Abstract

We present a novel method allowing high-power single-frequency emission with sub-kHz linewidth from a compact multi-frequency diode laser locked to high-Q optical microresonator. Using high-Q MgF2microresonator and multi-frequency diode laser operating at 1535 nm with the output power of 100 mW and an emission spectrum consisting of approximately 50 lines with MHz linewidth, we observed a spectrum collapse to a single line or several lines with a sub-kHz linewidth and output power power of 50 mW. The Bogatov effect predicted more than 30 years ago was observed and studied in the spectrum of the locked laser. For analysis of the considered effect, original theoretical model taking into account self-injection locking effect, mode competition and Bogatov asymmetric mode interaction was developed and numerical modeling was performed. All numerical results are in a good agreement with our experimental data. Accurate analytical estimations for the parameters critical for the considered effect were obtained. The proposed method may be applied for different types of diode lasers operating in different spectral ranges.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]

2018 (3)

N. Volet, X. Yi, Q. Yang, E. Stanton, P. Morton, K. Y. Yang, K. Vahala, and J. Bowers, “Micro-resonator soliton generated directly with a diode laser,” Laser & Photonics Rev. 12, 1700307 (2018).
[Crossref]

N. G. Pavlov, G. V. Lihachev, A. S. Voloshin, S. Koptyaev, N. M. Kondratiev, V. E. Lobanov, A. S. Gorodnitskii, and M. L. Gorodetsky, “Narrow linewidth diode laser self-injection locked to a high-Q microresonator,” AIP Conf. Proc. 1936, 020005 (2018).
[Crossref]

N. G. Pavlov, S. Koptyaev, G. V. Lihachev, A. S. Voloshin, A. S. Gorodnitskii, M. V. Ryabko, S. V. Polonsky, and M. L. Gorodetsky, “Narrow linewidth lasing and soliton Kerr-microcombs with ordinary laser diodes,” Nat. Photon. 12, 694–699 (2018).
[Crossref]

2017 (3)

2016 (4)

B. Sumpf, J. Kabitzke, J. Fricke, P. Ressel, A. Müller, M. Maiwald, and G. Tränkle, “Dual-wavelength diode laser with electrically adjustable wavelength distance at 785 nm,” Opt. Lett. 41, 3694–3697 (2016).
[Crossref] [PubMed]

N. Prtljaga, C. Bentham, J. O’Hara, B. Royall, E. Clarke, L. R. Wilson, M. S. Skolnick, and A. M. Fox, “On-chip interference of single photons from an embedded quantum dot and an external laser,” Appl. Phys. Lett. 108, 251101 (2016).
[Crossref]

C. Lecaplain, C. Javerzac-Galy, M. L. Gorodetsky, and T. J. Kippenberg, “Mid-infrared ultra-high-Q resonators based on fluoride crystalline materials,” Nat. Commun. 7, 13383 (2016).
[Crossref] [PubMed]

M. Gebrekidan, C. Knipfer, F. Stelzle, J. Popp, S. Will, and A. Braeuer, “A shifted-excitation Raman difference spectroscopy (SERDS) evaluation strategy for the efficient isolation of Raman spectra from extreme fluorescence interference,” J. Raman Spectrosc. 47, 198–209 (2016).
[Crossref]

2015 (3)

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, “Ultralow noise miniature external cavity semiconductor laser,” Nat. Commun. 6, 7371 (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]

2014 (2)

D. Lenstra and M. Yousefi, “Rate-equation model for multi-mode semiconductor lasers with spatial hole burning,” Opt. Express 22, 8143–8149 (2014).
[Crossref] [PubMed]

B. Bloom, T. Nicholson, J. Williams, S. Campbell, M. Bishof, X. Zhang, W. Zhang, S. Bromley, and J. Ye, “An optical lattice clock with accuracy and stability at the 10−18 level,” Nature 506, 71–75 (2014).
[Crossref] [PubMed]

2013 (1)

2012 (1)

2011 (2)

W.-C. Lai, S. Chakravarty, X. Wang, C. Lin, and R. T. Chen, “Photonic crystal slot waveguide absorption spectrometer for on-chip near-infrared spectroscopy of xylene in water,” Appl. Phys. Lett. 98, 023304 (2011).
[Crossref]

