1088–1090 (2001).
[CrossRef]

Hayes, D. J.

W. R. Cox, T. Chen, D. Ussery, D. J. Hayes, J. A. Tatum, and D. L. MacFarlane, “Microjetted lenslet triplet fibers,” Opt. Commun. 123, 492–496 (1996).
[CrossRef]

He, G.

G. He and F. W. Cuomo, “A light-intensity function suitable for multimode fiberoptic sensors,” J. Lightwave Technol. 9, 545–551 (1991).
[CrossRef]

Heitz, J.

S. Yakunin and J. Heitz, “Microgrinding of lensed fibers by means of a scanning-probe microscope setup,” Appl. Opt. 48, 6172–6177 (2009).
[CrossRef]

Hokkanen, A.

A. Hokkanen and S. Tammela, “Hemispherically ended optical fiber lenses,” Phys. Scr. T69, 159–162 (1997).
[CrossRef]

Horiuchi, T.

A. Mori, T. Horiuchi, M. Mizumachi, S. Seino, T. Nakagawa, and K. Suzuki, “Formation of micro lens by laser polymerization,” Electron. Commun. Jpn. 95, 59–67 (2012).
[CrossRef]

Hunger, D.

D. Hunger, C. Deutsch, R. J. Barbour, R. J. Warburton, and J. Reichel, “Laser micro-fabrication of concave, low-roughness features in silica,” AIP Adv. 2, 012119 (2012).
[CrossRef]

Jang, A.

H. Waechter, D. Munzke, A. Jang, and H. P. Loock, “Simultaneous and continuous multiple wavelength absorption spectroscopy on nanoliter volumes based on frequency-division multiplexing fiber-loop cavity ring-down spectroscopy,” Anal. Chem. 83, 2719–2725 (2011).
[CrossRef]

Kato, D.

D. Kato, “Light coupling from a stripe-geometry GaAs diode laser into an optical fiber with spherical end,” J. Appl. Phys. 44, 2756–2758 (1973).
[CrossRef]

Kim, J.

J. K. Kim, J. Kim, K. Oh, I. B. Sohn, W. Shin, H. Y. Choi, and B. Lee, “Fabrication of micro Fresnel zone plate lens on a mode-expanded hybrid optical fiber using a femtosecond laser ablation system,” IEEE Photonics Technol. Lett. 21, 21–23 (2009).
[CrossRef]

Kim, J. K.

J. K. Kim, J. Kim, K. Oh, I. B. Sohn, W. Shin, H. Y. Choi, and B. Lee, “Fabrication of micro Fresnel zone plate lens on a mode-expanded hybrid optical fiber using a femtosecond laser ablation system,” IEEE Photonics Technol. Lett. 21, 21–23 (2009).
[CrossRef]

Kumar, R.

F. Schiappelli, R. Kumar, M. Prasciolu, D. Cojoc, S. Cabrini, M. De Vittorio, G. Visimberga, A. Gerardino, V. Degiorgio, and E. Di Fabrizio, “Efficient fiber-to-waveguide coupling by a lens on the end of the optical fiber fabricated by focused ion beam milling,” Microelectron. Eng. 73–74, 397–404 (2004).
[CrossRef]

Kunert, D. M. B.

D. M. B. Kunert, T. P. Meyrath, and H. Giessen, “Fabrication of a fiber-based microcavity with spherical concave fiber tips,” Appl. Phys. B 98, 707–710 (2010).
[CrossRef]

Lee, B.

J. K. Kim, J. Kim, K. Oh, I. B. Sohn, W. Shin, H. Y. Choi, and B. Lee, “Fabrication of micro Fresnel zone plate lens on a mode-expanded hybrid optical fiber using a femtosecond laser ablation system,” IEEE Photonics Technol. Lett. 21, 21–23 (2009).
[CrossRef]

Liberale, C.

S. Cabrini, C. Liberale, D. Cojoc, A. Carpentiero, M. Prasciolu, S. Mora, V. Degiorgio, F. De Angelis, and E. Di Fabrizio, “Axicon lens on optical fiber forming optical tweezers, made by focused ion beam milling,” Microelectron. Eng. 83, 804–807 (2006).
[CrossRef]

Loock, H. P.

