Abstract

We present the analysis of the self-injection locking of a single-frequency laser diode to a high-Q whispering gallery mode (WGM) microresonator with Rayleigh backscattering. Simple analytical formulas for the width of the locking band and resulting laser linewidth are derived.

© 2017 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  19. L. Hollberg and M. Ohtsu, “Modulatable narrow–linewidth semiconductor lasers,” Appl. Phys. Lett. 53, 944–946 (1988).
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  20. P. Laurent, A. Clairon, and C. Breant, “Frequency noise analysis of optically self-locked diode lasers,” IEEE J. Quantum Electron. 25, 1131–1142 (1989).
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    [Crossref] [PubMed]
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    [Crossref]
  30. V. S. Ilchenko, E. Dale, W. Liang, J. Byrd, D. Eliyahu, A. A. Savchenkov, A. B. Matsko, D. Seidel, and L. Maleki, “Compact tunable kHz-linewidth semiconductor laser stabilized with a whispering-gallery mode microresonator,” in “Proc. SPIE,”, vol. 7913 (2011), vol. 7913, pp. 1G–1.
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    [Crossref]
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    [Crossref]
  33. W. Liang, V. S. Ilchenko, D. Eliyahu, E. Dale, A. A. Savchenkov, D. Seidel, A. B. Matsko, and L. Maleki, “Compact stabilized semiconductor laser for frequency metrology,” Appl. Opt. 54, 3353–3359 (2015).
    [Crossref] [PubMed]
  34. S. Borri, M. Siciliani de Cumis, G. Insero, G. Santambrogio, A. Savchenkov, D. Eliyahu, V. Ilchenko, A. Matsko, L. Maleki, and P. De Natale, “Whispering gallery mode stabilization of quantum cascade lasers for infrared sensing and spectroscopy,” Proc. SPIE 10090, 1009008 (2017).
    [Crossref]
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    [Crossref]
  38. A. N. Oraevsky, A. V. Yarovitsky, and V. L. Velichansky, “Frequency stabilisation of a diode laser by a whispering-gallery mode,” Quantum Electron. 31, 897 (2001).
    [Crossref]
  39. H. A. Haus, Waves and Fields in Optoelectronics, (Prentice-Hall, 1984), pp. 59–65.
  40. R. Adler, “A study of locking phenomena in oscillators,” Proc. IEEE 61, 1380–1385 (1973).
    [Crossref]
  41. S. Donati, “Developing self-mixing interferometry for instrumentation and measurements,” Laser Photonics Rev. 6, 393–417 (2012).
    [Crossref]
  42. R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16 (3), 347–355 (1980).
    [Crossref]
  43. V. S. Il’chenko and M. L. Gorodetskii, “Thermal nonlinear effects in optical whispering gallery microresonators,” Laser Phys. 2, 1004–1009 (1992).
  44. T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, “Temporal solitons in optical microresonators,” Nat. Photonics 8, 145–152 (2014).
    [Crossref]
  45. W. Liang, D. Eliyahu, V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, D. Seidel, and L. Maleki, “High spectral purity Kerr frequency comb radio frequency photonic oscillator,” Nat. Commun. 6, 7957 (2015).
    [Crossref] [PubMed]

2017 (1)

S. Borri, M. Siciliani de Cumis, G. Insero, G. Santambrogio, A. Savchenkov, D. Eliyahu, V. Ilchenko, A. Matsko, L. Maleki, and P. De Natale, “Whispering gallery mode stabilization of quantum cascade lasers for infrared sensing and spectroscopy,” Proc. SPIE 10090, 1009008 (2017).
[Crossref]

2016 (1)

2015 (3)

W. Liang, V. S. Ilchenko, D. Eliyahu, E. Dale, A. A. Savchenkov, D. Seidel, A. B. Matsko, and L. Maleki, “Compact stabilized semiconductor laser for frequency metrology,” Appl. Opt. 54, 3353–3359 (2015).
[Crossref] [PubMed]

W. Liang, V. S. Ilchenko, D. Eliyahu, A. A. Savchenkov, A. B. Matsko, D. Seidel, and L. Maleki, “Thermal-noise-limited optical cavity,” Nat. Commun. 6, 7371 (2015).
[Crossref]

W. Liang, D. Eliyahu, V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, D. Seidel, and L. Maleki, “High spectral purity Kerr frequency comb radio frequency photonic oscillator,” Nat. Commun. 6, 7957 (2015).
[Crossref] [PubMed]

2014 (1)

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, “Temporal solitons in optical microresonators,” Nat. Photonics 8, 145–152 (2014).
[Crossref]

2012 (3)

2010 (1)

2009 (1)

2008 (1)

J. Alnis, A. Matveev, N. Kolachevsky, T. Udem, and T. W. Hänsch, “Subhertz linewidth diode lasers by stabilization to vibrationally and thermally compensated ultralow-expansion glass Fabry-Pérot cavities,” Phys. Rev. A 77, 053809 (2008).
[Crossref]

2007 (2)

G. J. Steckman, W. Liu, R. Platz, D. Schroeder, C. Moser, and F. Havermeyer, “Volume holographic grating wavelength stabilized laser diodes,” IEEE J. Sel. Top. Quantum Electron. 13, 672–678 (2007).
[Crossref]

A. D. Ludlow, X. Huang, M. Notcutt, T. Zanon-Willette, S. M. Foreman, M. M. Boyd, S. Blatt, and J. Ye, “Compact, thermal-noise-limited optical cavity for diode laser stabilization at 1×10−15,” Opt. Lett. 32, 641–643 (2007).
[Crossref] [PubMed]

2006 (1)

I. S. Grudinin, A. B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko, and L. Maleki, “Ultra high Q crystalline microcavities,” Opt. Commun. 265, 33–38 (2006).
[Crossref]

2004 (1)

2003 (1)

V. Vassiliev, S. Il’ina, and V. Velichansky, “Diode laser coupled to a high-Q microcavity via a GRIN lens,” Appl. Phys. B 76, 521–523 (2003).
[Crossref]

2001 (1)

A. N. Oraevsky, A. V. Yarovitsky, and V. L. Velichansky, “Frequency stabilisation of a diode laser by a whispering-gallery mode,” Quantum Electron. 31, 897 (2001).
[Crossref]

2000 (1)

1998 (1)

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

1996 (1)

V. V. Vasil’ev, V. L. Velichansky, M. L. Gorodetskii, V. S. Il’chenko, L. Holberg, and A. V. Yarovitsky, “High-coherence diode laser with optical feedback via a microcavity with ’whispering gallery’ modes,” Quantum Electron. 26, 657 (1996).
[Crossref]

1995 (1)

L. Ricci, M. Weidemüller, T. Esslinger, A. Hemmerich, C. Zimmermann, V. Vuletic, W. König, and T. Hänsch, “A compact grating-stabilized diode laser system for atomic physics,” Opt. Commun. 117, 541–549 (1995).
[Crossref]

1994 (1)

1992 (2)

V. S. Il’chenko and M. L. Gorodetskii, “Thermal nonlinear effects in optical whispering gallery microresonators,” Laser Phys. 2, 1004–1009 (1992).

V. Ilchenko and M. Gorodetsky, “Thermal nonlinear effects in optical whispering gallery microresonators,” Laser Phys. 2, 1004–1009 (1992).