A. Brenier, “Tunable THz frequency difference from a diode-pumped dual-wavelength Yb3+:KGd(WO4)2laser with chirped volume Bragg gratings,” Laser Phys. Lett. 8, 520–524 (2011).
[Crossref]

2010 (4)

A. Makdissi, F. Vernotte, and E. D. Clercq, “Stability variances: a filter approach,” IEEE Transactions on Ultrason. Ferroelectr. Freq. Control. 57, 1011–1028 (2010).
[Crossref]

M. Ahmed and M. Yamada, “Inducing single-mode oscillation in Fabry-Perot InGaAsP lasers by applying external optical feedback,” IET Optoelectronics 4, 133–141 (2010).
[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]

G. D. Domenico, S. Schilt, and P. Thomann, “Simple approach to the relation between laser frequency noise and laser line shape,” Appl. Opt. 49, 4801–4807 (2010).
[Crossref] [PubMed]

2009 (1)

2008 (1)

C. S. Friedrich, C. Brenner, S. Hoffmann, A. Schmitz, I. C. Mayorga, A. Klehr, G. Erbert, and M. R. Hofmann, “New two-color laser concepts for THz generation,” IEEE J. Sel. Top. Quantum Electron. 14, 270–276 (2008).
[Crossref]

2007 (1)

I. M. White, H. Zhu, J. D. Suter, N. M. Hanumegowda, H. Oveys, M. Zourob, and X. Fan, “Refractometric sensors for lab-on-a-chip based on optical ring resonators,” IEEE Sensors J. 7, 28–35 (2007).
[Crossref]

2006 (1)

2004 (1)

R. Czarny, M. Alouini, C. Larat, M. Krakowski, and D. Dolfi, “THz-dual-frequency Yb3+:KGd(WO4)2laser for continuous wave THz generation through photomixing,” Electron. Lett. 40, 942 – 943 (2004).
[Crossref]

2003 (1)

M. Yousefi, A. Barsella, D. Lenstra, G. Morthier, R. Baets, S. McMurtry, and J. P. Vilcot, “Rate equations model for semiconductor lasers with multilongitudinal mode competition and gain dynamics,” IEEE J. Quantum Electron. 39, 1229–1237 (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,” Quant. El. 31, 897–903 (2001).
[Crossref]

2000 (2)

V. Anan’ev, B. Vasil’ev, A. Lobanov, A. Lytkin, C. Cho, and J. Kim, “Two-frequency lidar based on an ammonium laser,” Quantum Electron. 30, 535–539 (2000).
[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]

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. Vasiliev, V. Velichansky, M. Gorodetskii, V. Ilchenko, L. Holberg, and A. Yarovitsky, “High-coherence diode laser with optical feedback via a microcavity with ’whispering gallery’ modes,” Quantum Electron. 26(8), 657–658 (1996).
[Crossref]

1995 (2)

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]

N. Ninane and M. P. Georges, “Holographic interferometry using two-wavelength holography for the measurement of large deformations,” Appl. Opt. 34, 1923–1928 (1995).
[Crossref] [PubMed]

1991 (2)

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. Sci. Instrum. 62, 2593–2595 (1991).
[Crossref]

D. R. Hjelme, A. R. Mickelson, and R. G. Beausoleil, “Semiconductor laser stabilization by external optical feedback,” IEEE J. Quantum Electron. 27, 352–372 (1991).
[Crossref]

1989 (2)

M. Yamada, “Theoretical analysis of nonlinear optical phenomena taking into account the beating vibration of the electron density in semiconductor lasers,” J. Appl. Phys. 66, 81–89 (1989).
[Crossref]

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

1988 (1)

H. Li and N. B. Abraham, “Power spectrum of frequency noise of semiconductor lasers with optical feedback from a high-finesse resonator,” Appl. Phys. Lett. 53, 2257–2259 (1988).
[Crossref]

1984 (1)

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

1983 (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. Journ. Quant. El. 13, 792–798 (1983).
[Crossref]

1982 (1)

H. Ishikawa, M. Yano, and M. Takusagawa, “Mechanism of asymmetric longitudinal mode competition in InGaAsP/InP lasers,” Appl. Phys. Lett. 40, 553–555 (1982).
[Crossref]

1981 (1)

M. Yamada and Y. Suematsu, “Analysis of gain suppression in undoped injection lasers,” J. Appl. Phys. 52, 2653–2664 (1981).
[Crossref]

1980 (1)

R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16, 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), 438–439 (1978).

