Abstract

We propose a compact laser configuration based on resonating both the pump and signal light along a microfiber ring doped with active ions. We estimate the minimum Q-factor to obtain lasing and find that values already demonstrated in passive microfiber rings will be sufficient. We model the performance of this device in steady state using rate equations and show that pump resonance can significantly reduce the threshold and increase the quantum efficiency, especially for rings made of materials with weak active ion absorption. Numerical examples for erbium and ytterbium doped devices are presented. Taking into account scattering and coupling losses the optimum pump coupling factor is calculated. The dependences of the quantum efficiency and threshold power on the coupling losses are also investigated. We predict that efficient ytterbium-doped lasers can be obtained with a ring diameter down to a few tens of micrometers.

© 2006 Optical Society of America

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    [CrossRef]

2006 (2)

L. Tong, L. Hu, J. Zhang, J. Qiu, Q. Yang, J. Lou, Y. Shen, J. He, and Z. Ye, "Photonic nanowires directly drawn from bulk glasses," Opt. Express 14, 82-87 (2006).
[CrossRef] [PubMed]

X. Jiang, L. Tong, G. Vienne, X. Guo, A. Tsao, Q. Yang and D. Yang, "Demonstration of optical microfiber knot resonators," Appl. Phys. Lett. 88, 223501 (2006).
[CrossRef]

2005 (1)

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

2004 (5)

2003 (3)

J. R. Buck, and H. J. Kimble, "Optimal sizes of dielectric microspheres for cavity QED with strong Coupling," Phys. Rev. A 67, 033806 (2003).
[CrossRef]

L. Tong, R. R. Gattass, J. B. Ashcom, S. He, J. Lou, M. Shen, I. Maxwell, and E. Mazur, "Subwavelength-diameter silica wires for low-loss optical wave guiding," Nature 426, 816-819 (2003).
[CrossRef] [PubMed]

K. Srinivasan, P. E. Barclay, O. Painter, J. Chen, A. Y. Cho, and C. Gmachl, "Experimental demonstration of a high quality factor photonic crystal microcavity," Appl. Phys. Lett. 83, 1915-1917 (2003).
[CrossRef]

2002 (1)

F. Vollmer, D. Braun, A. Libchaber, S. M. Khoshsima, I. Teraoka, and S. Arnold, "Protein detection by optical shift of a resonant microcavity," Appl. Phys. Lett. 80, 4057-4059 (2002).
[CrossRef]

2000 (2)

M. Cai, O. Painter, K. J. Vahala, and P. C. Sercel, "Fiber-coupled microsphere laser," Opt. Lett. 25, 1430-1432 (2000).
[CrossRef]

M. Cai, O. Painter, and K. J. Vahala, "Observation of critical coupling in a fiber taper to a silica-microsphere whisper-gallery mode system," Phys. Rev. Lett. 85,74-77 (2000).
[CrossRef] [PubMed]

1998 (2)

G. G. Vienne, J. E. Caplen, L. Dong, J. D. Minelly, J. Nilsson, and D. N. Payne, "Fabrication and Characterization of Yb3+: Er3+ Phosphosilicate Fibers for Lasers," J. Lightwave Technol. 16, 1990-2001 (1998).
[CrossRef]

B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Thoen, S. T. Chu, H. A. Haus, and E. P. Ippen, "Ultra-compact Si-SiO2 microring resonator optical channel dropping filters," IEEE Photonics Tech. Lett. 10, 549-551 (1998).
[CrossRef]

1996 (1)

G. G. Vienne, W. S. Brocklesby, R. S. Brown, J. E. Caplen, Z. J. Chen, Z. E. Harutjunian, J. D. Minelly, J. E. Roman, D. N. Payne, "Role of aluminum in Er3+: Yb3+ codoped aluminiphosphosilicate optical fibres," Opt. Fiber Technol. 2, 387-393 (1996).
[CrossRef]

1995 (2)

1992 (1)

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, "Whispering-gallery mode microdisk lasers," Appl. Phys. Lett. 60, 289-291 (1992).
[CrossRef]

1991 (1)

W. L. Barnes, R. L. Laming, E. J. Tarbox, and P. R. Morkel, "Absorption and emission cross section of Er3+ doped silica fibers," IEEE J. Quantum Electron. 27, 1004-1010 (1991).
[CrossRef]

1982 (1)

Arnold, S.

F. Vollmer, D. Braun, A. Libchaber, S. M. Khoshsima, I. Teraoka, and S. Arnold, "Protein detection by optical shift of a resonant microcavity," Appl. Phys. Lett. 80, 4057-4059 (2002).
[CrossRef]

Ashcom, J. B.