H. Waechter, D. Munzke, A. Jang, and H. P. Loock, “Simultaneous and continuous multiple wavelength absorption spectroscopy on nanoliter volumes based on frequency-division multiplexing fiber-loop cavity ring-down spectroscopy,” Anal. Chem. 83, 2719–2725 (2011).
[CrossRef]

H. P. Loock, “Ring-down absorption spectroscopy for analytical microdevices,” TrAC Trends Anal. Chem. 25, 655–664 (2006).
[CrossRef]

Loock, H.-P.

H. Omrani, J. A. Barnes, A. E. Dudelzak, H.-P. Loock, and H. Waechter, “Fluorescence excitation–emission matrix (EEM) spectroscopy and cavity ring-down (CRD) absorption spectroscopy of oil-contaminated jet fuel using fiber-optic probes,” Analyst 137, 2782–2790 (2012).
[CrossRef]

D. Munzke, J. Saunders, H. Omrani, O. Reich, and H.-P. Loock, “Modeling of fiber-optic fluorescence probes for strongly absorbing samples,” Appl. Opt. 51, 6343–6351 (2012).
[CrossRef]

Lui, L.

Y. L. Yu, L. Lui, H. Tam, and W. Chung, “Fiber-laser-based wavelength-division multiplexed fiber Bragg grating sensor system,” IEEE Photonics Technol. Lett. 13, 702–704 (2001).
[CrossRef]

MacFarlane, D. L.

W. R. Cox, T. Chen, D. Ussery, D. J. Hayes, J. A. Tatum, and D. L. MacFarlane, “Microjetted lenslet triplet fibers,” Opt. Commun. 123, 492–496 (1996).
[CrossRef]

Mayeh, M.

M. Mayeh and F. Farahi, “Tailoring Gaussian laser beam shape through controlled etching of single-mode and multimode fibers: simulation and experimental studies,” IEEE Sens. J. 12, 168–173 (2012).
[CrossRef]

Mervis, J.

J. Mervis, A. H. Bloom, G. Bravo, L. Mills, F. Zarinetchi, M. Prentiss, and S. P. Smith, “Aligning and attaching a lens to an optical fiber using light pressure force,” Opt. Lett. 18, 325–327 (1993).
[CrossRef]

Meyrath, T. P.

D. M. B. Kunert, T. P. Meyrath, and H. Giessen, “Fabrication of a fiber-based microcavity with spherical concave fiber tips,” Appl. Phys. B 98, 707–710 (2010).
[CrossRef]

Mills, L.

J. Mervis, A. H. Bloom, G. Bravo, L. Mills, F. Zarinetchi, M. Prentiss, and S. P. Smith, “Aligning and attaching a lens to an optical fiber using light pressure force,” Opt. Lett. 18, 325–327 (1993).
[CrossRef]

Mirkhalaf, M.

M. Mirkhalaf, V. M. Murukeshan, S. B. Tor, V. K. Shinoj, and K. Sathiyamoorthy, “Characteristics of stand-alone microlenses in fiber-based fluorescence imaging applications,” Rev. Sci. Instrum. 82, 043110 (2011).

Mizumachi, M.

A. Mori, T. Horiuchi, M. Mizumachi, S. Seino, T. Nakagawa, and K. Suzuki, “Formation of micro lens by laser polymerization,” Electron. Commun. Jpn. 95, 59–67 (2012).
[CrossRef]

Mora, S.

S. Cabrini, C. Liberale, D. Cojoc, A. Carpentiero, M. Prasciolu, S. Mora, V. Degiorgio, F. De Angelis, and E. Di Fabrizio, “Axicon lens on optical fiber forming optical tweezers, made by focused ion beam milling,” Microelectron. Eng. 83, 804–807 (2006).
[CrossRef]

Mori, A.

A. Mori, T. Horiuchi, M. Mizumachi, S. Seino, T. Nakagawa, and K. Suzuki, “Formation of micro lens by laser polymerization,” Electron. Commun. Jpn. 95, 59–67 (2012).
[CrossRef]

Munzke, D.

D. Munzke, J. Saunders, H. Omrani, O. Reich, and H.-P. Loock, “Modeling of fiber-optic fluorescence probes for strongly absorbing samples,” Appl. Opt. 51, 6343–6351 (2012).
[CrossRef]

H. Waechter, D. Munzke, A. Jang, and H. P. Loock, “Simultaneous and continuous multiple wavelength absorption spectroscopy on nanoliter volumes based on frequency-division multiplexing fiber-loop cavity ring-down spectroscopy,” Anal. Chem. 83, 2719–2725 (2011).
[CrossRef]

Murukeshan, V. M.