1977 (1)

J. Olivero and R. Longbothum, “Empirical fits to the Voigt line width: A brief review,” J. Quant. Spectrosc. Radiat. Transf. 17, 233 – 236 (1977).
[Crossref]

1975 (1)

A. P. Bogatov, P. G. Eliseev, and B. N. Sverdlov, “Anomalous interaction of spectral modes in a semiconductor laser,” Sov. J. Quantum Electron. 4, 1275–1276 (1975).
[Crossref]

1972 (1)

P. Smith, “Mode selection in lasers,” Proc. IEEE 60, 422 – 440 (1972).
[Crossref]

Abraham, N. B.

H. Li and N. B. Abraham, “Power spectrum of frequency noise of semiconductor lasers with optical feedback from a high-finesse resonator,” Appl. Phys. Lett. 53, 2257–2259 (1988).
[Crossref]

Agrawal, G.

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

Sverdlov, B. N.

A. P. Bogatov, P. G. Eliseev, and B. N. Sverdlov, “Anomalous interaction of spectral modes in a semiconductor laser,” Sov. J. Quantum Electron. 4, 1275–1276 (1975).
[Crossref]

Takusagawa, M.

H. Ishikawa, M. Yano, and M. Takusagawa, “Mechanism of asymmetric longitudinal mode competition in InGaAsP/InP lasers,” Appl. Phys. Lett. 40, 553–555 (1982).
[Crossref]

Thomann, P.

Time, P. L. U.

W. Riley, P. L. U. Time, and F. Division, Handbook of Frequency Stability Analysis, NIST special publication (U.S. Department of Commerce, National Institute of Standards and Technology, 2008).

Tränkle, G.

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), 438–439 (1978).

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. Journ. Quant. El. 13, 792–798 (1983).
[Crossref]

Vahala, K.

N. Volet, X. Yi, Q. Yang, E. Stanton, P. Morton, K. Y. Yang, K. Vahala, and J. Bowers, “Micro-resonator soliton generated directly with a diode laser,” Laser & Photonics Rev. 12, 1700307 (2018).
[Crossref]

Vasil’ev, B.

V. Anan’ev, B. Vasil’ev, A. Lobanov, A. Lytkin, C. Cho, and J. Kim, “Two-frequency lidar based on an ammonium laser,” Quantum Electron. 30, 535–539 (2000).
[Crossref]

Vasiliev, V. V.

V. V. Vasiliev, V. Velichansky, M. Gorodetskii, V. Ilchenko, L. Holberg, and A. Yarovitsky, “High-coherence diode laser with optical feedback via a microcavity with ’whispering gallery’ modes,” Quantum Electron. 26(8), 657–658 (1996).
[Crossref]

Vassiliev, V.

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), 438–439 (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. Journ. Quant. El. 13, 792–798 (1983).
[Crossref]

Velichansky, V.

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. V. Vasiliev, V. Velichansky, M. Gorodetskii, V. Ilchenko, L. Holberg, and A. Yarovitsky, “High-coherence diode laser with optical feedback via a microcavity with ’whispering gallery’ modes,” Quantum Electron. 26(8), 657–658 (1996).
[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,” Quant. El. 31, 897–903 (2001).
[Crossref]

Vernotte, F.

A. Makdissi, F. Vernotte, and E. D. Clercq, “Stability variances: a filter approach,” IEEE Transactions on Ultrason. Ferroelectr. Freq. Control. 57, 1011–1028 (2010).
[Crossref]

Vilcot, J. P.

M. Yousefi, A. Barsella, D. Lenstra, G. Morthier, R. Baets, S. McMurtry, and J. P. Vilcot, “Rate equations model for semiconductor lasers with multilongitudinal mode competition and gain dynamics,” IEEE J. Quantum Electron. 39, 1229–1237 (2003).
[Crossref]

Volet, N.

N. Volet, X. Yi, Q. Yang, E. Stanton, P. Morton, K. Y. Yang, K. Vahala, and J. Bowers, “Micro-resonator soliton generated directly with a diode laser,” Laser & Photonics Rev. 12, 1700307 (2018).
[Crossref]

Voloshin, A. S.