1991 (3)

H. Patrick and C. E. Wieman, “Frequency stabilization of a diode laser using simultaneous optical feedback from a diffraction grating and a narrowband Fabry–Perot cavity,” Rev. Scient. Instrum. 62, 2593–2595 (1991).
[Crossref]

M. Kourogi and M. Ohtsu, “Novel optical frequency discriminator for FM noise reduction of semiconductor lasers,” Opt. Commun. 81, 204–208 (1991).
[Crossref]

C. E. Wieman and L. Hollberg, “Using diode lasers for atomic physics,” Rev. Scient. Instr. 62, 1–20 (1991).
[Crossref]

1989 (3)

V. Braginsky, M. Gorodetsky, and V. Ilchenko, “Quality-factor and nonlinear properties of optical whispering-gallery modes,” Phys. Lett. A 137, 393–397 (1989).
[Crossref]

H. Li and H. R. Telle, “Efficient frequency noise reduction of GaAlAs semiconductor lasers by optical feedback from an external high-finesse resonator,” IEEE J. Quantum Electron. 25, 257–264 (1989).
[Crossref]

P. Laurent, A. Clairon, and C. Breant, “Frequency noise analysis of optically self-locked diode lasers,” IEEE J. Quantum Electron. 25, 1131–1142 (1989).
[Crossref]

1988 (1)

L. Hollberg and M. Ohtsu, “Modulatable narrow–linewidth semiconductor lasers,” Appl. Phys. Lett. 53, 944–946 (1988).
[Crossref]

1987 (1)

1986 (1)

G. Hadley, “Injection locking of diode lasers,” IEEE J. Quantum Electron. 22, 419–426 (1986).
[Crossref]

1984 (1)

G. Agrawal, “Line narrowing in a single-mode injection laser due to external optical feedback,” IEEE J. Quantum Electron. 20, 468–471 (1984).
[Crossref]

1983 (4)

E. Patzak, H. O, A. Sugimura, S. Saito, and T. Mukai, “Spectral linewidth reduction in semiconductor lasers by an external cavity with weak optical feedback,” Electron. Lett. 19(2), 938–940 (1983).
[Crossref]

E. Belenov, V. L. Velichanskii, A. S. Zibrov, V. V. Nikitin, V. A. Sautenkov, and A. V. Uskov, “Methods for narrowing the emission line of an injection laser,” Sov. J. Quantum. Electron. 13, 792 (1983).
[Crossref]

H. Olesen, S. Saito, T. Mukai, T. Saitoh, and O. Mikami, “Solitary spectral linewidth and its reduction with external grating feedback for a 1.55 µ m InGaAsP BH laser,” Jpn. J. Appl. Phys. 22, L664 (1983).
[Crossref]

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[Crossref]

1982 (1)

S. Saito, O. Nilsson, and Y. Yamamoto, “Oscillation center frequency tuning, quantum FM noise, and direct frequency characteristics in external grating loaded semiconductor lasers,” IEEE J. Quantum Electron. 18, 961–970 (1982).
[Crossref]

1980 (1)

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16 (3), 347–355 (1980).
[Crossref]

1978 (1)

V. Velichanskii, A. Zibrov, V. Kargopoltsev, V. Molochev, V. Nikitin, V. Sautenkov, G. Kharisov, and D. Tyurikov, “Minimum line width of an injection laser,” Sov. Tech. Phys. Lett. 4(9), 438 (1978).

1973 (1)

R. Adler, “A study of locking phenomena in oscillators,” Proc. IEEE 61, 1380–1385 (1973).
[Crossref]

Adler, R.

R. Adler, “A study of locking phenomena in oscillators,” Proc. IEEE 61, 1380–1385 (1973).
[Crossref]

Agrawal, G.

G. Agrawal, “Line narrowing in a single-mode injection laser due to external optical feedback,” IEEE J. Quantum Electron. 20, 468–471 (1984).
[Crossref]

Alnis, J.

J. Alnis, A. Matveev, N. Kolachevsky, T. Udem, and T. W. Hänsch, “Subhertz linewidth diode lasers by stabilization to vibrationally and thermally compensated ultralow-expansion glass Fabry-Pérot cavities,” Phys. Rev. A 77, 053809 (2008).
[Crossref]

Ban, V. S.

Belenov, E.

E. Belenov, V. L. Velichanskii, A. S. Zibrov, V. V. Nikitin, V. A. Sautenkov, and A. V. Uskov, “Methods for narrowing the emission line of an injection laser,” Sov. J. Quantum. Electron. 13, 792 (1983).
[Crossref]

Blatt, S.

Borri, S.

S. Borri, M. Siciliani de Cumis, G. Insero, G. Santambrogio, A. Savchenkov, D. Eliyahu, V. Ilchenko, A. Matsko, L. Maleki, and P. De Natale, “Whispering gallery mode stabilization of quantum cascade lasers for infrared sensing and spectroscopy,” Proc. SPIE 10090, 1009008 (2017).
[Crossref]

Boyd, M. M.

Braginsky, V.

V. Braginsky, M. Gorodetsky, and V. Ilchenko, “Quality-factor and nonlinear properties of optical whispering-gallery modes,” Phys. Lett. A 137, 393–397 (1989).
[Crossref]

Brasch, V.

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, “Temporal solitons in optical microresonators,” Nat. Photonics 8, 145–152 (2014).
[Crossref]

Breant, C.

P. Laurent, A. Clairon, and C. Breant, “Frequency noise analysis of optically self-locked diode lasers,” IEEE J. Quantum Electron. 25, 1131–1142 (1989).
[Crossref]

Byrd, J.

V. S. Ilchenko, E. Dale, W. Liang, J. Byrd, D. Eliyahu, A. A. Savchenkov, A. B. Matsko, D. Seidel, and L. Maleki, “Compact tunable kHz-linewidth semiconductor laser stabilized with a whispering-gallery mode microresonator,” in “Proc. SPIE,”, vol. 7913 (2011), vol. 7913, pp. 1G–1.

Cai, H.

Cao, J.

Cao, S.

Chen, D.

Clairon, A.

P. Laurent, A. Clairon, and C. Breant, “Frequency noise analysis of optically self-locked diode lasers,” IEEE J. Quantum Electron. 25, 1131–1142 (1989).
[Crossref]

Dahmani, B.

Dale, E.

W. Liang, V. S. Ilchenko, D. Eliyahu, E. Dale, A. A. Savchenkov, D. Seidel, A. B. Matsko, and L. Maleki, “Compact stabilized semiconductor laser for frequency metrology,” Appl. Opt. 54, 3353–3359 (2015).
[Crossref] [PubMed]

V. S. Ilchenko, E. Dale, W. Liang, J. Byrd, D. Eliyahu, A. A. Savchenkov, A. B. Matsko, D. Seidel, and L. Maleki, “Compact tunable kHz-linewidth semiconductor laser stabilized with a whispering-gallery mode microresonator,” in “Proc. SPIE,”, vol. 7913 (2011), vol. 7913, pp. 1G–1.

De Natale, P.

S. Borri, M. Siciliani de Cumis, G. Insero, G. Santambrogio, A. Savchenkov, D. Eliyahu, V. Ilchenko, A. Matsko, L. Maleki, and P. De Natale, “Whispering gallery mode stabilization of quantum cascade lasers for infrared sensing and spectroscopy,” Proc. SPIE 10090, 1009008 (2017).
[Crossref]

Ding, M.

Dolgy, S. V.

Donati, S.

S. Donati, “Developing self-mixing interferometry for instrumentation and measurements,” Laser Photonics Rev. 6, 393–417 (2012).
[Crossref]

Downs, E.

Drever, R. W. P.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[Crossref]

Drullinger, R.

Eliyahu, D.

S. Borri, M. Siciliani de Cumis, G. Insero, G. Santambrogio, A. Savchenkov, D. Eliyahu, V. Ilchenko, A. Matsko, L. Maleki, and P. De Natale, “Whispering gallery mode stabilization of quantum cascade lasers for infrared sensing and spectroscopy,” Proc. SPIE 10090, 1009008 (2017).
[Crossref]

W. Liang, V. S. Ilchenko, D. Eliyahu, A. A. Savchenkov, A. B. Matsko, D. Seidel, and L. Maleki, “Thermal-noise-limited optical cavity,” Nat. Commun. 6, 7371 (2015).
[Crossref]

W. Liang, D. Eliyahu, V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, D. Seidel, and L. Maleki, “High spectral purity Kerr frequency comb radio frequency photonic oscillator,” Nat. Commun. 6, 7957 (2015).
[Crossref] [PubMed]

W. Liang, V. S. Ilchenko, D. Eliyahu, E. Dale, A. A. Savchenkov, D. Seidel, A. B. Matsko, and L. Maleki, “Compact stabilized semiconductor laser for frequency metrology,” Appl. Opt. 54, 3353–3359 (2015).
[Crossref] [PubMed]

V. S. Ilchenko, E. Dale, W. Liang, J. Byrd, D. Eliyahu, A. A. Savchenkov, A. B. Matsko, D. Seidel, and L. Maleki, “Compact tunable kHz-linewidth semiconductor laser stabilized with a whispering-gallery mode microresonator,” in “Proc. SPIE,”, vol. 7913 (2011), vol. 7913, pp. 1G–1.

Esslinger, T.