M. Mirkhalaf, V. M. Murukeshan, S. B. Tor, V. K. Shinoj, and K. Sathiyamoorthy, “Characteristics of stand-alone microlenses in fiber-based fluorescence imaging applications,” Rev. Sci. Instrum. 82, 043110 (2011).

Nakagawa, T.

A. Mori, T. Horiuchi, M. Mizumachi, S. Seino, T. Nakagawa, and K. Suzuki, “Formation of micro lens by laser polymerization,” Electron. Commun. Jpn. 95, 59–67 (2012).
[CrossRef]

Oh, K.

J. K. Kim, J. Kim, K. Oh, I. B. Sohn, W. Shin, H. Y. Choi, and B. Lee, “Fabrication of micro Fresnel zone plate lens on a mode-expanded hybrid optical fiber using a femtosecond laser ablation system,” IEEE Photonics Technol. Lett. 21, 21–23 (2009).
[CrossRef]

Omrani, H.

H. Omrani, J. A. Barnes, A. E. Dudelzak, H.-P. Loock, and H. Waechter, “Fluorescence excitation–emission matrix (EEM) spectroscopy and cavity ring-down (CRD) absorption spectroscopy of oil-contaminated jet fuel using fiber-optic probes,” Analyst 137, 2782–2790 (2012).
[CrossRef]

D. Munzke, J. Saunders, H. Omrani, O. Reich, and H.-P. Loock, “Modeling of fiber-optic fluorescence probes for strongly absorbing samples,” Appl. Opt. 51, 6343–6351 (2012).
[CrossRef]

Ouzounov, D. G.

D. R. Rivera, C. M. Brown, D. G. Ouzounov, W. W. Webb, and C. Xu, “Use of a lensed fiber for a large-field-of-view, high-resolution, fiber-scanning microendoscope,” Opt. Lett. 37, 881–883 (2012).
[CrossRef]

Paek, U. C.

U. C. Paek and A. L. Weaver, “Formation of a spherical lens at optical fiber ends with a CO2-laser,” Appl. Opt. 14, 294–298 (1975).
[CrossRef]

Prasciolu, M.

S. Cabrini, C. Liberale, D. Cojoc, A. Carpentiero, M. Prasciolu, S. Mora, V. Degiorgio, F. De Angelis, and E. Di Fabrizio, “Axicon lens on optical fiber forming optical tweezers, made by focused ion beam milling,” Microelectron. Eng. 83, 804–807 (2006).
[CrossRef]

F. Schiappelli, R. Kumar, M. Prasciolu, D. Cojoc, S. Cabrini, M. De Vittorio, G. Visimberga, A. Gerardino, V. Degiorgio, and E. Di Fabrizio, “Efficient fiber-to-waveguide coupling by a lens on the end of the optical fiber fabricated by focused ion beam milling,” Microelectron. Eng. 73–74, 397–404 (2004).
[CrossRef]

Prentiss, M.

J. Mervis, A. H. Bloom, G. Bravo, L. Mills, F. Zarinetchi, M. Prentiss, and S. P. Smith, “Aligning and attaching a lens to an optical fiber using light pressure force,” Opt. Lett. 18, 325–327 (1993).
[CrossRef]

Reich, O.

D. Munzke, J. Saunders, H. Omrani, O. Reich, and H.-P. Loock, “Modeling of fiber-optic fluorescence probes for strongly absorbing samples,” Appl. Opt. 51, 6343–6351 (2012).
[CrossRef]

Reichel, J.

D. Hunger, C. Deutsch, R. J. Barbour, R. J. Warburton, and J. Reichel, “Laser micro-fabrication of concave, low-roughness features in silica,” AIP Adv. 2, 012119 (2012).
[CrossRef]

Reiley, D. J.

D. M. Hartmann, D. J. Reiley, and S. C. Esener, “Microlenses self-aligned to optical fibers fabricated using the hydrophobic effect,” IEEE Photonics Technol. Lett. 13, 1088–1090 (2001).
[CrossRef]

Rivera, D. R.

D. R. Rivera, C. M. Brown, D. G. Ouzounov, W. W. Webb, and C. Xu, “Use of a lensed fiber for a large-field-of-view, high-resolution, fiber-scanning microendoscope,” Opt. Lett. 37, 881–883 (2012).
[CrossRef]

Sathiyamoorthy, K.