N. G. Pavlov, G. V. Lihachev, A. S. Voloshin, S. Koptyaev, N. M. Kondratiev, V. E. Lobanov, A. S. Gorodnitskii, and M. L. Gorodetsky, “Narrow linewidth diode laser self-injection locked to a high-Q microresonator,” AIP Conf. Proc. 1936, 020005 (2018).
[Crossref]

N. G. Pavlov, S. Koptyaev, G. V. Lihachev, A. S. Voloshin, A. S. Gorodnitskii, M. V. Ryabko, S. V. Polonsky, and M. L. Gorodetsky, “Narrow linewidth lasing and soliton Kerr-microcombs with ordinary laser diodes,” Nat. Photon. 12, 694–699 (2018).
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N. M. Kondratiev, V. E. Lobanov, A. V. Cherenkov, A. S. Voloshin, N. G. Pavlov, S. Koptyaev, and M. L. Gorodetsky, “Self-injection locking of a laser diode to a high-Q WGM microresonator,” Opt. Express 25, 28167–28178 (2017).
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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, L. J.

Wang, X.

W.-C. Lai, S. Chakravarty, X. Wang, C. Lin, and R. T. Chen, “Photonic crystal slot waveguide absorption spectrometer for on-chip near-infrared spectroscopy of xylene in water,” Appl. Phys. Lett. 98, 023304 (2011).
[Crossref]

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]

White, I. M.

I. M. White, H. Zhu, J. D. Suter, N. M. Hanumegowda, H. Oveys, M. Zourob, and X. Fan, “Refractometric sensors for lab-on-a-chip based on optical ring resonators,” IEEE Sensors J. 7, 28–35 (2007).
[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. Sci. Instrum. 62, 2593–2595 (1991).
[Crossref]

Will, S.

M. Gebrekidan, C. Knipfer, F. Stelzle, J. Popp, S. Will, and A. Braeuer, “A shifted-excitation Raman difference spectroscopy (SERDS) evaluation strategy for the efficient isolation of Raman spectra from extreme fluorescence interference,” J. Raman Spectrosc. 47, 198–209 (2016).
[Crossref]

Williams, J.

B. Bloom, T. Nicholson, J. Williams, S. Campbell, M. Bishof, X. Zhang, W. Zhang, S. Bromley, and J. Ye, “An optical lattice clock with accuracy and stability at the 10−18 level,” Nature 506, 71–75 (2014).
[Crossref] [PubMed]

Wilson, L. R.

N. Prtljaga, C. Bentham, J. O’Hara, B. Royall, E. Clarke, L. R. Wilson, M. S. Skolnick, and A. M. Fox, “On-chip interference of single photons from an embedded quantum dot and an external laser,” Appl. Phys. Lett. 108, 251101 (2016).
[Crossref]

Yamada, M.

M. Ahmed and M. Yamada, “Inducing single-mode oscillation in Fabry-Perot InGaAsP lasers by applying external optical feedback,” IET Optoelectronics 4, 133–141 (2010).
[Crossref]

M. Yamada, “Theoretical analysis of nonlinear optical phenomena taking into account the beating vibration of the electron density in semiconductor lasers,” J. Appl. Phys. 66, 81–89 (1989).
[Crossref]

M. Yamada and Y. Suematsu, “Analysis of gain suppression in undoped injection lasers,” J. Appl. Phys. 52, 2653–2664 (1981).
[Crossref]

Yang, K. Y.

N. Volet, X. Yi, Q. Yang, E. Stanton, P. Morton, K. Y. Yang, K. Vahala, and J. Bowers, “Micro-resonator soliton generated directly with a diode laser,” Laser & Photonics Rev. 12, 1700307 (2018).
[Crossref]

Yang, Q.

N. Volet, X. Yi, Q. Yang, E. Stanton, P. Morton, K. Y. Yang, K. Vahala, and J. Bowers, “Micro-resonator soliton generated directly with a diode laser,” Laser & Photonics Rev. 12, 1700307 (2018).
[Crossref]

Yano, M.

H. Ishikawa, M. Yano, and M. Takusagawa, “Mechanism of asymmetric longitudinal mode competition in InGaAsP/InP lasers,” Appl. Phys. Lett. 40, 553–555 (1982).
[Crossref]

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]

V. V. Vasiliev, V. Velichansky, M. Gorodetskii, V. Ilchenko, L. Holberg, and A. Yarovitsky, “High-coherence diode laser with optical feedback via a microcavity with ’whispering gallery’ modes,” Quantum Electron. 26(8), 657–658 (1996).
[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,” Quant. El. 31, 897–903 (2001).
[Crossref]

Ye, J.

