Abstract

We present a detailed analysis of a semiconductor hybrid laser exploiting spectral control from an external photonic waveguide circuit that provides frequency-selective feedback. Based on a spatially resolved transmission line model (TLM), we have investigated the output power, emission frequency, and the laser spectral linewidth. We find that, if the feedback becomes weaker, the spectral linewidth is larger than predicted by previous models that are based on a modified mean-field approximation, even if these take a strong spatial variation of the gain into account. The observed excess linewidth is caused by additional index fluctuations that are associated with strong spatial gain variations.

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

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References

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2015 (4)

T. Komljenovic, S. Srinivasan, E. Norberg, M. Davenport, G. Fish, and J. E. Bowers, “Widely tunable narrow-linewidth monolithically integrated external-cavity semiconductor lasers,” IEEE J. Sel. Topics Quantum Electron. 21(6), 214–222 (2015).
[Crossref]

S. Srinivasan, M. Davenport, T. Komljenovic, J. Hulme, D. T. Spencer, and J. E. Bowers, “Coupled-ring-resonator-mirror-based heterogeneous III–V silicon tunable laser,” IEEE Photon. J. 7(3), 1–8 (2015).
[Crossref]

R. Tang, T. Kita, and H. Yamada, “Narrow-spectral-linewidth silicon photonic wavelength-tunable laser with highly asymmetric Mach-Zehnder interferometer,” Opt. Lett. 40(7), 1504–1507 (2015).
[Crossref] [PubMed]

L. Zhuang, C. G. H. Roeloffzen, M. Hoekman, K.-J. Boller, and A. J. Lowery, “Programmable photonic signal processor chip for radiofrequency applications,” Optica 2(10), 854–859 (2015).
[Crossref]

2014 (3)

Y. Fan, R. M. Oldenbeuving, E. J. Klein, C. J. Lee, H. Song, M. R. H. Khan, H. L. Offerhaus, P. J. M. van der Slot, and K.-J. Boller, “A hybrid semiconductor-glass waveguide laser,” Proc. SPIE, vol.  9135, 91351B (2014).

C. T. Santis, S. T. Steger, Y. Vilenchik, A. Vasilyev, and A. Yariv, “High-coherence semiconductor lasers based on integral high-Q resonators in hybrid Si/III–V platforms,” Proc. Natl. Acad. Sci. U.S.A. 111(8), 2879–2884 (2014).
[Crossref] [PubMed]

T. Kita, K. Nemoto, and H. Yamada, “Silicon photonic wavelength-tunable laser diode with asymmetric Mach-Zehnder interferometer,” IEEE J. Sel. Topics Quantum Electron. 20(4), 344–349 (2014).
[Crossref]

2013 (4)

M. Faugeron, M. Tran, O. Parillaud, and M. Chtioui, “High-power tunable dilute mode DFB laser with low RIN and narrow linewidth,” IEEE Photon. Technol. Lett. 25(1), 7–10 (2013).
[Crossref]

R. M. Oldenbeuving, E. J. Klein, H. L. Offerhaus, C. J. Lee, H. Song, and K.-J. Boller, “25 kHz narrow spectral bandwidth of a wavelength tunable diode laser with a short waveguide-based external cavity,” Laser Phys. Lett. 10(1), 015804 (2013).
[Crossref]

J. C. Hulme, J. K. Doylend, and J. E. Bowers, “Widely tunable vernier ring laser on hybrid silicon,” Opt. Express 21(17), 19718–19722 (2013).
[Crossref] [PubMed]

C. G. H. Roeloffzen, L. Zhuang, C. Taddei, A. Leinse, R. G. Heideman, P. W. L. van Dijk, R. M. Oldenbeuving, D. A. I. Marpaung, M. Burla, and K.-J. Boller, “Silicon nitride microwave photonic circuits,” Opt. Express 21(19), 22937–22961 (2013).
[Crossref] [PubMed]

2011 (2)

L. He, Ş. Özdemir, J. Zhu, W. Kim, and L. Yang, “Detecting single viruses and nanoparticles using whispering gallery microlasers,” Nat. Nanotech. 6(7), 428–432 (2011).
[Crossref]

Y. Jiang, A. Ludlow, N. Lemke, R. Fox, J. Sherman, L.-S. Ma, and C. Oates, “Making optical atomic clocks more stable with 10−16-level laser stabilization,” Nat. Photonics 5(3), 158–161 (2011).
[Crossref]

2010 (1)

2009 (2)

T. Chu, N. Fujioka, and M. Ishizaka, “Compact, lower-power-consumption wavelength tunable laser fabricated with silicon photonic wire waveguide micro-ring resonators,” Opt. Express 17(16), 14063–14068 (2009).
[Crossref] [PubMed]

S. Zhang, P. Y. Kam, C. Yu, and J. Chen, “Laser linewidth tolerance of decision-aided maximum likelihood phase estimation in coherent optical M-ary PSK and QAM systems,” IEEE Photon. Technol. Lett. 21(15), 1075–1077 (2009).
[Crossref]

2004 (1)

K. A. Williams, M. G. Thompson, and I. H. White, “Long-wavelength monolithic mode-locked diode lasers,” New J. Phys. 6(1), 179 (2004).
[Crossref]

2003 (1)

2002 (1)