L. Ricci, M. Weidemüller, T. Esslinger, A. Hemmerich, C. Zimmermann, V. Vuletic, W. König, and T. Hänsch, “A compact grating-stabilized diode laser system for atomic physics,” Opt. Commun. 117, 541–549 (1995).
[Crossref]

Fang, Z.

Ford, G. M.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[Crossref]

Foreman, S. M.

Fürst, J.

Gorodetskii, M. L.

V. V. Vasil’ev, V. L. Velichansky, M. L. Gorodetskii, V. S. Il’chenko, L. Holberg, and A. V. Yarovitsky, “High-coherence diode laser with optical feedback via a microcavity with ’whispering gallery’ modes,” Quantum Electron. 26, 657 (1996).
[Crossref]

V. S. Il’chenko and M. L. Gorodetskii, “Thermal nonlinear effects in optical whispering gallery microresonators,” Laser Phys. 2, 1004–1009 (1992).

Gorodetsky, M.

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

V. Ilchenko and M. Gorodetsky, “Thermal nonlinear effects in optical whispering gallery microresonators,” Laser Phys. 2, 1004–1009 (1992).

V. Braginsky, M. Gorodetsky, and V. Ilchenko, “Quality-factor and nonlinear properties of optical whispering-gallery modes,” Phys. Lett. A 137, 393–397 (1989).
[Crossref]

Gorodetsky, M. L.

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, “Temporal solitons in optical microresonators,” Nat. Photonics 8, 145–152 (2014).
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M. L. Gorodetsky, A. D. Pryamikov, and V. S. Ilchenko, “Rayleigh scattering in high-Q microspheres,” J. Opt. Soc. Am. B 17, 1051–1057 (2000).
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Grudinin, I. S.

G. Lin, J. Fürst, D. V. Strekalov, I. S. Grudinin, and N. Yu, “High-Q UV whispering gallery mode resonators made of angle-cut BBO crystals,” Opt. Express 20, 21372–21378 (2012).
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I. S. Grudinin, A. B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko, and L. Maleki, “Ultra high Q crystalline microcavities,” Opt. Commun. 265, 33–38 (2006).
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Hadley, G.

G. Hadley, “Injection locking of diode lasers,” IEEE J. Quantum Electron. 22, 419–426 (1986).
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Hall, J. L.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[Crossref]

Hänsch, T.

L. Ricci, M. Weidemüller, T. Esslinger, A. Hemmerich, C. Zimmermann, V. Vuletic, W. König, and T. Hänsch, “A compact grating-stabilized diode laser system for atomic physics,” Opt. Commun. 117, 541–549 (1995).
[Crossref]

Hänsch, T. W.

J. Alnis, A. Matveev, N. Kolachevsky, T. Udem, and T. W. Hänsch, “Subhertz linewidth diode lasers by stabilization to vibrationally and thermally compensated ultralow-expansion glass Fabry-Pérot cavities,” Phys. Rev. A 77, 053809 (2008).
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A. Hemmerich, C. Zimmermann, and T. W. Hänsch, “Compact source of coherent blue light,” Appl. Opt. 33, 988–991 (1994).
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H. A. Haus, Waves and Fields in Optoelectronics, (Prentice-Hall, 1984), pp. 59–65.

Havermeyer, F.

G. J. Steckman, W. Liu, R. Platz, D. Schroeder, C. Moser, and F. Havermeyer, “Volume holographic grating wavelength stabilized laser diodes,” IEEE J. Sel. Top. Quantum Electron. 13, 672–678 (2007).
[Crossref]

Hemmerich, A.

L. Ricci, M. Weidemüller, T. Esslinger, A. Hemmerich, C. Zimmermann, V. Vuletic, W. König, and T. Hänsch, “A compact grating-stabilized diode laser system for atomic physics,” Opt. Commun. 117, 541–549 (1995).
[Crossref]

A. Hemmerich, C. Zimmermann, and T. W. Hänsch, “Compact source of coherent blue light,” Appl. Opt. 33, 988–991 (1994).
[Crossref] [PubMed]

Herr, T.

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, “Temporal solitons in optical microresonators,” Nat. Photonics 8, 145–152 (2014).
[Crossref]

Holberg, L.

V. V. Vasil’ev, V. L. Velichansky, M. L. Gorodetskii, V. S. Il’chenko, L. Holberg, and A. V. Yarovitsky, “High-coherence diode laser with optical feedback via a microcavity with ’whispering gallery’ modes,” Quantum Electron. 26, 657 (1996).
[Crossref]

Hollberg, L.

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

C. E. Wieman and L. Hollberg, “Using diode lasers for atomic physics,” Rev. Scient. Instr. 62, 1–20 (1991).
[Crossref]

L. Hollberg and M. Ohtsu, “Modulatable narrow–linewidth semiconductor lasers,” Appl. Phys. Lett. 53, 944–946 (1988).
[Crossref]

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

Hough, J.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[Crossref]

Huang, X.

Il’chenko, V. S.

V. V. Vasil’ev, V. L. Velichansky, M. L. Gorodetskii, V. S. Il’chenko, L. Holberg, and A. V. Yarovitsky, “High-coherence diode laser with optical feedback via a microcavity with ’whispering gallery’ modes,” Quantum Electron. 26, 657 (1996).
[Crossref]

V. S. Il’chenko and M. L. Gorodetskii, “Thermal nonlinear effects in optical whispering gallery microresonators,” Laser Phys. 2, 1004–1009 (1992).

Il’ina, S.

V. Vassiliev, S. Il’ina, and V. Velichansky, “Diode laser coupled to a high-Q microcavity via a GRIN lens,” Appl. Phys. B 76, 521–523 (2003).
[Crossref]

Ilchenko, V.

S. Borri, M. Siciliani de Cumis, G. Insero, G. Santambrogio, A. Savchenkov, D. Eliyahu, V. Ilchenko, A. Matsko, L. Maleki, and P. De Natale, “Whispering gallery mode stabilization of quantum cascade lasers for infrared sensing and spectroscopy,” Proc. SPIE 10090, 1009008 (2017).
[Crossref]

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

V. Ilchenko and M. Gorodetsky, “Thermal nonlinear effects in optical whispering gallery microresonators,” Laser Phys. 2, 1004–1009 (1992).

V. Braginsky, M. Gorodetsky, and V. Ilchenko, “Quality-factor and nonlinear properties of optical whispering-gallery modes,” Phys. Lett. A 137, 393–397 (1989).
[Crossref]

Ilchenko, V. S.

W. Liang, D. Eliyahu, V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, D. Seidel, and L. Maleki, “High spectral purity Kerr frequency comb radio frequency photonic oscillator,” Nat. Commun. 6, 7957 (2015).
[Crossref] [PubMed]

W. Liang, V. S. Ilchenko, D. Eliyahu, A. A. Savchenkov, A. B. Matsko, D. Seidel, and L. Maleki, “Thermal-noise-limited optical cavity,” Nat. Commun. 6, 7371 (2015).
[Crossref]

W. Liang, V. S. Ilchenko, D. Eliyahu, E. Dale, A. A. Savchenkov, D. Seidel, A. B. Matsko, and L. Maleki, “Compact stabilized semiconductor laser for frequency metrology,” Appl. Opt. 54, 3353–3359 (2015).
[Crossref] [PubMed]

W. Liang, V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, D. Seidel, and L. Maleki, “Whispering-gallery-mode-resonator-based ultranarrow linewidth external-cavity semiconductor laser,” Opt. Lett. 35, 2822–2824 (2010).
[Crossref] [PubMed]

I. S. Grudinin, A. B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko, and L. Maleki, “Ultra high Q crystalline microcavities,” Opt. Commun. 265, 33–38 (2006).
[Crossref]

M. L. Gorodetsky, A. D. Pryamikov, and V. S. Ilchenko, “Rayleigh scattering in high-Q microspheres,” J. Opt. Soc. Am. B 17, 1051–1057 (2000).
[Crossref]

V. S. Ilchenko, E. Dale, W. Liang, J. Byrd, D. Eliyahu, A. A. Savchenkov, A. B. Matsko, D. Seidel, and L. Maleki, “Compact tunable kHz-linewidth semiconductor laser stabilized with a whispering-gallery mode microresonator,” in “Proc. SPIE,”, vol. 7913 (2011), vol. 7913, pp. 1G–1.

Insero, G.