L. Tong, R. R. Gattass, J. B. Ashcom, S. He, J. Lou, M. Shen, I. Maxwell, and E. Mazur, "Subwavelength-diameter silica wires for low-loss optical wave guiding," Nature 426, 816-819 (2003).
[CrossRef] [PubMed]

Barclay, P. E.

K. Srinivasan, P. E. Barclay, O. Painter, J. Chen, A. Y. Cho, and C. Gmachl, "Experimental demonstration of a high quality factor photonic crystal microcavity," Appl. Phys. Lett. 83, 1915-1917 (2003).
[CrossRef]

Barnes, W. L.

W. L. Barnes, R. L. Laming, E. J. Tarbox, and P. R. Morkel, "Absorption and emission cross section of Er3+ doped silica fibers," IEEE J. Quantum Electron. 27, 1004-1010 (1991).
[CrossRef]

Birks, T. A.

Braun, D.

F. Vollmer, D. Braun, A. Libchaber, S. M. Khoshsima, I. Teraoka, and S. Arnold, "Protein detection by optical shift of a resonant microcavity," Appl. Phys. Lett. 80, 4057-4059 (2002).
[CrossRef]

Brocklesby, W. S.

G. G. Vienne, W. S. Brocklesby, R. S. Brown, J. E. Caplen, Z. J. Chen, Z. E. Harutjunian, J. D. Minelly, J. E. Roman, D. N. Payne, "Role of aluminum in Er3+: Yb3+ codoped aluminiphosphosilicate optical fibres," Opt. Fiber Technol. 2, 387-393 (1996).
[CrossRef]

Brown, R. S.

G. G. Vienne, W. S. Brocklesby, R. S. Brown, J. E. Caplen, Z. J. Chen, Z. E. Harutjunian, J. D. Minelly, J. E. Roman, D. N. Payne, "Role of aluminum in Er3+: Yb3+ codoped aluminiphosphosilicate optical fibres," Opt. Fiber Technol. 2, 387-393 (1996).
[CrossRef]

Buck, J. R.

J. R. Buck, and H. J. Kimble, "Optimal sizes of dielectric microspheres for cavity QED with strong Coupling," Phys. Rev. A 67, 033806 (2003).
[CrossRef]

Cai, M.

M. Cai, O. Painter, K. J. Vahala, and P. C. Sercel, "Fiber-coupled microsphere laser," Opt. Lett. 25, 1430-1432 (2000).
[CrossRef]

M. Cai, O. Painter, and K. J. Vahala, "Observation of critical coupling in a fiber taper to a silica-microsphere whisper-gallery mode system," Phys. Rev. Lett. 85,74-77 (2000).
[CrossRef] [PubMed]

Caplen, J. E.

G. G. Vienne, J. E. Caplen, L. Dong, J. D. Minelly, J. Nilsson, and D. N. Payne, "Fabrication and Characterization of Yb3+: Er3+ Phosphosilicate Fibers for Lasers," J. Lightwave Technol. 16, 1990-2001 (1998).
[CrossRef]

G. G. Vienne, W. S. Brocklesby, R. S. Brown, J. E. Caplen, Z. J. Chen, Z. E. Harutjunian, J. D. Minelly, J. E. Roman, D. N. Payne, "Role of aluminum in Er3+: Yb3+ codoped aluminiphosphosilicate optical fibres," Opt. Fiber Technol. 2, 387-393 (1996).
[CrossRef]

Chen, J.

K. Srinivasan, P. E. Barclay, O. Painter, J. Chen, A. Y. Cho, and C. Gmachl, "Experimental demonstration of a high quality factor photonic crystal microcavity," Appl. Phys. Lett. 83, 1915-1917 (2003).
[CrossRef]

Chen, Z. J.

G. G. Vienne, W. S. Brocklesby, R. S. Brown, J. E. Caplen, Z. J. Chen, Z. E. Harutjunian, J. D. Minelly, J. E. Roman, D. N. Payne, "Role of aluminum in Er3+: Yb3+ codoped aluminiphosphosilicate optical fibres," Opt. Fiber Technol. 2, 387-393 (1996).
[CrossRef]

Cho, A. Y.

K. Srinivasan, P. E. Barclay, O. Painter, J. Chen, A. Y. Cho, and C. Gmachl, "Experimental demonstration of a high quality factor photonic crystal microcavity," Appl. Phys. Lett. 83, 1915-1917 (2003).
[CrossRef]

Chodorow, M.

Chu, S. T.

B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Thoen, S. T. Chu, H. A. Haus, and E. P. Ippen, "Ultra-compact Si-SiO2 microring resonator optical channel dropping filters," IEEE Photonics Tech. Lett. 10, 549-551 (1998).
[CrossRef]

Dong, L.

Dulashko, Y.

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

Fini, J. M.

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

Foresi, J. S.

