Abstract

We experimentally demonstrate thermo-optic locking of a semiconductor laser to an integrated toroidal optical microcavity. The lock is maintained for time periods exceeding twelve hours, without requiring any electronic control systems. Fast control is achieved by optical feedback induced by scattering centers within the microcavity, with thermal locking due to optical heating maintaining constructive interference between the cavity and the laser. Furthermore, the optical feedback acts to narrow the laser linewidth, with ultra high quality microtoroid resonances offering the potential for ultralow linewidth on-chip lasers.

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  1. S. M. Spillane, T. J. Kippenberg, K. J. Vahala, K. W. Goh, E. Wilcut, and H. J. Kimble, “Ultrahigh-Q toroidal microresonators for cavity quantum electrodynamics,” Phys. Rev. A 71(1), 013817 (2005).
    [CrossRef]
  2. T. J. Kippenberg, H. Rokhsari, T. Carmon, A. Scherer, and K. J. Vahala, “Analysis of radiation-pressure induced mechanical oscillation of an optical microcavity,” Phys. Rev. Lett. 95(3), 033901 (2005).
    [CrossRef] [PubMed]
  3. A. Polman, B. Min, J. Kalkman, T. J. Kippenberg, and K. J. Vahala, “Ultra-low-threshold erbium-implanted toroidal microlaser on silicon,” Appl. Phys. Lett. 84(7), 1037–1039 (2004).
    [CrossRef]
  4. A. M. Armani, R. P. Kulkarni, S. E. Fraser, R. C. Flagan, and K. J. Vahala, “Label-free, single-molecule detection with optical microcavities,” Science 317(5839), 783–787 (2007).
    [CrossRef] [PubMed]
  5. D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421(6926), 925–928 (2003).
    [CrossRef] [PubMed]
  6. C. E. Wieman and L. Hollberg, “Using diode lasers for atomic physics,” Rev. Sci. Instrum. 62(1), 1 (1991).
    [CrossRef]
  7. B. Dahmani, L. Hollberg, and R. Drullinger, “Frequency stabilization of semiconductor lasers by resonant optical feedback,” Opt. Lett. 12(11), 876–878 (1987).
    [CrossRef] [PubMed]
  8. F. Favre and D. Le Guen, “Spectral properties of a semiconductor laser coupled to a single mode fiber resonator,” IEEE J. Quantum Electron. 21(12), 1937–1946 (1985).
    [CrossRef]
  9. K. Kieu and M. Mansuripur, “Fiber laser using a microsphere resonator as a feedback element,” Opt. Lett. 32(3), 244–246 (2007).
    [CrossRef] [PubMed]
  10. A. Schoof, J. Grünert, S. Ritter, and A. Hemmerich, “Reducing the linewidth of a diode laser below 30 Hz by stabilization to a reference cavity with a finesse above 10(5).,” Opt. Lett. 26(20), 1562–1564 (2001).
    [CrossRef] [PubMed]
  11. D. S. Weiss, V. Sandoghdar, J. Hare, V. Lefèvre-Seguin, J. M. Raimond, and S. Haroche, “Splitting of high-Q Mie modes induced by light backscattering in silica microspheres,” Opt. Lett. 20(18), 1835–1837 (1995).
    [CrossRef] [PubMed]
  12. H. Rokhsari, S. M. Spillane, and K. J. Vahala, “Loss characterization in microcavities using the thermal bistability effect,” Appl. Phys. Lett. 85(15), 3029–3031 (2004).
    [CrossRef]
  13. W. P. Bowen, “Semiclassical modelling of cavity quantum electrodynamics with microtoroidal resonators in the weak driving limit,” Curr. Appl. Phys. 8(3-4), 429–432 (2008).
    [CrossRef]
  14. T. G. McRae and W. P. Bowen, “Time delayed entanglement from coherently coupled nonlinear cavities,” Phys. Rev. A 80, 010303(R) (2009).
  15. M. McGovern, T. G. McRae, G. Turner, A. J. Kay, R. J. Blaikie, and W. P. Bowen, “Laser frequency stabilization with toroidal optical microresonators,” Proc. SPIE 6801, 68010Y–1-68010Y–11 (2008).
  16. T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Modal coupling in traveling-wave resonators,” Opt. Lett. 27(19), 1669–1671 (2002).
    [CrossRef] [PubMed]
  17. T. Carmon, L. Yang, and K. J. Vahala, “Dynamical thermal behavior and thermal self-stability of microcavities,” Opt. Express 12(20), 4742–4750 (2004).
    [CrossRef] [PubMed]
  18. V. V. Vassiliev, V. L. Velichansky, V. S. Ilchenko, M. L. Gorodetsky, L. Hollberg, and A. V. Yarovitsky, “Narrow-line-width diode laser with a high-Q microsphere resonator,” Opt. Commun. 158(1-6), 305–312 (1998).
    [CrossRef]
  19. D. Armani, B. Min, A. Martin, and K. J. Vahala, “Electrical thermo-optic tuning of ultrahigh-Q microtoroid resonators,” Appl. Phys. Lett. 85(22), 5439–5441 (2004).
    [CrossRef]