M. Mirkhalaf, V. M. Murukeshan, S. B. Tor, V. K. Shinoj, and K. Sathiyamoorthy, “Characteristics of stand-alone microlenses in fiber-based fluorescence imaging applications,” Rev. Sci. Instrum. 82, 043110 (2011).

Saunders, J.

D. Munzke, J. Saunders, H. Omrani, O. Reich, and H.-P. Loock, “Modeling of fiber-optic fluorescence probes for strongly absorbing samples,” Appl. Opt. 51, 6343–6351 (2012).
[CrossRef]

Schiappelli, F.

F. Schiappelli, R. Kumar, M. Prasciolu, D. Cojoc, S. Cabrini, M. De Vittorio, G. Visimberga, A. Gerardino, V. Degiorgio, and E. Di Fabrizio, “Efficient fiber-to-waveguide coupling by a lens on the end of the optical fiber fabricated by focused ion beam milling,” Microelectron. Eng. 73–74, 397–404 (2004).
[CrossRef]

Seino, S.

A. Mori, T. Horiuchi, M. Mizumachi, S. Seino, T. Nakagawa, and K. Suzuki, “Formation of micro lens by laser polymerization,” Electron. Commun. Jpn. 95, 59–67 (2012).
[CrossRef]

Shin, W.

J. K. Kim, J. Kim, K. Oh, I. B. Sohn, W. Shin, H. Y. Choi, and B. Lee, “Fabrication of micro Fresnel zone plate lens on a mode-expanded hybrid optical fiber using a femtosecond laser ablation system,” IEEE Photonics Technol. Lett. 21, 21–23 (2009).
[CrossRef]

Shinoj, V. K.

M. Mirkhalaf, V. M. Murukeshan, S. B. Tor, V. K. Shinoj, and K. Sathiyamoorthy, “Characteristics of stand-alone microlenses in fiber-based fluorescence imaging applications,” Rev. Sci. Instrum. 82, 043110 (2011).

Smith, S. P.

J. Mervis, A. H. Bloom, G. Bravo, L. Mills, F. Zarinetchi, M. Prentiss, and S. P. Smith, “Aligning and attaching a lens to an optical fiber using light pressure force,” Opt. Lett. 18, 325–327 (1993).
[CrossRef]

Sohn, I. B.

J. K. Kim, J. Kim, K. Oh, I. B. Sohn, W. Shin, H. Y. Choi, and B. Lee, “Fabrication of micro Fresnel zone plate lens on a mode-expanded hybrid optical fiber using a femtosecond laser ablation system,” IEEE Photonics Technol. Lett. 21, 21–23 (2009).
[CrossRef]

Suzuki, K.

A. Mori, T. Horiuchi, M. Mizumachi, S. Seino, T. Nakagawa, and K. Suzuki, “Formation of micro lens by laser polymerization,” Electron. Commun. Jpn. 95, 59–67 (2012).
[CrossRef]

Tam, H.

Y. L. Yu, L. Lui, H. Tam, and W. Chung, “Fiber-laser-based wavelength-division multiplexed fiber Bragg grating sensor system,” IEEE Photonics Technol. Lett. 13, 702–704 (2001).
[CrossRef]

Tammela, S.

A. Hokkanen and S. Tammela, “Hemispherically ended optical fiber lenses,” Phys. Scr. T69, 159–162 (1997).
[CrossRef]

Tatum, J. A.

W. R. Cox, T. Chen, D. Ussery, D. J. Hayes, J. A. Tatum, and D. L. MacFarlane, “Microjetted lenslet triplet fibers,” Opt. Commun. 123, 492–496 (1996).
[CrossRef]

Tor, S. B.

M. Mirkhalaf, V. M. Murukeshan, S. B. Tor, V. K. Shinoj, and K. Sathiyamoorthy, “Characteristics of stand-alone microlenses in fiber-based fluorescence imaging applications,” Rev. Sci. Instrum. 82, 043110 (2011).

Ussery, D.

W. R. Cox, T. Chen, D. Ussery, D. J. Hayes, J. A. Tatum, and D. L. MacFarlane, “Microjetted lenslet triplet fibers,” Opt. Commun. 123, 492–496 (1996).
[CrossRef]

Visimberga, G.