B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Thoen, S. T. Chu, H. A. Haus, and E. P. Ippen, "Ultra-compact Si-SiO2 microring resonator optical channel dropping filters," IEEE Photonics Tech. Lett. 10, 549-551 (1998).
[CrossRef]

Gattass, R. R.

L. Tong, R. R. Gattass, J. B. Ashcom, S. He, J. Lou, M. Shen, I. Maxwell, and E. Mazur, "Subwavelength-diameter silica wires for low-loss optical wave guiding," Nature 426, 816-819 (2003).
[CrossRef] [PubMed]

Gmachl, C.

K. Srinivasan, P. E. Barclay, O. Painter, J. Chen, A. Y. Cho, and C. Gmachl, "Experimental demonstration of a high quality factor photonic crystal microcavity," Appl. Phys. Lett. 83, 1915-1917 (2003).
[CrossRef]

Guo, X.

X. Jiang, L. Tong, G. Vienne, X. Guo, A. Tsao, Q. Yang and D. Yang, "Demonstration of optical microfiber knot resonators," Appl. Phys. Lett. 88, 223501 (2006).
[CrossRef]

Hale, A.

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

Harutjunian, Z. E.

G. G. Vienne, W. S. Brocklesby, R. S. Brown, J. E. Caplen, Z. J. Chen, Z. E. Harutjunian, J. D. Minelly, J. E. Roman, D. N. Payne, "Role of aluminum in Er3+: Yb3+ codoped aluminiphosphosilicate optical fibres," Opt. Fiber Technol. 2, 387-393 (1996).
[CrossRef]

Haus, H. A.

B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Thoen, S. T. Chu, H. A. Haus, and E. P. Ippen, "Ultra-compact Si-SiO2 microring resonator optical channel dropping filters," IEEE Photonics Tech. Lett. 10, 549-551 (1998).
[CrossRef]

He, J.

He, S.

L. Tong, R. R. Gattass, J. B. Ashcom, S. He, J. Lou, M. Shen, I. Maxwell, and E. Mazur, "Subwavelength-diameter silica wires for low-loss optical wave guiding," Nature 426, 816-819 (2003).
[CrossRef] [PubMed]

Hsu, K.

Hu, L.

Ippen, E. P.

B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Thoen, S. T. Chu, H. A. Haus, and E. P. Ippen, "Ultra-compact Si-SiO2 microring resonator optical channel dropping filters," IEEE Photonics Tech. Lett. 10, 549-551 (1998).
[CrossRef]

Jeong, Y.

Jiang, X.

X. Jiang, L. Tong, G. Vienne, X. Guo, A. Tsao, Q. Yang and D. Yang, "Demonstration of optical microfiber knot resonators," Appl. Phys. Lett. 88, 223501 (2006).
[CrossRef]

Kalkman, J.

A. Polman, B. Min, J. Kalkman, T. J. Kippenberg and K. J. Vahala, "Ultralow-threshold erbium-implanted toroidal microlaser on silicon," Appl. Phys. Lett. 84, 1037-1039 (2004).
[CrossRef]

Khoshsima, S. M.

F. Vollmer, D. Braun, A. Libchaber, S. M. Khoshsima, I. Teraoka, and S. Arnold, "Protein detection by optical shift of a resonant microcavity," Appl. Phys. Lett. 80, 4057-4059 (2002).
[CrossRef]

Kimble, H. J.

J. R. Buck, and H. J. Kimble, "Optimal sizes of dielectric microspheres for cavity QED with strong Coupling," Phys. Rev. A 67, 033806 (2003).
[CrossRef]

Kippenberg, T. J.

A. Polman, B. Min, J. Kalkman, T. J. Kippenberg and K. J. Vahala, "Ultralow-threshold erbium-implanted toroidal microlaser on silicon," Appl. Phys. Lett. 84, 1037-1039 (2004).
[CrossRef]

Kringlebotn, J. T.

Laming, R. L.

W. L. Barnes, R. L. Laming, E. J. Tarbox, and P. R. Morkel, "Absorption and emission cross section of Er3+ doped silica fibers," IEEE J. Quantum Electron. 27, 1004-1010 (1991).
[CrossRef]

Leon-Saval, S. G.

Levi, A. F. J.

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, "Whispering-gallery mode microdisk lasers," Appl. Phys. Lett. 60, 289-291 (1992).
[CrossRef]

Libchaber, A.

F. Vollmer, D. Braun, A. Libchaber, S. M. Khoshsima, I. Teraoka, and S. Arnold, "Protein detection by optical shift of a resonant microcavity," Appl. Phys. Lett. 80, 4057-4059 (2002).
[CrossRef]

Little, B. E.

B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Thoen, S. T. Chu, H. A. Haus, and E. P. Ippen, "Ultra-compact Si-SiO2 microring resonator optical channel dropping filters," IEEE Photonics Tech. Lett. 10, 549-551 (1998).
[CrossRef]

Logan, R. A.