2008

W. P. Bowen, “Semiclassical modelling of cavity quantum electrodynamics with microtoroidal resonators in the weak driving limit,” Curr. Appl. Phys. 8(3-4), 429–432 (2008).
[CrossRef]

2007

A. M. Armani, R. P. Kulkarni, S. E. Fraser, R. C. Flagan, and K. J. Vahala, “Label-free, single-molecule detection with optical microcavities,” Science 317(5839), 783–787 (2007).
[CrossRef] [PubMed]

K. Kieu and M. Mansuripur, “Fiber laser using a microsphere resonator as a feedback element,” Opt. Lett. 32(3), 244–246 (2007).
[CrossRef] [PubMed]

2005

S. M. Spillane, T. J. Kippenberg, K. J. Vahala, K. W. Goh, E. Wilcut, and H. J. Kimble, “Ultrahigh-Q toroidal microresonators for cavity quantum electrodynamics,” Phys. Rev. A 71(1), 013817 (2005).
[CrossRef]

T. J. Kippenberg, H. Rokhsari, T. Carmon, A. Scherer, and K. J. Vahala, “Analysis of radiation-pressure induced mechanical oscillation of an optical microcavity,” Phys. Rev. Lett. 95(3), 033901 (2005).
[CrossRef] [PubMed]

2004

A. Polman, B. Min, J. Kalkman, T. J. Kippenberg, and K. J. Vahala, “Ultra-low-threshold erbium-implanted toroidal microlaser on silicon,” Appl. Phys. Lett. 84(7), 1037–1039 (2004).
[CrossRef]

T. Carmon, L. Yang, and K. J. Vahala, “Dynamical thermal behavior and thermal self-stability of microcavities,” Opt. Express 12(20), 4742–4750 (2004).
[CrossRef] [PubMed]

H. Rokhsari, S. M. Spillane, and K. J. Vahala, “Loss characterization in microcavities using the thermal bistability effect,” Appl. Phys. Lett. 85(15), 3029–3031 (2004).
[CrossRef]

D. Armani, B. Min, A. Martin, and K. J. Vahala, “Electrical thermo-optic tuning of ultrahigh-Q microtoroid resonators,” Appl. Phys. Lett. 85(22), 5439–5441 (2004).
[CrossRef]

2003

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421(6926), 925–928 (2003).
[CrossRef] [PubMed]

2002

2001

1998

V. V. Vassiliev, V. L. Velichansky, V. S. Ilchenko, M. L. Gorodetsky, L. Hollberg, and A. V. Yarovitsky, “Narrow-line-width diode laser with a high-Q microsphere resonator,” Opt. Commun. 158(1-6), 305–312 (1998).
[CrossRef]

1995

1991

C. E. Wieman and L. Hollberg, “Using diode lasers for atomic physics,” Rev. Sci. Instrum. 62(1), 1 (1991).
[CrossRef]

1987

1985

F. Favre and D. Le Guen, “Spectral properties of a semiconductor laser coupled to a single mode fiber resonator,” IEEE J. Quantum Electron. 21(12), 1937–1946 (1985).
[CrossRef]

Armani, A. M.