S. Borri, M. Siciliani de Cumis, G. Insero, G. Santambrogio, A. Savchenkov, D. Eliyahu, V. Ilchenko, A. Matsko, L. Maleki, and P. De Natale, “Whispering gallery mode stabilization of quantum cascade lasers for infrared sensing and spectroscopy,” Proc. SPIE 10090, 1009008 (2017).
[Crossref]

Jost, J. D.

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, “Temporal solitons in optical microresonators,” Nat. Photonics 8, 145–152 (2014).
[Crossref]

Kargopoltsev, V.

V. Velichanskii, A. Zibrov, V. Kargopoltsev, V. Molochev, V. Nikitin, V. Sautenkov, G. Kharisov, and D. Tyurikov, “Minimum line width of an injection laser,” Sov. Tech. Phys. Lett. 4(9), 438 (1978).

Kharisov, G.

V. Velichanskii, A. Zibrov, V. Kargopoltsev, V. Molochev, V. Nikitin, V. Sautenkov, G. Kharisov, and D. Tyurikov, “Minimum line width of an injection laser,” Sov. Tech. Phys. Lett. 4(9), 438 (1978).

Kippenberg, T. J.

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, “Temporal solitons in optical microresonators,” Nat. Photonics 8, 145–152 (2014).
[Crossref]

Kobayashi, K.

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16 (3), 347–355 (1980).
[Crossref]

Kolachevsky, N.

J. Alnis, A. Matveev, N. Kolachevsky, T. Udem, and T. W. Hänsch, “Subhertz linewidth diode lasers by stabilization to vibrationally and thermally compensated ultralow-expansion glass Fabry-Pérot cavities,” Phys. Rev. A 77, 053809 (2008).
[Crossref]

Kondratiev, N. M.

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, “Temporal solitons in optical microresonators,” Nat. Photonics 8, 145–152 (2014).
[Crossref]

König, W.

L. Ricci, M. Weidemüller, T. Esslinger, A. Hemmerich, C. Zimmermann, V. Vuletic, W. König, and T. Hänsch, “A compact grating-stabilized diode laser system for atomic physics,” Opt. Commun. 117, 541–549 (1995).
[Crossref]

Kourogi, M.

M. Kourogi and M. Ohtsu, “Novel optical frequency discriminator for FM noise reduction of semiconductor lasers,” Opt. Commun. 81, 204–208 (1991).
[Crossref]

Kowalski, F. V.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[Crossref]

Lang, R.

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16 (3), 347–355 (1980).
[Crossref]

Laurent, P.

P. Laurent, A. Clairon, and C. Breant, “Frequency noise analysis of optically self-locked diode lasers,” IEEE J. Quantum Electron. 25, 1131–1142 (1989).
[Crossref]

Li, H.

H. Li and H. R. Telle, “Efficient frequency noise reduction of GaAlAs semiconductor lasers by optical feedback from an external high-finesse resonator,” IEEE J. Quantum Electron. 25, 257–264 (1989).
[Crossref]

Li, T.

Li, Y.

Liang, W.

W. Liang, V. S. Ilchenko, D. Eliyahu, E. Dale, A. A. Savchenkov, D. Seidel, A. B. Matsko, and L. Maleki, “Compact stabilized semiconductor laser for frequency metrology,” Appl. Opt. 54, 3353–3359 (2015).
[Crossref] [PubMed]

W. Liang, D. Eliyahu, V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, D. Seidel, and L. Maleki, “High spectral purity Kerr frequency comb radio frequency photonic oscillator,” Nat. Commun. 6, 7957 (2015).
[Crossref] [PubMed]

W. Liang, V. S. Ilchenko, D. Eliyahu, A. A. Savchenkov, A. B. Matsko, D. Seidel, and L. Maleki, “Thermal-noise-limited optical cavity,” Nat. Commun. 6, 7371 (2015).
[Crossref]

W. Liang, V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, D. Seidel, and L. Maleki, “Whispering-gallery-mode-resonator-based ultranarrow linewidth external-cavity semiconductor laser,” Opt. Lett. 35, 2822–2824 (2010).
[Crossref] [PubMed]

V. S. Ilchenko, E. Dale, W. Liang, J. Byrd, D. Eliyahu, A. A. Savchenkov, A. B. Matsko, D. Seidel, and L. Maleki, “Compact tunable kHz-linewidth semiconductor laser stabilized with a whispering-gallery mode microresonator,” in “Proc. SPIE,”, vol. 7913 (2011), vol. 7913, pp. 1G–1.

Lin, B.

Lin, G.

Lin, Y.

Liu, W.

G. J. Steckman, W. Liu, R. Platz, D. Schroeder, C. Moser, and F. Havermeyer, “Volume holographic grating wavelength stabilized laser diodes,” IEEE J. Sel. Top. Quantum Electron. 13, 672–678 (2007).
[Crossref]

Ludlow, A. D.

Maleki, L.

S. Borri, M. Siciliani de Cumis, G. Insero, G. Santambrogio, A. Savchenkov, D. Eliyahu, V. Ilchenko, A. Matsko, L. Maleki, and P. De Natale, “Whispering gallery mode stabilization of quantum cascade lasers for infrared sensing and spectroscopy,” Proc. SPIE 10090, 1009008 (2017).
[Crossref]

W. Liang, V. S. Ilchenko, D. Eliyahu, A. A. Savchenkov, A. B. Matsko, D. Seidel, and L. Maleki, “Thermal-noise-limited optical cavity,” Nat. Commun. 6, 7371 (2015).
[Crossref]

W. Liang, D. Eliyahu, V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, D. Seidel, and L. Maleki, “High spectral purity Kerr frequency comb radio frequency photonic oscillator,” Nat. Commun. 6, 7957 (2015).
[Crossref] [PubMed]

W. Liang, V. S. Ilchenko, D. Eliyahu, E. Dale, A. A. Savchenkov, D. Seidel, A. B. Matsko, and L. Maleki, “Compact stabilized semiconductor laser for frequency metrology,” Appl. Opt. 54, 3353–3359 (2015).
[Crossref] [PubMed]

W. Liang, V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, D. Seidel, and L. Maleki, “Whispering-gallery-mode-resonator-based ultranarrow linewidth external-cavity semiconductor laser,” Opt. Lett. 35, 2822–2824 (2010).
[Crossref] [PubMed]

I. S. Grudinin, A. B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko, and L. Maleki, “Ultra high Q crystalline microcavities,” Opt. Commun. 265, 33–38 (2006).
[Crossref]

V. S. Ilchenko, E. Dale, W. Liang, J. Byrd, D. Eliyahu, A. A. Savchenkov, A. B. Matsko, D. Seidel, and L. Maleki, “Compact tunable kHz-linewidth semiconductor laser stabilized with a whispering-gallery mode microresonator,” in “Proc. SPIE,”, vol. 7913 (2011), vol. 7913, pp. 1G–1.

Matsko, A.

S. Borri, M. Siciliani de Cumis, G. Insero, G. Santambrogio, A. Savchenkov, D. Eliyahu, V. Ilchenko, A. Matsko, L. Maleki, and P. De Natale, “Whispering gallery mode stabilization of quantum cascade lasers for infrared sensing and spectroscopy,” Proc. SPIE 10090, 1009008 (2017).
[Crossref]

Matsko, A. B.

W. Liang, V. S. Ilchenko, D. Eliyahu, A. A. Savchenkov, A. B. Matsko, D. Seidel, and L. Maleki, “Thermal-noise-limited optical cavity,” Nat. Commun. 6, 7371 (2015).
[Crossref]

W. Liang, D. Eliyahu, V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, D. Seidel, and L. Maleki, “High spectral purity Kerr frequency comb radio frequency photonic oscillator,” Nat. Commun. 6, 7957 (2015).
[Crossref] [PubMed]

W. Liang, V. S. Ilchenko, D. Eliyahu, E. Dale, A. A. Savchenkov, D. Seidel, A. B. Matsko, and L. Maleki, “Compact stabilized semiconductor laser for frequency metrology,” Appl. Opt. 54, 3353–3359 (2015).
[Crossref] [PubMed]

W. Liang, V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, D. Seidel, and L. Maleki, “Whispering-gallery-mode-resonator-based ultranarrow linewidth external-cavity semiconductor laser,” Opt. Lett. 35, 2822–2824 (2010).
[Crossref] [PubMed]

I. S. Grudinin, A. B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko, and L. Maleki, “Ultra high Q crystalline microcavities,” Opt. Commun. 265, 33–38 (2006).
[Crossref]

V. S. Ilchenko, E. Dale, W. Liang, J. Byrd, D. Eliyahu, A. A. Savchenkov, A. B. Matsko, D. Seidel, and L. Maleki, “Compact tunable kHz-linewidth semiconductor laser stabilized with a whispering-gallery mode microresonator,” in “Proc. SPIE,”, vol. 7913 (2011), vol. 7913, pp. 1G–1.