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, "Whispering-gallery mode microdisk lasers," Appl. Phys. Lett. 60, 289-291 (1992).
[CrossRef]

Lou, J.

Mason, M. W.

Maxwell, I.

L. Tong, R. R. Gattass, J. B. Ashcom, S. He, J. Lou, M. Shen, I. Maxwell, and E. Mazur, "Subwavelength-diameter silica wires for low-loss optical wave guiding," Nature 426, 816-819 (2003).
[CrossRef] [PubMed]

Mazur, E.

L. Tong, J. Lou, and E. Mazur, "Single-mode guiding properties of subwavelength-diameter silica and silicon wire waveguides," Opt. Express 12, 1025-1035 (2004).
[CrossRef] [PubMed]

L. Tong, R. R. Gattass, J. B. Ashcom, S. He, J. Lou, M. Shen, I. Maxwell, and E. Mazur, "Subwavelength-diameter silica wires for low-loss optical wave guiding," Nature 426, 816-819 (2003).
[CrossRef] [PubMed]

McCall, S. L.

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, "Whispering-gallery mode microdisk lasers," Appl. Phys. Lett. 60, 289-291 (1992).
[CrossRef]

Miller, C. M.

Min, B.

A. Polman, B. Min, J. Kalkman, T. J. Kippenberg and K. J. Vahala, "Ultralow-threshold erbium-implanted toroidal microlaser on silicon," Appl. Phys. Lett. 84, 1037-1039 (2004).
[CrossRef]

Minelly, J. D.

G. G. Vienne, J. E. Caplen, L. Dong, J. D. Minelly, J. Nilsson, and D. N. Payne, "Fabrication and Characterization of Yb3+: Er3+ Phosphosilicate Fibers for Lasers," J. Lightwave Technol. 16, 1990-2001 (1998).
[CrossRef]

G. G. Vienne, W. S. Brocklesby, R. S. Brown, J. E. Caplen, Z. J. Chen, Z. E. Harutjunian, J. D. Minelly, J. E. Roman, D. N. Payne, "Role of aluminum in Er3+: Yb3+ codoped aluminiphosphosilicate optical fibres," Opt. Fiber Technol. 2, 387-393 (1996).
[CrossRef]

Morkel, P. R.

W. L. Barnes, R. L. Laming, E. J. Tarbox, and P. R. Morkel, "Absorption and emission cross section of Er3+ doped silica fibers," IEEE J. Quantum Electron. 27, 1004-1010 (1991).
[CrossRef]

Nilsson, J.

Painter, O.

K. Srinivasan, P. E. Barclay, O. Painter, J. Chen, A. Y. Cho, and C. Gmachl, "Experimental demonstration of a high quality factor photonic crystal microcavity," Appl. Phys. Lett. 83, 1915-1917 (2003).
[CrossRef]

M. Cai, O. Painter, K. J. Vahala, and P. C. Sercel, "Fiber-coupled microsphere laser," Opt. Lett. 25, 1430-1432 (2000).
[CrossRef]

M. Cai, O. Painter, and K. J. Vahala, "Observation of critical coupling in a fiber taper to a silica-microsphere whisper-gallery mode system," Phys. Rev. Lett. 85,74-77 (2000).
[CrossRef] [PubMed]

Payne, D.

Payne, D. N.

Pearton, S. J.

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, "Whispering-gallery mode microdisk lasers," Appl. Phys. Lett. 60, 289-291 (1992).
[CrossRef]

Polman, A.

A. Polman, B. Min, J. Kalkman, T. J. Kippenberg and K. J. Vahala, "Ultralow-threshold erbium-implanted toroidal microlaser on silicon," Appl. Phys. Lett. 84, 1037-1039 (2004).
[CrossRef]

Qiu, J.

Roman, J. E.

G. G. Vienne, W. S. Brocklesby, R. S. Brown, J. E. Caplen, Z. J. Chen, Z. E. Harutjunian, J. D. Minelly, J. E. Roman, D. N. Payne, "Role of aluminum in Er3+: Yb3+ codoped aluminiphosphosilicate optical fibres," Opt. Fiber Technol. 2, 387-393 (1996).
[CrossRef]

Russell, P. St. J.

Sahu, J.

Sercel, P. C.

Shaw, H. J.

Shen, M.

L. Tong, R. R. Gattass, J. B. Ashcom, S. He, J. Lou, M. Shen, I. Maxwell, and E. Mazur, "Subwavelength-diameter silica wires for low-loss optical wave guiding," Nature 426, 816-819 (2003).
[CrossRef] [PubMed]

Shen, Y.

Slusher, R. E.

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, "Whispering-gallery mode microdisk lasers," Appl. Phys. Lett. 60, 289-291 (1992).
[CrossRef]

Srinivasan, K.