A. M. Armani, R. P. Kulkarni, S. E. Fraser, R. C. Flagan, and K. J. Vahala, “Label-free, single-molecule detection with optical microcavities,” Science 317(5839), 783–787 (2007).
[CrossRef] [PubMed]

Armani, D.

D. Armani, B. Min, A. Martin, and K. J. Vahala, “Electrical thermo-optic tuning of ultrahigh-Q microtoroid resonators,” Appl. Phys. Lett. 85(22), 5439–5441 (2004).
[CrossRef]

Armani, D. K.

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421(6926), 925–928 (2003).
[CrossRef] [PubMed]

Bowen, W. P.

W. P. Bowen, “Semiclassical modelling of cavity quantum electrodynamics with microtoroidal resonators in the weak driving limit,” Curr. Appl. Phys. 8(3-4), 429–432 (2008).
[CrossRef]

Carmon, T.

T. J. Kippenberg, H. Rokhsari, T. Carmon, A. Scherer, and K. J. Vahala, “Analysis of radiation-pressure induced mechanical oscillation of an optical microcavity,” Phys. Rev. Lett. 95(3), 033901 (2005).
[CrossRef] [PubMed]

T. Carmon, L. Yang, and K. J. Vahala, “Dynamical thermal behavior and thermal self-stability of microcavities,” Opt. Express 12(20), 4742–4750 (2004).
[CrossRef] [PubMed]

Dahmani, B.

Drullinger, R.

Favre, F.

F. Favre and D. Le Guen, “Spectral properties of a semiconductor laser coupled to a single mode fiber resonator,” IEEE J. Quantum Electron. 21(12), 1937–1946 (1985).
[CrossRef]

Flagan, R. C.

A. M. Armani, R. P. Kulkarni, S. E. Fraser, R. C. Flagan, and K. J. Vahala, “Label-free, single-molecule detection with optical microcavities,” Science 317(5839), 783–787 (2007).
[CrossRef] [PubMed]

Fraser, S. E.

A. M. Armani, R. P. Kulkarni, S. E. Fraser, R. C. Flagan, and K. J. Vahala, “Label-free, single-molecule detection with optical microcavities,” Science 317(5839), 783–787 (2007).
[CrossRef] [PubMed]

Goh, K. W.

S. M. Spillane, T. J. Kippenberg, K. J. Vahala, K. W. Goh, E. Wilcut, and H. J. Kimble, “Ultrahigh-Q toroidal microresonators for cavity quantum electrodynamics,” Phys. Rev. A 71(1), 013817 (2005).
[CrossRef]

Gorodetsky, M. L.

V. V. Vassiliev, V. L. Velichansky, V. S. Ilchenko, M. L. Gorodetsky, L. Hollberg, and A. V. Yarovitsky, “Narrow-line-width diode laser with a high-Q microsphere resonator,” Opt. Commun. 158(1-6), 305–312 (1998).
[CrossRef]

Grünert, J.

Hare, J.

Haroche, S.

Hemmerich, A.

Hollberg, L.

V. V. Vassiliev, V. L. Velichansky, V. S. Ilchenko, M. L. Gorodetsky, L. Hollberg, and A. V. Yarovitsky, “Narrow-line-width diode laser with a high-Q microsphere resonator,” Opt. Commun. 158(1-6), 305–312 (1998).
[CrossRef]

C. E. Wieman and L. Hollberg, “Using diode lasers for atomic physics,” Rev. Sci. Instrum. 62(1), 1 (1991).
[CrossRef]

B. Dahmani, L. Hollberg, and R. Drullinger, “Frequency stabilization of semiconductor lasers by resonant optical feedback,” Opt. Lett. 12(11), 876–878 (1987).
[CrossRef] [PubMed]

Ilchenko, V. S.