Matveev, A.

J. Alnis, A. Matveev, N. Kolachevsky, T. Udem, and T. W. Hänsch, “Subhertz linewidth diode lasers by stabilization to vibrationally and thermally compensated ultralow-expansion glass Fabry-Pérot cavities,” Phys. Rev. A 77, 053809 (2008).
[Crossref]

Melnik, E. D.

Meng, F.

Mikami, O.

H. Olesen, S. Saito, T. Mukai, T. Saitoh, and O. Mikami, “Solitary spectral linewidth and its reduction with external grating feedback for a 1.55 µ m InGaAsP BH laser,” Jpn. J. Appl. Phys. 22, L664 (1983).
[Crossref]

Molochev, V.

V. Velichanskii, A. Zibrov, V. Kargopoltsev, V. Molochev, V. Nikitin, V. Sautenkov, G. Kharisov, and D. Tyurikov, “Minimum line width of an injection laser,” Sov. Tech. Phys. Lett. 4(9), 438 (1978).

Moser, C.

G. J. Steckman, W. Liu, R. Platz, D. Schroeder, C. Moser, and F. Havermeyer, “Volume holographic grating wavelength stabilized laser diodes,” IEEE J. Sel. Top. Quantum Electron. 13, 672–678 (2007).
[Crossref]

Mukai, T.

H. Olesen, S. Saito, T. Mukai, T. Saitoh, and O. Mikami, “Solitary spectral linewidth and its reduction with external grating feedback for a 1.55 µ m InGaAsP BH laser,” Jpn. J. Appl. Phys. 22, L664 (1983).
[Crossref]

E. Patzak, H. O, A. Sugimura, S. Saito, and T. Mukai, “Spectral linewidth reduction in semiconductor lasers by an external cavity with weak optical feedback,” Electron. Lett. 19(2), 938–940 (1983).
[Crossref]

Munley, A. J.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[Crossref]

Nikitin, V.

V. Velichanskii, A. Zibrov, V. Kargopoltsev, V. Molochev, V. Nikitin, V. Sautenkov, G. Kharisov, and D. Tyurikov, “Minimum line width of an injection laser,” Sov. Tech. Phys. Lett. 4(9), 438 (1978).

Nikitin, V. V.

E. Belenov, V. L. Velichanskii, A. S. Zibrov, V. V. Nikitin, V. A. Sautenkov, and A. V. Uskov, “Methods for narrowing the emission line of an injection laser,” Sov. J. Quantum. Electron. 13, 792 (1983).
[Crossref]

Nilsson, O.

S. Saito, O. Nilsson, and Y. Yamamoto, “Oscillation center frequency tuning, quantum FM noise, and direct frequency characteristics in external grating loaded semiconductor lasers,” IEEE J. Quantum Electron. 18, 961–970 (1982).
[Crossref]

Notcutt, M.

O, H.

E. Patzak, H. O, A. Sugimura, S. Saito, and T. Mukai, “Spectral linewidth reduction in semiconductor lasers by an external cavity with weak optical feedback,” Electron. Lett. 19(2), 938–940 (1983).
[Crossref]

Ohtsu, M.

M. Kourogi and M. Ohtsu, “Novel optical frequency discriminator for FM noise reduction of semiconductor lasers,” Opt. Commun. 81, 204–208 (1991).
[Crossref]

L. Hollberg and M. Ohtsu, “Modulatable narrow–linewidth semiconductor lasers,” Appl. Phys. Lett. 53, 944–946 (1988).
[Crossref]

Olesen, H.

H. Olesen, S. Saito, T. Mukai, T. Saitoh, and O. Mikami, “Solitary spectral linewidth and its reduction with external grating feedback for a 1.55 µ m InGaAsP BH laser,” Jpn. J. Appl. Phys. 22, L664 (1983).
[Crossref]

Oraevsky, A. N.

A. N. Oraevsky, A. V. Yarovitsky, and V. L. Velichansky, “Frequency stabilisation of a diode laser by a whispering-gallery mode,” Quantum Electron. 31, 897 (2001).
[Crossref]

Patrick, H.

H. Patrick and C. E. Wieman, “Frequency stabilization of a diode laser using simultaneous optical feedback from a diffraction grating and a narrowband Fabry–Perot cavity,” Rev. Scient. Instrum. 62, 2593–2595 (1991).
[Crossref]

Patzak, E.

E. Patzak, H. O, A. Sugimura, S. Saito, and T. Mukai, “Spectral linewidth reduction in semiconductor lasers by an external cavity with weak optical feedback,” Electron. Lett. 19(2), 938–940 (1983).
[Crossref]

Platz, R.

G. J. Steckman, W. Liu, R. Platz, D. Schroeder, C. Moser, and F. Havermeyer, “Volume holographic grating wavelength stabilized laser diodes,” IEEE J. Sel. Top. Quantum Electron. 13, 672–678 (2007).
[Crossref]

Pryamikov, A. D.

Ricci, L.

L. Ricci, M. Weidemüller, T. Esslinger, A. Hemmerich, C. Zimmermann, V. Vuletic, W. König, and T. Hänsch, “A compact grating-stabilized diode laser system for atomic physics,” Opt. Commun. 117, 541–549 (1995).
[Crossref]

Saito, S.

H. Olesen, S. Saito, T. Mukai, T. Saitoh, and O. Mikami, “Solitary spectral linewidth and its reduction with external grating feedback for a 1.55 µ m InGaAsP BH laser,” Jpn. J. Appl. Phys. 22, L664 (1983).
[Crossref]

E. Patzak, H. O, A. Sugimura, S. Saito, and T. Mukai, “Spectral linewidth reduction in semiconductor lasers by an external cavity with weak optical feedback,” Electron. Lett. 19(2), 938–940 (1983).
[Crossref]

S. Saito, O. Nilsson, and Y. Yamamoto, “Oscillation center frequency tuning, quantum FM noise, and direct frequency characteristics in external grating loaded semiconductor lasers,” IEEE J. Quantum Electron. 18, 961–970 (1982).
[Crossref]

Saitoh, T.

H. Olesen, S. Saito, T. Mukai, T. Saitoh, and O. Mikami, “Solitary spectral linewidth and its reduction with external grating feedback for a 1.55 µ m InGaAsP BH laser,” Jpn. J. Appl. Phys. 22, L664 (1983).
[Crossref]

Santambrogio, G.

S. Borri, M. Siciliani de Cumis, G. Insero, G. Santambrogio, A. Savchenkov, D. Eliyahu, V. Ilchenko, A. Matsko, L. Maleki, and P. De Natale, “Whispering gallery mode stabilization of quantum cascade lasers for infrared sensing and spectroscopy,” Proc. SPIE 10090, 1009008 (2017).
[Crossref]

Sautenkov, V.

V. Velichanskii, A. Zibrov, V. Kargopoltsev, V. Molochev, V. Nikitin, V. Sautenkov, G. Kharisov, and D. Tyurikov, “Minimum line width of an injection laser,” Sov. Tech. Phys. Lett. 4(9), 438 (1978).

Sautenkov, V. A.

E. Belenov, V. L. Velichanskii, A. S. Zibrov, V. V. Nikitin, V. A. Sautenkov, and A. V. Uskov, “Methods for narrowing the emission line of an injection laser,” Sov. J. Quantum. Electron. 13, 792 (1983).
[Crossref]

Savchenkov, A.

S. Borri, M. Siciliani de Cumis, G. Insero, G. Santambrogio, A. Savchenkov, D. Eliyahu, V. Ilchenko, A. Matsko, L. Maleki, and P. De Natale, “Whispering gallery mode stabilization of quantum cascade lasers for infrared sensing and spectroscopy,” Proc. SPIE 10090, 1009008 (2017).
[Crossref]

Savchenkov, A. A.