K. Srinivasan, P. E. Barclay, O. Painter, J. Chen, A. Y. Cho, and C. Gmachl, "Experimental demonstration of a high quality factor photonic crystal microcavity," Appl. Phys. Lett. 83, 1915-1917 (2003).
[CrossRef]

Steinmeyer, G.

B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Thoen, S. T. Chu, H. A. Haus, and E. P. Ippen, "Ultra-compact Si-SiO2 microring resonator optical channel dropping filters," IEEE Photonics Tech. Lett. 10, 549-551 (1998).
[CrossRef]

Stokes, L. F.

Sumetsky, M.

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

M. Sumetsky, "Optical fiber microcoil resonator," Opt. Express 12, 2303-2316 (2004).
[CrossRef] [PubMed]

Tarbox, E. J.

W. L. Barnes, R. L. Laming, E. J. Tarbox, and P. R. Morkel, "Absorption and emission cross section of Er3+ doped silica fibers," IEEE J. Quantum Electron. 27, 1004-1010 (1991).
[CrossRef]

Teraoka, I.

F. Vollmer, D. Braun, A. Libchaber, S. M. Khoshsima, I. Teraoka, and S. Arnold, "Protein detection by optical shift of a resonant microcavity," Appl. Phys. Lett. 80, 4057-4059 (2002).
[CrossRef]

Thoen, E. R.

B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Thoen, S. T. Chu, H. A. Haus, and E. P. Ippen, "Ultra-compact Si-SiO2 microring resonator optical channel dropping filters," IEEE Photonics Tech. Lett. 10, 549-551 (1998).
[CrossRef]

Tong, L.

X. Jiang, L. Tong, G. Vienne, X. Guo, A. Tsao, Q. Yang and D. Yang, "Demonstration of optical microfiber knot resonators," Appl. Phys. Lett. 88, 223501 (2006).
[CrossRef]

L. Tong, L. Hu, J. Zhang, J. Qiu, Q. Yang, J. Lou, Y. Shen, J. He, and Z. Ye, "Photonic nanowires directly drawn from bulk glasses," Opt. Express 14, 82-87 (2006).
[CrossRef] [PubMed]

L. Tong, J. Lou, and E. Mazur, "Single-mode guiding properties of subwavelength-diameter silica and silicon wire waveguides," Opt. Express 12, 1025-1035 (2004).
[CrossRef] [PubMed]

L. Tong, R. R. Gattass, J. B. Ashcom, S. He, J. Lou, M. Shen, I. Maxwell, and E. Mazur, "Subwavelength-diameter silica wires for low-loss optical wave guiding," Nature 426, 816-819 (2003).
[CrossRef] [PubMed]

Toratani, H.

X. Zou and H. Toratani, "Evaluation of spectroscopic properties of Yb3+-doped glasses," Phys. Rev. B 52,15889-15897 (1995).
[CrossRef]

Tsao, A.

X. Jiang, L. Tong, G. Vienne, X. Guo, A. Tsao, Q. Yang and D. Yang, "Demonstration of optical microfiber knot resonators," Appl. Phys. Lett. 88, 223501 (2006).
[CrossRef]

Vahala, K. J.

A. Polman, B. Min, J. Kalkman, T. J. Kippenberg and K. J. Vahala, "Ultralow-threshold erbium-implanted toroidal microlaser on silicon," Appl. Phys. Lett. 84, 1037-1039 (2004).
[CrossRef]

M. Cai, O. Painter, K. J. Vahala, and P. C. Sercel, "Fiber-coupled microsphere laser," Opt. Lett. 25, 1430-1432 (2000).
[CrossRef]

M. Cai, O. Painter, and K. J. Vahala, "Observation of critical coupling in a fiber taper to a silica-microsphere whisper-gallery mode system," Phys. Rev. Lett. 85,74-77 (2000).
[CrossRef] [PubMed]

Vienne, G.

X. Jiang, L. Tong, G. Vienne, X. Guo, A. Tsao, Q. Yang and D. Yang, "Demonstration of optical microfiber knot resonators," Appl. Phys. Lett. 88, 223501 (2006).
[CrossRef]

Vienne, G. G.

G. G. Vienne, J. E. Caplen, L. Dong, J. D. Minelly, J. Nilsson, and D. N. Payne, "Fabrication and Characterization of Yb3+: Er3+ Phosphosilicate Fibers for Lasers," J. Lightwave Technol. 16, 1990-2001 (1998).
[CrossRef]

G. G. Vienne, W. S. Brocklesby, R. S. Brown, J. E. Caplen, Z. J. Chen, Z. E. Harutjunian, J. D. Minelly, J. E. Roman, D. N. Payne, "Role of aluminum in Er3+: Yb3+ codoped aluminiphosphosilicate optical fibres," Opt. Fiber Technol. 2, 387-393 (1996).
[CrossRef]

Vollmer, F.