F. Schiappelli, R. Kumar, M. Prasciolu, D. Cojoc, S. Cabrini, M. De Vittorio, G. Visimberga, A. Gerardino, V. Degiorgio, and E. Di Fabrizio, “Efficient fiber-to-waveguide coupling by a lens on the end of the optical fiber fabricated by focused ion beam milling,” Microelectron. Eng. 73–74, 397–404 (2004).
[CrossRef]

Waechter, H.

H. Omrani, J. A. Barnes, A. E. Dudelzak, H.-P. Loock, and H. Waechter, “Fluorescence excitation–emission matrix (EEM) spectroscopy and cavity ring-down (CRD) absorption spectroscopy of oil-contaminated jet fuel using fiber-optic probes,” Analyst 137, 2782–2790 (2012).
[CrossRef]

H. Waechter, D. Munzke, A. Jang, and H. P. Loock, “Simultaneous and continuous multiple wavelength absorption spectroscopy on nanoliter volumes based on frequency-division multiplexing fiber-loop cavity ring-down spectroscopy,” Anal. Chem. 83, 2719–2725 (2011).
[CrossRef]

Warburton, R. J.

D. Hunger, C. Deutsch, R. J. Barbour, R. J. Warburton, and J. Reichel, “Laser micro-fabrication of concave, low-roughness features in silica,” AIP Adv. 2, 012119 (2012).
[CrossRef]

Weaver, A. L.

U. C. Paek and A. L. Weaver, “Formation of a spherical lens at optical fiber ends with a CO2-laser,” Appl. Opt. 14, 294–298 (1975).
[CrossRef]

Webb, W. W.

D. R. Rivera, C. M. Brown, D. G. Ouzounov, W. W. Webb, and C. Xu, “Use of a lensed fiber for a large-field-of-view, high-resolution, fiber-scanning microendoscope,” Opt. Lett. 37, 881–883 (2012).
[CrossRef]

Xu, C.

D. R. Rivera, C. M. Brown, D. G. Ouzounov, W. W. Webb, and C. Xu, “Use of a lensed fiber for a large-field-of-view, high-resolution, fiber-scanning microendoscope,” Opt. Lett. 37, 881–883 (2012).
[CrossRef]

Yakunin, S.

S. Yakunin and J. Heitz, “Microgrinding of lensed fibers by means of a scanning-probe microscope setup,” Appl. Opt. 48, 6172–6177 (2009).
[CrossRef]

Yu, Y. L.

Y. L. Yu, L. Lui, H. Tam, and W. Chung, “Fiber-laser-based wavelength-division multiplexed fiber Bragg grating sensor system,” IEEE Photonics Technol. Lett. 13, 702–704 (2001).
[CrossRef]

Zarinetchi, F.

J. Mervis, A. H. Bloom, G. Bravo, L. Mills, F. Zarinetchi, M. Prentiss, and S. P. Smith, “Aligning and attaching a lens to an optical fiber using light pressure force,” Opt. Lett. 18, 325–327 (1993).
[CrossRef]

AIP Adv. (1)

D. Hunger, C. Deutsch, R. J. Barbour, R. J. Warburton, and J. Reichel, “Laser micro-fabrication of concave, low-roughness features in silica,” AIP Adv. 2, 012119 (2012).
[CrossRef]

Anal. Chem. (1)

H. Waechter, D. Munzke, A. Jang, and H. P. Loock, “Simultaneous and continuous multiple wavelength absorption spectroscopy on nanoliter volumes based on frequency-division multiplexing fiber-loop cavity ring-down spectroscopy,” Anal. Chem. 83, 2719–2725 (2011).
[CrossRef]

Analyst (1)

H. Omrani, J. A. Barnes, A. E. Dudelzak, H.-P. Loock, and H. Waechter, “Fluorescence excitation–emission matrix (EEM) spectroscopy and cavity ring-down (CRD) absorption spectroscopy of oil-contaminated jet fuel using fiber-optic probes,” Analyst 137, 2782–2790 (2012).
[CrossRef]

Appl. Opt. (3)

D. Munzke, J. Saunders, H. Omrani, O. Reich, and H.-P. Loock, “Modeling of fiber-optic fluorescence probes for strongly absorbing samples,” Appl. Opt. 51, 6343–6351 (2012).
[CrossRef]