W. Liang, V. S. Ilchenko, D. Eliyahu, A. A. Savchenkov, A. B. Matsko, D. Seidel, and L. Maleki, “Thermal-noise-limited optical cavity,” Nat. Commun. 6, 7371 (2015).
[Crossref]

W. Liang, D. Eliyahu, V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, D. Seidel, and L. Maleki, “High spectral purity Kerr frequency comb radio frequency photonic oscillator,” Nat. Commun. 6, 7957 (2015).
[Crossref] [PubMed]

W. Liang, V. S. Ilchenko, D. Eliyahu, E. Dale, A. A. Savchenkov, D. Seidel, A. B. Matsko, and L. Maleki, “Compact stabilized semiconductor laser for frequency metrology,” Appl. Opt. 54, 3353–3359 (2015).
[Crossref] [PubMed]

W. Liang, V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, D. Seidel, and L. Maleki, “Whispering-gallery-mode-resonator-based ultranarrow linewidth external-cavity semiconductor laser,” Opt. Lett. 35, 2822–2824 (2010).
[Crossref] [PubMed]

I. S. Grudinin, A. B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko, and L. Maleki, “Ultra high Q crystalline microcavities,” Opt. Commun. 265, 33–38 (2006).
[Crossref]

V. S. Ilchenko, E. Dale, W. Liang, J. Byrd, D. Eliyahu, A. A. Savchenkov, A. B. Matsko, D. Seidel, and L. Maleki, “Compact tunable kHz-linewidth semiconductor laser stabilized with a whispering-gallery mode microresonator,” in “Proc. SPIE,”, vol. 7913 (2011), vol. 7913, pp. 1G–1.

Schroeder, D.

G. J. Steckman, W. Liu, R. Platz, D. Schroeder, C. Moser, and F. Havermeyer, “Volume holographic grating wavelength stabilized laser diodes,” IEEE J. Sel. Top. Quantum Electron. 13, 672–678 (2007).
[Crossref]

Schwefel, H. G. L.

Seidel, D.

W. Liang, V. S. Ilchenko, D. Eliyahu, E. Dale, A. A. Savchenkov, D. Seidel, A. B. Matsko, and L. Maleki, “Compact stabilized semiconductor laser for frequency metrology,” Appl. Opt. 54, 3353–3359 (2015).
[Crossref] [PubMed]

W. Liang, V. S. Ilchenko, D. Eliyahu, A. A. Savchenkov, A. B. Matsko, D. Seidel, and L. Maleki, “Thermal-noise-limited optical cavity,” Nat. Commun. 6, 7371 (2015).
[Crossref]

W. Liang, D. Eliyahu, V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, D. Seidel, and L. Maleki, “High spectral purity Kerr frequency comb radio frequency photonic oscillator,” Nat. Commun. 6, 7957 (2015).
[Crossref] [PubMed]

W. Liang, V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, D. Seidel, and L. Maleki, “Whispering-gallery-mode-resonator-based ultranarrow linewidth external-cavity semiconductor laser,” Opt. Lett. 35, 2822–2824 (2010).
[Crossref] [PubMed]

V. S. Ilchenko, E. Dale, W. Liang, J. Byrd, D. Eliyahu, A. A. Savchenkov, A. B. Matsko, D. Seidel, and L. Maleki, “Compact tunable kHz-linewidth semiconductor laser stabilized with a whispering-gallery mode microresonator,” in “Proc. SPIE,”, vol. 7913 (2011), vol. 7913, pp. 1G–1.

Shaw, J.

Siciliani de Cumis, M.

S. Borri, M. Siciliani de Cumis, G. Insero, G. Santambrogio, A. Savchenkov, D. Eliyahu, V. Ilchenko, A. Matsko, L. Maleki, and P. De Natale, “Whispering gallery mode stabilization of quantum cascade lasers for infrared sensing and spectroscopy,” Proc. SPIE 10090, 1009008 (2017).
[Crossref]

Sprenger, B.

Steckman, G. J.

G. J. Steckman, W. Liu, R. Platz, D. Schroeder, C. Moser, and F. Havermeyer, “Volume holographic grating wavelength stabilized laser diodes,” IEEE J. Sel. Top. Quantum Electron. 13, 672–678 (2007).
[Crossref]

Strekalov, D.

I. S. Grudinin, A. B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko, and L. Maleki, “Ultra high Q crystalline microcavities,” Opt. Commun. 265, 33–38 (2006).
[Crossref]

Strekalov, D. V.

Sugimura, A.

E. Patzak, H. O, A. Sugimura, S. Saito, and T. Mukai, “Spectral linewidth reduction in semiconductor lasers by an external cavity with weak optical feedback,” Electron. Lett. 19(2), 938–940 (1983).
[Crossref]

Telle, H. R.

H. Li and H. R. Telle, “Efficient frequency noise reduction of GaAlAs semiconductor lasers by optical feedback from an external high-finesse resonator,” IEEE J. Quantum Electron. 25, 257–264 (1989).
[Crossref]

Tyurikov, D.

V. Velichanskii, A. Zibrov, V. Kargopoltsev, V. Molochev, V. Nikitin, V. Sautenkov, G. Kharisov, and D. Tyurikov, “Minimum line width of an injection laser,” Sov. Tech. Phys. Lett. 4(9), 438 (1978).

Udem, T.

J. Alnis, A. Matveev, N. Kolachevsky, T. Udem, and T. W. Hänsch, “Subhertz linewidth diode lasers by stabilization to vibrationally and thermally compensated ultralow-expansion glass Fabry-Pérot cavities,” Phys. Rev. A 77, 053809 (2008).
[Crossref]

Uskov, A. V.

E. Belenov, V. L. Velichanskii, A. S. Zibrov, V. V. Nikitin, V. A. Sautenkov, and A. V. Uskov, “Methods for narrowing the emission line of an injection laser,” Sov. J. Quantum. Electron. 13, 792 (1983).
[Crossref]

Vasil’ev, V. V.

V. V. Vasil’ev, V. L. Velichansky, M. L. Gorodetskii, V. S. Il’chenko, L. Holberg, and A. V. Yarovitsky, “High-coherence diode laser with optical feedback via a microcavity with ’whispering gallery’ modes,” Quantum Electron. 26, 657 (1996).
[Crossref]

Vassiliev, V.

V. Vassiliev, S. Il’ina, and V. Velichansky, “Diode laser coupled to a high-Q microcavity via a GRIN lens,” Appl. Phys. B 76, 521–523 (2003).
[Crossref]

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

Velichanskii, V.

V. Velichanskii, A. Zibrov, V. Kargopoltsev, V. Molochev, V. Nikitin, V. Sautenkov, G. Kharisov, and D. Tyurikov, “Minimum line width of an injection laser,” Sov. Tech. Phys. Lett. 4(9), 438 (1978).

Velichanskii, V. L.

E. Belenov, V. L. Velichanskii, A. S. Zibrov, V. V. Nikitin, V. A. Sautenkov, and A. V. Uskov, “Methods for narrowing the emission line of an injection laser,” Sov. J. Quantum. Electron. 13, 792 (1983).
[Crossref]

Velichansky, V.

V. Vassiliev, S. Il’ina, and V. Velichansky, “Diode laser coupled to a high-Q microcavity via a GRIN lens,” Appl. Phys. B 76, 521–523 (2003).
[Crossref]

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

Velichansky, V. L.

A. N. Oraevsky, A. V. Yarovitsky, and V. L. Velichansky, “Frequency stabilisation of a diode laser by a whispering-gallery mode,” Quantum Electron. 31, 897 (2001).
[Crossref]

V. V. Vasil’ev, V. L. Velichansky, M. L. Gorodetskii, V. S. Il’chenko, L. Holberg, and A. V. Yarovitsky, “High-coherence diode laser with optical feedback via a microcavity with ’whispering gallery’ modes,” Quantum Electron. 26, 657 (1996).
[Crossref]

Volodin, B. L.

Vuletic, V.

L. Ricci, M. Weidemüller, T. Esslinger, A. Hemmerich, C. Zimmermann, V. Vuletic, W. König, and T. Hänsch, “A compact grating-stabilized diode laser system for atomic physics,” Opt. Commun. 117, 541–549 (1995).
[Crossref]

Wang, C. Y.

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, “Temporal solitons in optical microresonators,” Nat. Photonics 8, 145–152 (2014).
[Crossref]

Wang, L. J.