B. Bloom, T. Nicholson, J. Williams, S. Campbell, M. Bishof, X. Zhang, W. Zhang, S. Bromley, and J. Ye, “An optical lattice clock with accuracy and stability at the 10−18 level,” Nature 506, 71–75 (2014).
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Yi, X.

N. Volet, X. Yi, Q. Yang, E. Stanton, P. Morton, K. Y. Yang, K. Vahala, and J. Bowers, “Micro-resonator soliton generated directly with a diode laser,” Laser & Photonics Rev. 12, 1700307 (2018).
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D. Lenstra and M. Yousefi, “Rate-equation model for multi-mode semiconductor lasers with spatial hole burning,” Opt. Express 22, 8143–8149 (2014).
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M. Yousefi, A. Barsella, D. Lenstra, G. Morthier, R. Baets, S. McMurtry, and J. P. Vilcot, “Rate equations model for semiconductor lasers with multilongitudinal mode competition and gain dynamics,” IEEE J. Quantum Electron. 39, 1229–1237 (2003).
[Crossref]

Yu, N.

Zhang, W.

B. Bloom, T. Nicholson, J. Williams, S. Campbell, M. Bishof, X. Zhang, W. Zhang, S. Bromley, and J. Ye, “An optical lattice clock with accuracy and stability at the 10−18 level,” Nature 506, 71–75 (2014).
[Crossref] [PubMed]

Zhang, X.

B. Bloom, T. Nicholson, J. Williams, S. Campbell, M. Bishof, X. Zhang, W. Zhang, S. Bromley, and J. Ye, “An optical lattice clock with accuracy and stability at the 10−18 level,” Nature 506, 71–75 (2014).
[Crossref] [PubMed]

Zhu, H.

I. M. White, H. Zhu, J. D. Suter, N. M. Hanumegowda, H. Oveys, M. Zourob, and X. Fan, “Refractometric sensors for lab-on-a-chip based on optical ring resonators,” IEEE Sensors J. 7, 28–35 (2007).
[Crossref]

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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), 438–439 (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. Journ. Quant. El. 13, 792–798 (1983).
[Crossref]

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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]

Zourob, M.

I. M. White, H. Zhu, J. D. Suter, N. M. Hanumegowda, H. Oveys, M. Zourob, and X. Fan, “Refractometric sensors for lab-on-a-chip based on optical ring resonators,” IEEE Sensors J. 7, 28–35 (2007).
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N. G. Pavlov, G. V. Lihachev, A. S. Voloshin, S. Koptyaev, N. M. Kondratiev, V. E. Lobanov, A. S. Gorodnitskii, and M. L. Gorodetsky, “Narrow linewidth diode laser self-injection locked to a high-Q microresonator,” AIP Conf. Proc. 1936, 020005 (2018).
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W.-C. Lai, S. Chakravarty, X. Wang, C. Lin, and R. T. Chen, “Photonic crystal slot waveguide absorption spectrometer for on-chip near-infrared spectroscopy of xylene in water,” Appl. Phys. Lett. 98, 023304 (2011).
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N. Prtljaga, C. Bentham, J. O’Hara, B. Royall, E. Clarke, L. R. Wilson, M. S. Skolnick, and A. M. Fox, “On-chip interference of single photons from an embedded quantum dot and an external laser,” Appl. Phys. Lett. 108, 251101 (2016).
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IET Optoelectronics (1)

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M. Yamada and Y. Suematsu, “Analysis of gain suppression in undoped injection lasers,” J. Appl. Phys. 52, 2653–2664 (1981).
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N. Volet, X. Yi, Q. Yang, E. Stanton, P. Morton, K. Y. Yang, K. Vahala, and J. Bowers, “Micro-resonator soliton generated directly with a diode laser,” Laser & Photonics Rev. 12, 1700307 (2018).
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Nature (1)

B. Bloom, T. Nicholson, J. Williams, S. Campbell, M. Bishof, X. Zhang, W. Zhang, S. Bromley, and J. Ye, “An optical lattice clock with accuracy and stability at the 10−18 level,” Nature 506, 71–75 (2014).
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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).
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Figures (5)