S. Yakunin and J. Heitz, “Microgrinding of lensed fibers by means of a scanning-probe microscope setup,” Appl. Opt. 48, 6172–6177 (2009).
[CrossRef]

U. C. Paek and A. L. Weaver, “Formation of a spherical lens at optical fiber ends with a CO2-laser,” Appl. Opt. 14, 294–298 (1975).
[CrossRef]

Appl. Phys. B (1)

D. M. B. Kunert, T. P. Meyrath, and H. Giessen, “Fabrication of a fiber-based microcavity with spherical concave fiber tips,” Appl. Phys. B 98, 707–710 (2010).
[CrossRef]

Electron. Commun. Jpn. (1)

A. Mori, T. Horiuchi, M. Mizumachi, S. Seino, T. Nakagawa, and K. Suzuki, “Formation of micro lens by laser polymerization,” Electron. Commun. Jpn. 95, 59–67 (2012).
[CrossRef]

IEEE Photonics Technol. Lett. (3)

D. M. Hartmann, D. J. Reiley, and S. C. Esener, “Microlenses self-aligned to optical fibers fabricated using the hydrophobic effect,” IEEE Photonics Technol. Lett. 13, 1088–1090 (2001).
[CrossRef]

J. K. Kim, J. Kim, K. Oh, I. B. Sohn, W. Shin, H. Y. Choi, and B. Lee, “Fabrication of micro Fresnel zone plate lens on a mode-expanded hybrid optical fiber using a femtosecond laser ablation system,” IEEE Photonics Technol. Lett. 21, 21–23 (2009).
[CrossRef]

Y. L. Yu, L. Lui, H. Tam, and W. Chung, “Fiber-laser-based wavelength-division multiplexed fiber Bragg grating sensor system,” IEEE Photonics Technol. Lett. 13, 702–704 (2001).
[CrossRef]

IEEE Sens. J. (1)

M. Mayeh and F. Farahi, “Tailoring Gaussian laser beam shape through controlled etching of single-mode and multimode fibers: simulation and experimental studies,” IEEE Sens. J. 12, 168–173 (2012).
[CrossRef]

J. Appl. Phys. (2)

C. A. Brackett, “Efficiency of coupling light from stripe-geometry GaAs lasers into multimode optical fibers,” J. Appl. Phys. 45, 2636–2637 (1974).
[CrossRef]

D. Kato, “Light coupling from a stripe-geometry GaAs diode laser into an optical fiber with spherical end,” J. Appl. Phys. 44, 2756–2758 (1973).
[CrossRef]

J. Lightwave Technol. (1)

G. He and F. W. Cuomo, “A light-intensity function suitable for multimode fiberoptic sensors,” J. Lightwave Technol. 9, 545–551 (1991).
[CrossRef]

Microelectron. Eng. (2)

S. Cabrini, C. Liberale, D. Cojoc, A. Carpentiero, M. Prasciolu, S. Mora, V. Degiorgio, F. De Angelis, and E. Di Fabrizio, “Axicon lens on optical fiber forming optical tweezers, made by focused ion beam milling,” Microelectron. Eng. 83, 804–807 (2006).
[CrossRef]

F. Schiappelli, R. Kumar, M. Prasciolu, D. Cojoc, S. Cabrini, M. De Vittorio, G. Visimberga, A. Gerardino, V. Degiorgio, and E. Di Fabrizio, “Efficient fiber-to-waveguide coupling by a lens on the end of the optical fiber fabricated by focused ion beam milling,” Microelectron. Eng. 73–74, 397–404 (2004).
[CrossRef]

Opt. Commun. (1)

W. R. Cox, T. Chen, D. Ussery, D. J. Hayes, J. A. Tatum, and D. L. MacFarlane, “Microjetted lenslet triplet fibers,” Opt. Commun. 123, 492–496 (1996).
[CrossRef]

Opt. Lett. (2)

J. Mervis, A. H. Bloom, G. Bravo, L. Mills, F. Zarinetchi, M. Prentiss, and S. P. Smith, “Aligning and attaching a lens to an optical fiber using light pressure force,” Opt. Lett. 18, 325–327 (1993).
[CrossRef]

D. R. Rivera, C. M. Brown, D. G. Ouzounov, W. W. Webb, and C. Xu, “Use of a lensed fiber for a large-field-of-view, high-resolution, fiber-scanning microendoscope,” Opt. Lett. 37, 881–883 (2012).
[CrossRef]

Phys. Scr. (1)

A. Hokkanen and S. Tammela, “Hemispherically ended optical fiber lenses,” Phys. Scr. T69, 159–162 (1997).
[CrossRef]

Rev. Sci. Instrum. (1)

M. Mirkhalaf, V. M. Murukeshan, S. B. Tor, V. K. Shinoj, and K. Sathiyamoorthy, “Characteristics of stand-alone microlenses in fiber-based fluorescence imaging applications,” Rev. Sci. Instrum. 82, 043110 (2011).