Wang, Q.

Wang, S.

Ward, H.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[Crossref]

Wei, F.

Weidemüller, M.

L. Ricci, M. Weidemüller, T. Esslinger, A. Hemmerich, C. Zimmermann, V. Vuletic, W. König, and T. Hänsch, “A compact grating-stabilized diode laser system for atomic physics,” Opt. Commun. 117, 541–549 (1995).
[Crossref]

Wieman, C. E.

H. Patrick and C. E. Wieman, “Frequency stabilization of a diode laser using simultaneous optical feedback from a diffraction grating and a narrowband Fabry–Perot cavity,” Rev. Scient. Instrum. 62, 2593–2595 (1991).
[Crossref]

C. E. Wieman and L. Hollberg, “Using diode lasers for atomic physics,” Rev. Scient. Instr. 62, 1–20 (1991).
[Crossref]

Xijia, G.

Xu, D.

Yamamoto, Y.

S. Saito, O. Nilsson, and Y. Yamamoto, “Oscillation center frequency tuning, quantum FM noise, and direct frequency characteristics in external grating loaded semiconductor lasers,” IEEE J. Quantum Electron. 18, 961–970 (1982).
[Crossref]

Yang, F.

Yarovitsky, A.

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

Yarovitsky, A. V.

A. N. Oraevsky, A. V. Yarovitsky, and V. L. Velichansky, “Frequency stabilisation of a diode laser by a whispering-gallery mode,” Quantum Electron. 31, 897 (2001).
[Crossref]

V. V. Vasil’ev, V. L. Velichansky, M. L. Gorodetskii, V. S. Il’chenko, L. Holberg, and A. V. Yarovitsky, “High-coherence diode laser with optical feedback via a microcavity with ’whispering gallery’ modes,” Quantum Electron. 26, 657 (1996).
[Crossref]

Ye, J.

Yu, N.

Zang, E.

Zanon-Willette, T.

Zhang, L.

Zhang, X.

Zhao, Y.

Zibrov, A.

V. Velichanskii, A. Zibrov, V. Kargopoltsev, V. Molochev, V. Nikitin, V. Sautenkov, G. Kharisov, and D. Tyurikov, “Minimum line width of an injection laser,” Sov. Tech. Phys. Lett. 4(9), 438 (1978).

Zibrov, A. S.

E. Belenov, V. L. Velichanskii, A. S. Zibrov, V. V. Nikitin, V. A. Sautenkov, and A. V. Uskov, “Methods for narrowing the emission line of an injection laser,” Sov. J. Quantum. Electron. 13, 792 (1983).
[Crossref]

Zimmermann, C.

L. Ricci, M. Weidemüller, T. Esslinger, A. Hemmerich, C. Zimmermann, V. Vuletic, W. König, and T. Hänsch, “A compact grating-stabilized diode laser system for atomic physics,” Opt. Commun. 117, 541–549 (1995).
[Crossref]

A. Hemmerich, C. Zimmermann, and T. W. Hänsch, “Compact source of coherent blue light,” Appl. Opt. 33, 988–991 (1994).
[Crossref] [PubMed]

Appl. Opt. (2)

Appl. Phys. B (2)

V. Vassiliev, S. Il’ina, and V. Velichansky, “Diode laser coupled to a high-Q microcavity via a GRIN lens,” Appl. Phys. B 76, 521–523 (2003).
[Crossref]

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[Crossref]

Appl. Phys. Lett. (1)

L. Hollberg and M. Ohtsu, “Modulatable narrow–linewidth semiconductor lasers,” Appl. Phys. Lett. 53, 944–946 (1988).
[Crossref]

Electron. Lett. (1)

E. Patzak, H. O, A. Sugimura, S. Saito, and T. Mukai, “Spectral linewidth reduction in semiconductor lasers by an external cavity with weak optical feedback,” Electron. Lett. 19(2), 938–940 (1983).
[Crossref]

IEEE J. Quantum Electron. (6)

G. Agrawal, “Line narrowing in a single-mode injection laser due to external optical feedback,” IEEE J. Quantum Electron. 20, 468–471 (1984).
[Crossref]

P. Laurent, A. Clairon, and C. Breant, “Frequency noise analysis of optically self-locked diode lasers,” IEEE J. Quantum Electron. 25, 1131–1142 (1989).
[Crossref]

S. Saito, O. Nilsson, and Y. Yamamoto, “Oscillation center frequency tuning, quantum FM noise, and direct frequency characteristics in external grating loaded semiconductor lasers,” IEEE J. Quantum Electron. 18, 961–970 (1982).
[Crossref]

G. Hadley, “Injection locking of diode lasers,” IEEE J. Quantum Electron. 22, 419–426 (1986).
[Crossref]

H. Li and H. R. Telle, “Efficient frequency noise reduction of GaAlAs semiconductor lasers by optical feedback from an external high-finesse resonator,” IEEE J. Quantum Electron. 25, 257–264 (1989).
[Crossref]

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16 (3), 347–355 (1980).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

G. J. Steckman, W. Liu, R. Platz, D. Schroeder, C. Moser, and F. Havermeyer, “Volume holographic grating wavelength stabilized laser diodes,” IEEE J. Sel. Top. Quantum Electron. 13, 672–678 (2007).
[Crossref]

J. Opt. Soc. Am. B (1)

Jpn. J. Appl. Phys. (1)

H. Olesen, S. Saito, T. Mukai, T. Saitoh, and O. Mikami, “Solitary spectral linewidth and its reduction with external grating feedback for a 1.55 µ m InGaAsP BH laser,” Jpn. J. Appl. Phys. 22, L664 (1983).
[Crossref]

Laser Photonics Rev. (1)

S. Donati, “Developing self-mixing interferometry for instrumentation and measurements,” Laser Photonics Rev. 6, 393–417 (2012).
[Crossref]

Laser Phys. (2)

V. S. Il’chenko and M. L. Gorodetskii, “Thermal nonlinear effects in optical whispering gallery microresonators,” Laser Phys. 2, 1004–1009 (1992).

V. Ilchenko and M. Gorodetsky, “Thermal nonlinear effects in optical whispering gallery microresonators,” Laser Phys. 2, 1004–1009 (1992).

Nat. Commun. (2)

W. Liang, D. Eliyahu, V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, D. Seidel, and L. Maleki, “High spectral purity Kerr frequency comb radio frequency photonic oscillator,” Nat. Commun. 6, 7957 (2015).
[Crossref] [PubMed]

W. Liang, V. S. Ilchenko, D. Eliyahu, A. A. Savchenkov, A. B. Matsko, D. Seidel, and L. Maleki, “Thermal-noise-limited optical cavity,” Nat. Commun. 6, 7371 (2015).
[Crossref]

Nat. Photonics (1)

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, “Temporal solitons in optical microresonators,” Nat. Photonics 8, 145–152 (2014).
[Crossref]

Opt. Commun. (4)

I. S. Grudinin, A. B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko, and L. Maleki, “Ultra high Q crystalline microcavities,” Opt. Commun. 265, 33–38 (2006).
[Crossref]

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

L. Ricci, M. Weidemüller, T. Esslinger, A. Hemmerich, C. Zimmermann, V. Vuletic, W. König, and T. Hänsch, “A compact grating-stabilized diode laser system for atomic physics,” Opt. Commun. 117, 541–549 (1995).
[Crossref]

M. Kourogi and M. Ohtsu, “Novel optical frequency discriminator for FM noise reduction of semiconductor lasers,” Opt. Commun. 81, 204–208 (1991).
[Crossref]

Opt. Express (2)

Opt. Lett. (6)

Phys. Lett. A (1)

V. Braginsky, M. Gorodetsky, and V. Ilchenko, “Quality-factor and nonlinear properties of optical whispering-gallery modes,” Phys. Lett. A 137, 393–397 (1989).
[Crossref]

Phys. Rev. A (1)

J. Alnis, A. Matveev, N. Kolachevsky, T. Udem, and T. W. Hänsch, “Subhertz linewidth diode lasers by stabilization to vibrationally and thermally compensated ultralow-expansion glass Fabry-Pérot cavities,” Phys. Rev. A 77, 053809 (2008).
[Crossref]

Proc. IEEE (1)

R. Adler, “A study of locking phenomena in oscillators,” Proc. IEEE 61, 1380–1385 (1973).
[Crossref]

Proc. SPIE (1)