Fig. 1
Fig. 1 Experimental setup. Diode laser at 1535 nm (multi-frequency); PD – photodetector; ESA – electrical spectrum analyzer; OSA – optical spectrum analyzer; OSC – oscilloscope; b: photo of the microresonator with the coupling prism.
Fig. 2
Fig. 2 a: Experimental (blue line) and numerically calculated (red line) emission spectrum of the free-running multi-frequency diode laser [Eq. (6)Eq. (7)]; b: Experimental (blue line) and numerically calculated (red line) emission spectrum of the self-injection locked multi-frequency diode laser [Eq. (6), Eq. (7), Eq. (14)]. The model parameters are shown in Table 1.
Fig. 3
Fig. 3 a: Beating signal (near 7.5 GHz) of the self-injection locked laser with the reference NKT Koheras Adjustik laser (red line) and Voigt approximation of this signal (black line). ESA resolution bandwidth is 20 kHz and video bandwidth is 20 kHz; sweep time is 2.4 ms, no averaging. The sweep time was optimally selected to minimize frequency drift and low-frequency noise losses [42]. b: The Hadamard and Allan deviations of the frequency difference between two lasers self-injection locked on different modes (beating frequency 2.8 GHz) in one microresonator and flicker frequency noise approximation ∝ τ0 (blue line) and ∝ τ1 approximation (red line), which corresponds to ∝ f−3 frequency noise.
Fig. 4
Fig. 4 Optical spectrum of the several-frequency radiation of the self-injection locked laser (blue - the experiment, orange - the model): a: two-frequency regime; a: four-frequency regime; a: six-frequency regime. The model parameters are presented in Table 1; additional feedback is added to corresponding modes.
Fig. 5
Fig. 5 a: Experimentally obtained spectra of the self-injection locked laser at different feedback levels (colored solid lines) with numerically calculated envelopes (black lines) for Γ1= 1 × 10−2, Γ2= 1.2 × 10−2, Γ3= 1.5 × 10−2, respectively. The green spectrum is not approximated well; b: Numerically calculated dependence of the single mode energy concentration (η) on the feedback level (blue line) and experimentally obtained energy concentration points (squares). A circle corresponds to the green spectrum in upper figure (a) and a triangle corresponds to the free-running laser [Fig. 2(a)]. The model parameters are shown in Table 1.

Tables (1)

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Table 1 Parameters, used in the model. Several parameters were obtained by fitting the experimental spectrum [see Fig.4(b)] with the calculated one [Eq.6, 7 and 14] (labeled as "fit"). Parameters, labeled as "doc" were taken from the laser documentation. The parameters known in literature provided for comparison with fitted ones together with corresponding references.

Equations (16)

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σ H 2 ( τ ) = a 2 τ 2 + a 0 τ 0 .
S v ( f ) = 0.8 π 2 v 0 2 a 2 f 3 + 0.89 v 0 2 a 0 f 1 + Δ v Lorentz π ,
Δ v eff S v f 2 d f = 1 π ,
Δ v locked Δ v free ~ Q d 2 Q 2 1 16 η d 2 Γ ( 1 + α 2 ) ,
Q d = 2 π v 0 τ d R o 1 R o 2 ,
N ˙ = I e N τ s l G l ( 1 ) S l ,
S ˙ l = ( G l G th ) S l + N F l ,
F l = β ˜ [ 2 ( λ l λ peak ) / Δ λ ] 2 + 1 ,
G th = c n D α loss + 1 τ d ln 1 R o R e ,
G l = G l ( 1 ) G l ( 3 ) S l k l ( G l ( k ) ( 3 ) + G l ( k ) Bogatov ) S k ,
G l ( 1 ) = θ ( N N g D ( λ l λ peak ) 2 ) ,
G l ( k ) Bogatov = 3 4 θ 2 ( N N g ) 1 τ s + 3 2 θ S + α Ω l ( k ) ( 1 τ s + 3 2 θ S ) 2 + Ω l ( k ) 2 ,
δ S feedback = 2 κ ˜ o l S l ( t τ ) S l cos ( ψ l + ϕ l ( t ) ϕ l ( t τ ) ) ,
δ S feedback = δ l p 2 κ ˜ o l S l cos ( ψ l ) ,
S l S p .
2 κ ˜ o p S p N F p .

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