F. Vollmer, D. Braun, A. Libchaber, S. M. Khoshsima, I. Teraoka, and S. Arnold, "Protein detection by optical shift of a resonant microcavity," Appl. Phys. Lett. 80, 4057-4059 (2002).
[CrossRef]

Wadsworth, W. J.

Yang, D.

X. Jiang, L. Tong, G. Vienne, X. Guo, A. Tsao, Q. Yang and D. Yang, "Demonstration of optical microfiber knot resonators," Appl. Phys. Lett. 88, 223501 (2006).
[CrossRef]

Yang, Q.

X. Jiang, L. Tong, G. Vienne, X. Guo, A. Tsao, Q. Yang and D. Yang, "Demonstration of optical microfiber knot resonators," Appl. Phys. Lett. 88, 223501 (2006).
[CrossRef]

L. Tong, L. Hu, J. Zhang, J. Qiu, Q. Yang, J. Lou, Y. Shen, J. He, and Z. Ye, "Photonic nanowires directly drawn from bulk glasses," Opt. Express 14, 82-87 (2006).
[CrossRef] [PubMed]

Ye, Z.

Zhang, J.

Zou, X.

X. Zou and H. Toratani, "Evaluation of spectroscopic properties of Yb3+-doped glasses," Phys. Rev. B 52,15889-15897 (1995).
[CrossRef]

Appl. Phys. Lett. (6)

F. Vollmer, D. Braun, A. Libchaber, S. M. Khoshsima, I. Teraoka, and S. Arnold, "Protein detection by optical shift of a resonant microcavity," Appl. Phys. Lett. 80, 4057-4059 (2002).
[CrossRef]

K. Srinivasan, P. E. Barclay, O. Painter, J. Chen, A. Y. Cho, and C. Gmachl, "Experimental demonstration of a high quality factor photonic crystal microcavity," Appl. Phys. Lett. 83, 1915-1917 (2003).
[CrossRef]

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, "Whispering-gallery mode microdisk lasers," Appl. Phys. Lett. 60, 289-291 (1992).
[CrossRef]

A. Polman, B. Min, J. Kalkman, T. J. Kippenberg and K. J. Vahala, "Ultralow-threshold erbium-implanted toroidal microlaser on silicon," Appl. Phys. Lett. 84, 1037-1039 (2004).
[CrossRef]

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

X. Jiang, L. Tong, G. Vienne, X. Guo, A. Tsao, Q. Yang and D. Yang, "Demonstration of optical microfiber knot resonators," Appl. Phys. Lett. 88, 223501 (2006).
[CrossRef]

IEEE J. Quantum Electron. (1)

W. L. Barnes, R. L. Laming, E. J. Tarbox, and P. R. Morkel, "Absorption and emission cross section of Er3+ doped silica fibers," IEEE J. Quantum Electron. 27, 1004-1010 (1991).
[CrossRef]

IEEE Photonics Tech. Lett. (1)

B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Thoen, S. T. Chu, H. A. Haus, and E. P. Ippen, "Ultra-compact Si-SiO2 microring resonator optical channel dropping filters," IEEE Photonics Tech. Lett. 10, 549-551 (1998).
[CrossRef]

J. Lightwave Technol. (1)

Nature (1)

L. Tong, R. R. Gattass, J. B. Ashcom, S. He, J. Lou, M. Shen, I. Maxwell, and E. Mazur, "Subwavelength-diameter silica wires for low-loss optical wave guiding," Nature 426, 816-819 (2003).
[CrossRef] [PubMed]

Opt. Express (5)

Opt. Fiber Technol. (1)

G. G. Vienne, W. S. Brocklesby, R. S. Brown, J. E. Caplen, Z. J. Chen, Z. E. Harutjunian, J. D. Minelly, J. E. Roman, D. N. Payne, "Role of aluminum in Er3+: Yb3+ codoped aluminiphosphosilicate optical fibres," Opt. Fiber Technol. 2, 387-393 (1996).
[CrossRef]

Opt. Lett. (3)

Phys. Rev. A (1)

J. R. Buck, and H. J. Kimble, "Optimal sizes of dielectric microspheres for cavity QED with strong Coupling," Phys. Rev. A 67, 033806 (2003).
[CrossRef]

Phys. Rev. B (1)

X. Zou and H. Toratani, "Evaluation of spectroscopic properties of Yb3+-doped glasses," Phys. Rev. B 52,15889-15897 (1995).
[CrossRef]

Phys. Rev. Lett. (1)

M. Cai, O. Painter, and K. J. Vahala, "Observation of critical coupling in a fiber taper to a silica-microsphere whisper-gallery mode system," Phys. Rev. Lett. 85,74-77 (2000).
[CrossRef] [PubMed]

Other (6)

AnthonyE.  Siegman, Laser (Mill Valley, California, 1986).