S. Borri, M. Siciliani de Cumis, G. Insero, G. Santambrogio, A. Savchenkov, D. Eliyahu, V. Ilchenko, A. Matsko, L. Maleki, and P. De Natale, “Whispering gallery mode stabilization of quantum cascade lasers for infrared sensing and spectroscopy,” Proc. SPIE 10090, 1009008 (2017).
[Crossref]

Quantum Electron. (2)

V. V. Vasil’ev, V. L. Velichansky, M. L. Gorodetskii, V. S. Il’chenko, L. Holberg, and A. V. Yarovitsky, “High-coherence diode laser with optical feedback via a microcavity with ’whispering gallery’ modes,” Quantum Electron. 26, 657 (1996).
[Crossref]

A. N. Oraevsky, A. V. Yarovitsky, and V. L. Velichansky, “Frequency stabilisation of a diode laser by a whispering-gallery mode,” Quantum Electron. 31, 897 (2001).
[Crossref]

Rev. Scient. Instr. (1)

C. E. Wieman and L. Hollberg, “Using diode lasers for atomic physics,” Rev. Scient. Instr. 62, 1–20 (1991).
[Crossref]

Rev. Scient. Instrum. (1)

H. Patrick and C. E. Wieman, “Frequency stabilization of a diode laser using simultaneous optical feedback from a diffraction grating and a narrowband Fabry–Perot cavity,” Rev. Scient. Instrum. 62, 2593–2595 (1991).
[Crossref]

Sov. J. Quantum. Electron. (1)

E. Belenov, V. L. Velichanskii, A. S. Zibrov, V. V. Nikitin, V. A. Sautenkov, and A. V. Uskov, “Methods for narrowing the emission line of an injection laser,” Sov. J. Quantum. Electron. 13, 792 (1983).
[Crossref]

Sov. Tech. Phys. Lett. (1)

V. Velichanskii, A. Zibrov, V. Kargopoltsev, V. Molochev, V. Nikitin, V. Sautenkov, G. Kharisov, and D. Tyurikov, “Minimum line width of an injection laser,” Sov. Tech. Phys. Lett. 4(9), 438 (1978).

Other (2)

V. S. Ilchenko, E. Dale, W. Liang, J. Byrd, D. Eliyahu, A. A. Savchenkov, A. B. Matsko, D. Seidel, and L. Maleki, “Compact tunable kHz-linewidth semiconductor laser stabilized with a whispering-gallery mode microresonator,” in “Proc. SPIE,”, vol. 7913 (2011), vol. 7913, pp. 1G–1.

H. A. Haus, Waves and Fields in Optoelectronics, (Prentice-Hall, 1984), pp. 59–65.

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Figures (4)

Fig. 1
Fig. 1 Schematic of the WGM microresonator-based self-injection locking.
Fig. 2
Fig. 2 (a) Tuning curves (10) for different initial phases: I–IV correspond to phases ψ0 = [0, π/3, 2π/3, π] with κτs ≪ 1. The envelope for the family of curves with different ψ0 is shown with black dash-dotted line, the green solid line shows a tuning curve for a free running laser; (b) Tuning curves I-IV corresponding ψ0 = 0 and long delay, so that κmτs/2 = [0, 1, 2, 3]; (c) Tuning curves for different K values: I–III correspond to ψ0 = π, and K = [5, 3, 1], lines IV–VII correspond to ψ0 = 0, K = 0, 2, 4, 6 ; (d) An optimal self-injection locking curve with ψ0 = 0, κmτs ≪ 1, and K ≫4. Unstable branches are shown with dashed lines, and bistable transitions with blue arrows.
Fig. 3
Fig. 3 Comparison of analytical theory and numerical modeling. a) Curves I–IV - dependencies of generated frequency detuning from the laser frequency detuning for different phases ψ 0 = [ 0 , π 2 , π , 3 π 2 ]. Theoretical tuning curves (10) are shown with dashed for comparison. b) Simulated dependence of the intensity inside WGM microresonator over the laser frequency detuning for different phase delays for the same parameters.
Fig. 4
Fig. 4 Experimental laser generated intensity. a) The frequency of a DFB laser diode is swept by current through different WGM resonator modes. Arrows indicate modes that have different initial phase delays ψ0 analogously to 3(b). b) Responses for the same mode with different adjusted phases ψ0

Tables (2)

Tables Icon

Table 1 Typical laser and crystalline WGM parameters and locking properties estimates.

Tables Icon

Table 2 Typical laser parameters were used for numerical simulation.

Equations (23)

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

A ( t ) e i ϕ ( t ) = i T o B ( t ) + R e R o A ( t τ d ) e i ω τ d + 2 ( γ α ) L + i ϕ ( t τ d ) ,
A ˙ + i ϕ ˙ + ( κ d 2 g ( | A | 2 ) 2 ( 1 + i α g ) i ( ω ω d ) ) A = i κ d o T o B e i ϕ .
κ d i = 2 α c n , κ d c = 2 1 R e R o τ d R e R o , 2 γ c n = ( 1 + i α g ) g ( | A | 2 ) .
B ( t ) = i T o Γ ( ω ) R o A ( t τ s ) e i ω τ s + i ϕ ( t τ s ) ,
A ˙ = ( g ( | A | 2 ) / 2 κ d / 2 ) A κ d o R o | Γ ( ω ) | A ( t τ s ) cos ψ ,
ϕ ˙ = α g g ( | A | 2 ) / 2 + ( ω ω d ) κ d o R o | Γ ( ω ) | A ( t τ s ) A ( t ) sin ψ ,
ω ω ¯ d = | Γ ( ω ) | κ ¯ d o sin ( ψ arctan α g ) ,
Γ ( ω ) = i η κ m 2 β / 2 ( κ m / 2 i ( ω ω m ) ) 2 + ( β κ m / 2 ) 2 .
ω ¯ d ω m = ( ω ω m ) + η κ m 2 β κ ¯ d o 2 ( ω ω m ) κ m cos ψ ¯ + ( ( 1 + β 2 ) κ m 2 / 4 ( ω ω m ) 2 ) sin ψ ¯ ( κ m 2 / 4 ( 1 + β 2 ) ( ω ω m ) 2 ) 2 + ( ω ω m ) 2 κ m 2 ,
ξ = ζ + K 2 2 ζ cos ψ ¯ + ( 1 + β 2 ζ 2 ) sin ψ ¯ ( 1 + β 2 ζ 2 ) 2 + 4 ζ 2 .
ψ ¯ = ψ 0 + ( ω ω m ) τ s = ψ 0 + κ m τ s 2 ζ .
δ ω δ d = κ m 2 ζ ψ 0 2 c ψ 0 τ s = ( ξ ψ 0 / ξ ζ ) ψ 0 = 0 κ m ω m c = K ( K + 1 ) ω m 2 2 Q m c .
ξ = ζ + K ζ ( 1 + ζ 2 ) 2 .
ζ 6 + 3 ζ 4 3 ( K 1 ) ζ 2 + K + 1 = 0 .
ζ 1 , 2 = ± 2 K cos ( π 3 + 1 3 arccos ( 2 K ) ) 1 = ± 3 ( 1 3 + 32 81 K ) + O ( K 2 ) , ξ ( ζ 1 , 2 ) = ± 3 ( 3 16 K + 1 3 ) + O ( K 1 ) ,
ζ 3 , 4 = ± 2 K sin ( π 6 + 1 3 arccos ( 2 K ) ) 1 = ± ( 3 K 4 5 6 3 K 4 ) + O ( K 3 / 4 ) , ξ ( ζ 3 , 4 ) = ± ( 4 3 K 4 3 2 3 3 K 4 ) + O ( K 3 / 4 ) .
Δ ω lock ω 1 + α g 2 Γ m Q d .
δ ω δ ω free Q d 2 Q m 2 1 16 Γ m 2 ( 1 + α g 2 ) ,
ψ 0 ω m δ ω m = τ s Δ ω lock < π 4 .
d N d t = J N κ N κ m N N g N | A | 2 ,
d A d t = ( ( 1 + i α g ) N g N κ d κ m + i ( ξ 0 v ω t ) ) A 2 κ d o κ m T m T o e i ω m τ s / 2 A ,
d A + d t = A + + i β A 2 η T o T m e i ω m τ s / 2 A ,
d A d t = A + i β A + .

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