V. V. Vassiliev, V. L. Velichansky, V. S. Ilchenko, M. L. Gorodetsky, L. Hollberg, and A. V. Yarovitsky, “Narrow-line-width diode laser with a high-Q microsphere resonator,” Opt. Commun. 158(1-6), 305–312 (1998).
[CrossRef]

Kalkman, J.

A. Polman, B. Min, J. Kalkman, T. J. Kippenberg, and K. J. Vahala, “Ultra-low-threshold erbium-implanted toroidal microlaser on silicon,” Appl. Phys. Lett. 84(7), 1037–1039 (2004).
[CrossRef]

Kieu, K.

Kimble, H. J.

S. M. Spillane, T. J. Kippenberg, K. J. Vahala, K. W. Goh, E. Wilcut, and H. J. Kimble, “Ultrahigh-Q toroidal microresonators for cavity quantum electrodynamics,” Phys. Rev. A 71(1), 013817 (2005).
[CrossRef]

Kippenberg, T. J.

T. J. Kippenberg, H. Rokhsari, T. Carmon, A. Scherer, and K. J. Vahala, “Analysis of radiation-pressure induced mechanical oscillation of an optical microcavity,” Phys. Rev. Lett. 95(3), 033901 (2005).
[CrossRef] [PubMed]

S. M. Spillane, T. J. Kippenberg, K. J. Vahala, K. W. Goh, E. Wilcut, and H. J. Kimble, “Ultrahigh-Q toroidal microresonators for cavity quantum electrodynamics,” Phys. Rev. A 71(1), 013817 (2005).
[CrossRef]

A. Polman, B. Min, J. Kalkman, T. J. Kippenberg, and K. J. Vahala, “Ultra-low-threshold erbium-implanted toroidal microlaser on silicon,” Appl. Phys. Lett. 84(7), 1037–1039 (2004).
[CrossRef]

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421(6926), 925–928 (2003).
[CrossRef] [PubMed]

T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Modal coupling in traveling-wave resonators,” Opt. Lett. 27(19), 1669–1671 (2002).
[CrossRef] [PubMed]

Kulkarni, R. P.

A. M. Armani, R. P. Kulkarni, S. E. Fraser, R. C. Flagan, and K. J. Vahala, “Label-free, single-molecule detection with optical microcavities,” Science 317(5839), 783–787 (2007).
[CrossRef] [PubMed]

Le Guen, D.

F. Favre and D. Le Guen, “Spectral properties of a semiconductor laser coupled to a single mode fiber resonator,” IEEE J. Quantum Electron. 21(12), 1937–1946 (1985).
[CrossRef]

Lefèvre-Seguin, V.

Mansuripur, M.

Martin, A.

D. Armani, B. Min, A. Martin, and K. J. Vahala, “Electrical thermo-optic tuning of ultrahigh-Q microtoroid resonators,” Appl. Phys. Lett. 85(22), 5439–5441 (2004).
[CrossRef]

Min, B.

D. Armani, B. Min, A. Martin, and K. J. Vahala, “Electrical thermo-optic tuning of ultrahigh-Q microtoroid resonators,” Appl. Phys. Lett. 85(22), 5439–5441 (2004).
[CrossRef]

A. Polman, B. Min, J. Kalkman, T. J. Kippenberg, and K. J. Vahala, “Ultra-low-threshold erbium-implanted toroidal microlaser on silicon,” Appl. Phys. Lett. 84(7), 1037–1039 (2004).
[CrossRef]

Polman, A.

A. Polman, B. Min, J. Kalkman, T. J. Kippenberg, and K. J. Vahala, “Ultra-low-threshold erbium-implanted toroidal microlaser on silicon,” Appl. Phys. Lett. 84(7), 1037–1039 (2004).
[CrossRef]

Raimond, J. M.