TrAC Trends Anal. Chem. (1)

H. P. Loock, “Ring-down absorption spectroscopy for analytical microdevices,” TrAC Trends Anal. Chem. 25, 655–664 (2006).
[CrossRef]

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Figures (6)

Fig. 1.
Fig. 1.

(a) SEM picture of the concave lens at the fiber ferrule. (b) Micrograph at 10× magnification of the R=150μm ruby microsphere inserted in a stainless steel fiber ferrule. This template was used to fabricate a concave fiber lens.

Fig. 2.
Fig. 2.

Ray diagrams showing the calculation of the limiting angles (left) β1 and (right) β2 as a function of the lens radius, R, and the critical angle for wave guiding θc.

Fig. 3.
Fig. 3.

Fiber lens emission cones with a fiber lens radius R=75μm in water (n0=1.33). In this and all other images the intensity is color coded to produce a false color image. The simulation window is 0.4 mm high and 1.0 mm long. The fiber core diameter is 100 μm, NA=0.22, nclad=1.433. (a) As calculated from Eq. (3), (b) after normalization and translation to include a lens using Eq. (9), and (c) after Abel transformation using Eq. (10). Ripples at short distance from the fiber lens are a discretization artifact of the simulation. (d) Experimental data on the same scale recorded using a microscope and adapted from [4].

Fig. 4.
Fig. 4.

Simulated emission from fiber lens with NA=0.22, R=150μm, rcore=50μm, ncore=1.433. The refractive indices of the medium are (a) n0=1.0 (air), (b) n0=1.365 (ethanol), (c) n0=1.4785 (DMSO), and (d) n0=1.77 (sapphire). The figure shows the Abel-transformed images.

Fig. 5.
Fig. 5.

Coupling efficiencies of the fiber lens with radii between R=60μm to +60μm in media with different refractive indices. The fiber core diameter is 100 μm, NA=0.22, nclad=1.433. The circles in the bottom left panel were obtained by reanalysis of the ringdown times recorded from a convex lens (R+75μm) in water [5]. Simulations with a convex or concave lens radius of less than about 80 μm could not be performed when n0=1.0, since then Eqs. (6) and (8) are no longer valid.

Fig. 6.
Fig. 6.

Theoretical and experimental fiber lens emission (top) with a flat fiber end (simulated as R=1m) and (bottom) with R=150μm in (left) pure DMSO and (right) pure ethanol. The window is 0.4 mm high and 1.0 mm long. The fiber core diameter is 100 μm, NA=0.22, nclad=1.433. In each group the simulation is shown above the experimental image.

Equations (10)

Equations on this page are rendered with MathJax. Learn more.

I(x,z)=rcore+rcoreI(α,r)w(β1,α,β2)dr.
α=arctan(xrz),
I(x,z)=r=r0r0I(α,r)ifβ1(r)<α(r,x,z)<β2(r),0ifβ1(r)>α(r,x,z)orα(r,x,z)>β2(r).
γ=arcsin(rR),θc=arcsin(ncladncore),n0sinϕs=ncoresinϕf.
ϕf=π2θc+γ,β1=ϕsγ,
β1=arcsin(rR)+arcsin[ncoren0cos(arcsin(rR)arcsin(ncladncore))]=arcsin(rR)+arcsin[NAR2r2+rncladRn0].
ϕf=π2θcγ,β2=γ+ϕs,
β2=arcsin(rR)+arcsin[NAR2r2rncladRn0].
zzRR2r2ifR<0andr<rcore,zzRR2rcore2ifR<0andr>rcore,zz+R2r2R2rcore2ifR>0andr<rcore,zzifR>0andr>rcore.
I(x,z)=2x02πI(r,ρ,z)rr2x2dρdr=4πxI(r,z)rr2x2dr.

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