B. E. A. Saleh, and M. C. Teich, Fundamental of photonics (John Wiley & Sons, New York, 1991).
[CrossRef]

E. Desurvire, Erbium-Doped Fiber Amplifiers (Wiley, New York, 1994).

E. Udd, ed., Fiber Optic Sensors (Wiley, New York, 1991).

C. K. Madsen, and J. H. Zhao, Optical filter design and analysis: A signal processing approach (Wiley, New York, 1999).

P. Hariharan, Opital Interferometry, 2nd ed. (Academic, New York, 2003).

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Figures (7)

Fig. 1.
Fig. 1.

Schematic of a microfiber ring resonator. (a) The pump light I1,p is partially coupled into the ring by a fiber taper at the coupling region of the ring, of intensity coupling coefficient K p, and of coupling loss γp . The pump experiences loss of coefficient αp , as well as dephasing while propagating along the ring, and is partially coupled outside at the coupling region, resulting in a transmitted intensity, I4,p . Loss for the pump light is due to absorption and scattering, thus αp =αabs,p ,+αsc,p . For a glass microfiber suspended in air the refractive index contrast is at least 30% and the bending loss is neglected here. (b) The signal light resonates in the ring in two directions, I +,s and I -,s , and is coupled out at the coupling region, resulting in transmitted intensities I1,s and I4,s . The loss coefficient, the gain coefficient, the coupling loss at the coupling region, and the signal coupling factor, are denoted as αs , G, γs , and K s, respectively. Loss is assumed to be solely due to scattering, so αs =αsc,s .

Fig. 2.
Fig. 2.

(a) Intensity enhancement factor E versus pump coupling coefficient Kp . Each curve corresponds to different αpπD for the pump light, see labels. Kp =0 is the nonresonant case, whereas the peak values correspond to critical coupling. (b) Maximum of E versus αpπD. The coupling loss is assumed to be 0.003 for both (a) and (b).

Fig. 3.
Fig. 3.

Schematic diagram for three-level transitions (TLT) with corresponding rates. σabs,p , σabs , σem stand for the cross sectional areas for the pump absorption, the signal re-absorption, and the stimulated emission, respectively. Since only a fraction of light propagates in the sub wavelength fiber [19], the average pump and signal intensities in the fiber core are reduced by the overlap factors Γp and Γs . τ32 and τ are the spontaneous radiation lifetimes from |E3> to |E2> and |E2> to |E1>, respectively.

Fig. 4.
Fig. 4.

Threshold power Pth (dotted line) and quantum efficiency ηq (solid line) for glass microfiber rings made of (a) Er3+ doped Al2O3-SiO2 and (b) Yb3+ doped phosphate glass of spectroscopic parameters listed in Table 1. The diameters of the rings are assumed to be 1 mm for both (a) and (b). The diameters of the fibers are chosen to be 1.0 and 0.63 μm for (a) and (b) respectively, in order to maintain single-mode operation for the signal light and the same Γs in both cases [19]. The coupling loss γps) at the coupling region is assumed to be 0.3% [17]. The intensity coupling coefficient for the signal light (Ks) is set to the optimum values, 0.979 for (a) and 0.937 for (b). The scattering loss is assumed to be the same for the pump and the signal light, and is set to 0.001 dB/mm (0.002 cm-1) according to Ref [26]. The fractions of pump and signal intensities (Γp and Γs ) inside the fiber are calculated according Ref. [19], and are listed on the graphs.

Fig. 5.
Fig. 5.

Optimal threshold power Pth (dotted line) and quantum efficiency ηq (solid line) against the coupling loss γps) for (a) Er3+ doped Al2O3-SiO2 glass, and (b) Yb3+ doped phosphate glass microfiber rings. Curves of different colors stand for different K s, as labeled; the maximum values of γ (labeled as γmax ) are also shown. The parameters used for this simulation are listed on the graphs.

Fig. 6.
Fig. 6.

Threshold power Pth (dotted line), and quantum efficiency ηq (solid line) v.s. ring diameter D for three different values of Ks, in (a) Er3+ doped Al2O3-SiO2 glass and (b)Yb3+ doped phosphate glass microfiber rings. In (b), the concentration of Yb3+ ions is 5.0×10-20 cm-3 and Ks=0.939 is the optimum for a 0.2 mm diameter ring. Other parameters used for this simulation are listed in the figure and Table 1. The lowest limit of D (Dmin) for the three different values of Ks is also indicated. The region below 50 μm is shaded to indicate that below this diameter radiation losses may need to be taken into account.

Fig. 7.
Fig. 7.