Ritter, S.

Rokhsari, H.

T. J. Kippenberg, H. Rokhsari, T. Carmon, A. Scherer, and K. J. Vahala, “Analysis of radiation-pressure induced mechanical oscillation of an optical microcavity,” Phys. Rev. Lett. 95(3), 033901 (2005).
[CrossRef] [PubMed]

H. Rokhsari, S. M. Spillane, and K. J. Vahala, “Loss characterization in microcavities using the thermal bistability effect,” Appl. Phys. Lett. 85(15), 3029–3031 (2004).
[CrossRef]

Sandoghdar, V.

Scherer, A.

T. J. Kippenberg, H. Rokhsari, T. Carmon, A. Scherer, and K. J. Vahala, “Analysis of radiation-pressure induced mechanical oscillation of an optical microcavity,” Phys. Rev. Lett. 95(3), 033901 (2005).
[CrossRef] [PubMed]

Schoof, A.

Spillane, S. M.

S. M. Spillane, T. J. Kippenberg, K. J. Vahala, K. W. Goh, E. Wilcut, and H. J. Kimble, “Ultrahigh-Q toroidal microresonators for cavity quantum electrodynamics,” Phys. Rev. A 71(1), 013817 (2005).
[CrossRef]

H. Rokhsari, S. M. Spillane, and K. J. Vahala, “Loss characterization in microcavities using the thermal bistability effect,” Appl. Phys. Lett. 85(15), 3029–3031 (2004).
[CrossRef]

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421(6926), 925–928 (2003).
[CrossRef] [PubMed]

T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Modal coupling in traveling-wave resonators,” Opt. Lett. 27(19), 1669–1671 (2002).
[CrossRef] [PubMed]

Vahala, K. J.

A. M. Armani, R. P. Kulkarni, S. E. Fraser, R. C. Flagan, and K. J. Vahala, “Label-free, single-molecule detection with optical microcavities,” Science 317(5839), 783–787 (2007).
[CrossRef] [PubMed]

T. J. Kippenberg, H. Rokhsari, T. Carmon, A. Scherer, and K. J. Vahala, “Analysis of radiation-pressure induced mechanical oscillation of an optical microcavity,” Phys. Rev. Lett. 95(3), 033901 (2005).
[CrossRef] [PubMed]

S. M. Spillane, T. J. Kippenberg, K. J. Vahala, K. W. Goh, E. Wilcut, and H. J. Kimble, “Ultrahigh-Q toroidal microresonators for cavity quantum electrodynamics,” Phys. Rev. A 71(1), 013817 (2005).
[CrossRef]

A. Polman, B. Min, J. Kalkman, T. J. Kippenberg, and K. J. Vahala, “Ultra-low-threshold erbium-implanted toroidal microlaser on silicon,” Appl. Phys. Lett. 84(7), 1037–1039 (2004).
[CrossRef]

T. Carmon, L. Yang, and K. J. Vahala, “Dynamical thermal behavior and thermal self-stability of microcavities,” Opt. Express 12(20), 4742–4750 (2004).
[CrossRef] [PubMed]

H. Rokhsari, S. M. Spillane, and K. J. Vahala, “Loss characterization in microcavities using the thermal bistability effect,” Appl. Phys. Lett. 85(15), 3029–3031 (2004).
[CrossRef]

D. Armani, B. Min, A. Martin, and K. J. Vahala, “Electrical thermo-optic tuning of ultrahigh-Q microtoroid resonators,” Appl. Phys. Lett. 85(22), 5439–5441 (2004).
[CrossRef]

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421(6926), 925–928 (2003).
[CrossRef] [PubMed]

T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Modal coupling in traveling-wave resonators,” Opt. Lett. 27(19), 1669–1671 (2002).
[CrossRef] [PubMed]

Vassiliev, V. V.