Schematic of four-level-transition lasing process. The symbols used here are identical to the ones used for the three-level case, see caption of Fig. 3. In addition τ43 and τ21 stand for the spontaneous radiation lifetimes from |E4> to |E3> and from |E2> to |E1>, respectively.

Tables (1)

Tables Icon

Table 1 Spectroscopic parameters for Er/Al/Si glass and Yb/P glass

Equations (25)

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

{ E 3 , p = ( 1 γ p ) 1 2 [ ( 1 K p ) 1 2 E 1 , p + j K p 1 2 E 2 , p ] E 4 , p = ( 1 γ p ) 1 2 [ j K p 1 2 E 1 , p + ( 1 K p ) 1 2 E 2 , p ] } and E 2 , p = E 3 , p e α p π D 2 e jβπD ,
{ I 3 , p I 1 , p = 1 γ p I 4 , p I 1 , p = ( 1 γ p ) 2 e α p π D } .
{ I 3 , p I 1 , p = ( 1 γ p ) ( 1 K p ) ( 1 ( 1 γ p ) 1 2 K p 1 2 e α p π D 2 ) 2 I 4 , p I 1 , p = ( 1 γ p ) ( K p 1 2 ( 1 γ p ) 1 2 e α p π D 2 ) 2 ( 1 ( 1 γ p ) 1 2 K p 1 2 e α p π D 2 ) 2 } .
I p = 1 π D 0 π D I 3 , p e z α p dz = I 3 , p ( 1 e α p π D ) α p π D .
E = I p I 1 , p = ( 1 γ p ) ( 1 K p ) ( 1 ( 1 γ p ) 1 2 K p 1 2 e α p π D 2 ) 2 1 e α p π D α p π D .
E max = 1 γ p 1 ( 1 γ p ) e α p π D 1 e α p π D α p π D = 1 1 ( 1 γ p ) + e α p π D 1 e α p π D α p π D 1 γ p + 1 e α p π D 1 e α p π D α p π D ,
I 1 , s I , s = I 4 , s I + , s = ( 1 γ s ) ( 1 K s )
{ d N 1 dt = R N 1 + N 2 τ + N 2 W 21 N 1 W 12 N 1 + N 2 = N } ,
K s ( 1 γ s ) e α s π D e GπD = e GπD α tot , s π D = 1
α tot , s = α sc , s + 1 π D ln 1 K s + 1 π D ln 1 1 γ s .
I + , s + I , s = 1 Γ s h v s σ em ( 1 α tot , s Γ s N σ em ) Γ p I 3 , p h v p 1 e α p π D α p π D σ abs , p ( σ abs σ em + σ tot , s Γ s N σ em ) 1 τ ( 1 + σ abs σ em ) α tot , s Γ s N σ em .
α tot , s < Γ s σ em N .
Q s > 2 π n λ Γ s σ em N .
P th = 1 Γ p h v p σ abs , p 1 τ σ abs σ em + α tot , s ( Γ s σ em N ) 1 α tot , s ( Γ s σ em N ) 1 E A
α abs , p = Γ p N 1 σ abs , p = 1 α tot , s ( Γ s N σ em ) 1 + σ abs σ em Γ p N σ abs , p .
η q = ( I 3 , s + I 4 , s ) ( h υ s ) I p ( h υ p ) = Γ p Γ s [ ( 1 γ s ) ( 1 K s ) ] [ 1 α tot , s ( Γ s N σ em ) ] α tot , s ( 1 + σ abs σ em ) Γ s N σ abs , p E .
η q = α abs , p 1 E ( 1 K s ) ( 1 γ s ) α tot , s ,
η q α abs , p γ p 1 γ p 1 π D + α p 1 K s π D ( 1 γ s ) α sc , s + 1 n 1 K s π D + 1 n 1 1 γ s π D
α abs , p γ p π D + α abs , p + α sc , p 1 K s π D ( 1 γ s ) α sc , s + 1 K s π D + γ s π D .
D min = 1 n 1 K s + 1 n 1 1 γ s ( Γ s N σ em α sc , s ) π .
{ d N 3 dt = R N 1 W N 3 N 3 τ N 1 + N 3 = N } ,
P th = 1 Γ p h ν p σ abs , p 1 τ α tot , s ( Γ s σ em N ) 1 α tot , s ( Γ s σ em N ) 1 E A .
η q = ( I 3 , s + I 4 , s ) ( h υ s ) I p ( h υ p ) = Γ p Γ s ( 1 γ s ) ( 1 K s ) ( Γ s N σ em α tot , s 1 ) α abs , p σ em E .
η q = α abs , s 1 E ( 1 K s ) ( 1 γ s ) α tot , s ,
α abs , p = Γ p N 1 σ abs , p = ( 1 α tot , s Γ s N σ em ) Γ p N σ abs , p .

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