V. V. Vassiliev, V. L. Velichansky, V. S. Ilchenko, M. L. Gorodetsky, L. Hollberg, and A. V. Yarovitsky, “Narrow-line-width diode laser with a high-Q microsphere resonator,” Opt. Commun. 158(1-6), 305–312 (1998).
[CrossRef]

Velichansky, V. L.

V. V. Vassiliev, V. L. Velichansky, V. S. Ilchenko, M. L. Gorodetsky, L. Hollberg, and A. V. Yarovitsky, “Narrow-line-width diode laser with a high-Q microsphere resonator,” Opt. Commun. 158(1-6), 305–312 (1998).
[CrossRef]

Weiss, D. S.

Wieman, C. E.

C. E. Wieman and L. Hollberg, “Using diode lasers for atomic physics,” Rev. Sci. Instrum. 62(1), 1 (1991).
[CrossRef]

Wilcut, E.

S. M. Spillane, T. J. Kippenberg, K. J. Vahala, K. W. Goh, E. Wilcut, and H. J. Kimble, “Ultrahigh-Q toroidal microresonators for cavity quantum electrodynamics,” Phys. Rev. A 71(1), 013817 (2005).
[CrossRef]

Yang, L.

Yarovitsky, A. V.

V. V. Vassiliev, V. L. Velichansky, V. S. Ilchenko, M. L. Gorodetsky, L. Hollberg, and A. V. Yarovitsky, “Narrow-line-width diode laser with a high-Q microsphere resonator,” Opt. Commun. 158(1-6), 305–312 (1998).
[CrossRef]

Appl. Phys. Lett.

A. Polman, B. Min, J. Kalkman, T. J. Kippenberg, and K. J. Vahala, “Ultra-low-threshold erbium-implanted toroidal microlaser on silicon,” Appl. Phys. Lett. 84(7), 1037–1039 (2004).
[CrossRef]

H. Rokhsari, S. M. Spillane, and K. J. Vahala, “Loss characterization in microcavities using the thermal bistability effect,” Appl. Phys. Lett. 85(15), 3029–3031 (2004).
[CrossRef]

D. Armani, B. Min, A. Martin, and K. J. Vahala, “Electrical thermo-optic tuning of ultrahigh-Q microtoroid resonators,” Appl. Phys. Lett. 85(22), 5439–5441 (2004).
[CrossRef]

Curr. Appl. Phys.

W. P. Bowen, “Semiclassical modelling of cavity quantum electrodynamics with microtoroidal resonators in the weak driving limit,” Curr. Appl. Phys. 8(3-4), 429–432 (2008).
[CrossRef]

IEEE J. Quantum Electron.

F. Favre and D. Le Guen, “Spectral properties of a semiconductor laser coupled to a single mode fiber resonator,” IEEE J. Quantum Electron. 21(12), 1937–1946 (1985).
[CrossRef]

Nature

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421(6926), 925–928 (2003).
[CrossRef] [PubMed]

Opt. Commun.

V. V. Vassiliev, V. L. Velichansky, V. S. Ilchenko, M. L. Gorodetsky, L. Hollberg, and A. V. Yarovitsky, “Narrow-line-width diode laser with a high-Q microsphere resonator,” Opt. Commun. 158(1-6), 305–312 (1998).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. A

S. M. Spillane, T. J. Kippenberg, K. J. Vahala, K. W. Goh, E. Wilcut, and H. J. Kimble, “Ultrahigh-Q toroidal microresonators for cavity quantum electrodynamics,” Phys. Rev. A 71(1), 013817 (2005).
[CrossRef]

Phys. Rev. Lett.

T. J. Kippenberg, H. Rokhsari, T. Carmon, A. Scherer, and K. J. Vahala, “Analysis of radiation-pressure induced mechanical oscillation of an optical microcavity,” Phys. Rev. Lett. 95(3), 033901 (2005).
[CrossRef] [PubMed]

Rev. Sci. Instrum.

C. E. Wieman and L. Hollberg, “Using diode lasers for atomic physics,” Rev. Sci. Instrum. 62(1), 1 (1991).
[CrossRef]

Science

A. M. Armani, R. P. Kulkarni, S. E. Fraser, R. C. Flagan, and K. J. Vahala, “Label-free, single-molecule detection with optical microcavities,” Science 317(5839), 783–787 (2007).
[CrossRef] [PubMed]

Other

T. G. McRae and W. P. Bowen, “Time delayed entanglement from coherently coupled nonlinear cavities,” Phys. Rev. A 80, 010303(R) (2009).

M. McGovern, T. G. McRae, G. Turner, A. J. Kay, R. J. Blaikie, and W. P. Bowen, “Laser frequency stabilization with toroidal optical microresonators,” Proc. SPIE 6801, 68010Y–1-68010Y–11 (2008).

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Figures (7)

Fig. 1
Fig. 1

(Color online). Thermo-optic locking of a laser diode using a WGM cavity.

Fig. 4
Fig. 4

Measurement and model of thermo-optic locking process for a toroid with γ l /2π = 61 MHz. γ in /2π = 31 MHz, g/2π = 8 MHz, and nL = 1.8 m. (a) Measurement showing the back reflected power immediately after obtaining lock. (b-d) Model of the thermally shifted microtoroid spectral response with the laser locking frequency indicated by the vertical line, corresponding to the three labeled points in the experimental data. The thermal detuning of the resonator was Δ/2π = 0, 20, and 40 MHz respectively for b), c), and d).

Fig. 2
Fig. 2

(Color online) Schematic of the experimental setup. Solid and dashed red lines respectively show optical paths in fiber and in free space. “A” indicates the point where switching between the reference laser and the laser diode is performed.

Fig. 3
Fig. 3

(Color online) Spectral response of the forward and backward propagating fields in the microtoroid in the critically coupled (a) and under-coupled (b) regimes. Top curve: forwards propagating field. Bottom curve: backwards propagating field. Solid lines: theoretical model of the transmission T = |ET /Ein |2 and reflection R = |ER /Ein |2 with g/2π = 33 MHz, Δ = 0, and γ l /2π = 15 MHz; and input coupling rates of γ in /2π = 36 and 5.4 MHz, respectively, for the critically coupled and under-coupled regimes.

Fig. 5
Fig. 5

(Color online) Typical trace of the laser acquiring lock. (a) Forward- propagating power. (b) Backward-propagating power. (c) Laser diode power tapped off from partial reflector.

Fig. 6
Fig. 6

(Color online) Comparison of beat signals for thermo-optically locked and free running lasers. (a) Beat signal for unlocked laser (100 kHz RBW; 30 kHz video bandwidth). (b) Beat signal for locked laser (300 kHz RBW; 30 kHz video bandwidth). Solid lines: Lorentzian fit. (c) Root Allan variance of unlocked (solid blue line) and locked (dashed red line) laser beat signals (300 kHz RBW, 30 kHz video bandwidth).

Fig. 7
Fig. 7

(Color online) (a) Schematic of single chip with multiple integrated microtoroids; with each cavity enabling low linewidth thermo-optically locked lasers at different wavelengths. (b) Wavelength spectrum from two different microtoroids with far separated cavity resonance wavelengths. (c) Typical beat spectra for each laser (300 kHz RBW).

Equations (3)

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E R ( ω ) = E i n ( ω ) exp ( 2 π i n L λ ) { 2 i γ i n g [ γ + i ( ω + Δ ) ] 2 + g 2 }
E T ( ω ) = E i n ( ω ) exp ( 2 π i n L λ ) { 1 2 γ i n [ γ + i ( ω + Δ ) ] [ γ + i ( ω + Δ ) ] 2 + g 2 }
E f b ( ω ) = E R ( ω ) exp ( 2 π i n L λ ) = E i n ( ω ) exp ( 2 π i ω ω F S R ) { 2 γ i n g [ γ + i ( ω + Δ ) ] 2 + g 2 }

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