Y. A. Akulova, G. A. Fish, P.-C. Koh, C. L. Schow, P. Kozodoy, A. P. Dahl, S. Nakagawa, M. C. Larson, M. P. Mack, T. A. Strand, C. W. Coldren, E. Hegblom, S. K. Penniman, T. Wipiejewski, and L. A. Coldren, “Widely tunable electroabsorption-modulated sampled-grating DBR laser transmitter,” IEEE J. Sel. Topics Quantum Electron. 8(6), 1349–1357 (2002).
[Crossref]

2001 (1)

B. Liu, A. Shakouri, and J. E. Bowers, “Passive microring-resonator-coupled lasers,” Appl. Phys. Lett. 79(22), 3561–3563 (2001).
[Crossref]

1996 (1)

F. Girardin, G.-H. Duan, and P. Gallion, “Linewidth rebroadening due to nonlinear gain and index induced by carrier heating in strained quantum-well lasers,” IEEE Photon. Technol. Lett. 8(3), 334–336 (1996).
[Crossref]

1994 (1)

K. A. Williams, P. S. Griffin, I. H. White, B. Garrett, J. E. A. Whiteaway, and G. H. B. Thompson, “Carrier transport effects in long-wavelength multiquantum-well lasers under large-signal modulation,” IEEE J. Quantum Electron. 30(6), 1355–1357 (1994).
[Crossref]

1992 (2)

R. Nagarajan, M. Ishikawa, T. Fukushima, R. S. Geels, and J. E. Bowers, “High speed quantum-well lasers and carrier transport effects,” IEEE J. Quantum Electron. 28(10), 1990–2008 (1992).
[Crossref]

L. M. Zhang and J. E. Carroll, “Large-signal dynamic model of the DFB laser,” IEEE J. Quantum Electron. 28(3), 604–611 (1992).
[Crossref]

1990 (3)

B. Bennett, R. A. Soref, and J. del Alamo, “Carrier-induced change in refractive index of InP, GaAs and InGaAsP,” IEEE J. Quant. Electron. 26(1), 113–122 (1990).
[Crossref]

T. L. Koch and U. Koren, “Semiconductor lasers for coherent optical fiber communications,” J. Lightw. Technol. 8(3), 274–293 (1990).
[Crossref]

A. Hemmerich, D. McIntyre, D. Schropp, D. Meschede, and T. Hänsch, “Optically stabilized narrow linewidth semiconductor laser for high resolution spectroscopy,” Opt. Commun. 75(2), 118–122 (1990).
[Crossref]

1988 (1)

M. Wu, Y. Lo, and S. Wang, “Linewidth broadening due to longitudinal spatial hole burning in a long distributed feedback laser,” Appl. Phys. Lett. 52(14), 1119–1121 (1988).
[Crossref]

1987 (3)

A. Lowery, “New dynamic semiconductor laser model based on the transmission-line modelling method,” IEE Proc.-J 134(5), 281 (1987).

R. Kazarinov and C. Henry, “The relation of line narrowing and chirp reduction resulting from the coupling of a semiconductor laser to passive resonator,” IEEE J. Quantum Electron. 23(9), 1401–1409 (1987).
[Crossref]

G. Bjork and O. Nilsson, “A tool to calculate the linewidth of complicated semiconductor lasers,” IEEE J. Quant. Electron. 23(8), 1303–1313 (1987).
[Crossref]

1986 (1)

C. Henry, “Theory of spontaneous emission noise in open resonators and its application to lasers and optical amplifiers,” J. Lightw. Technol. 4(3), 288–297 (1986).
[Crossref]

1985 (1)

W. Hoefer, “The transmission-line matrix method - theory and applications,” IEEE Trans. Microw. Theory Techn. 33(10), 882–893 (1985).
[Crossref]

1984 (1)

K. Ujihara, “Phase noise in a laser with output coupling,” IEEE J. Quant. Electron. 20(7), 814–818 (1984).
[Crossref]

1982 (1)

C. Henry, “Theory of the linewidth of semiconductor lasers,” IEEE J. Quantum Electron. 18(2), 259–264 (1982).
[Crossref]

1973 (1)

A. Yariv, “Coupled-mode theory for guided-wave optics,” IEEE J. Quant. Electron. 9(9), 919–933 (1973).
[Crossref]

Akulova, Y. A.

Y. A. Akulova, G. A. Fish, P.-C. Koh, C. L. Schow, P. Kozodoy, A. P. Dahl, S. Nakagawa, M. C. Larson, M. P. Mack, T. A. Strand, C. W. Coldren, E. Hegblom, S. K. Penniman, T. Wipiejewski, and L. A. Coldren, “Widely tunable electroabsorption-modulated sampled-grating DBR laser transmitter,” IEEE J. Sel. Topics Quantum Electron. 8(6), 1349–1357 (2002).
[Crossref]

Bennett, B.

B. Bennett, R. A. Soref, and J. del Alamo, “Carrier-induced change in refractive index of InP, GaAs and InGaAsP,” IEEE J. Quant. Electron. 26(1), 113–122 (1990).
[Crossref]

Bjork, G.

G. Bjork and O. Nilsson, “A tool to calculate the linewidth of complicated semiconductor lasers,” IEEE J. Quant. Electron. 23(8), 1303–1313 (1987).
[Crossref]

Boller, K.-J.

L. Zhuang, C. G. H. Roeloffzen, M. Hoekman, K.-J. Boller, and A. J. Lowery, “Programmable photonic signal processor chip for radiofrequency applications,” Optica 2(10), 854–859 (2015).
[Crossref]

Y. Fan, R. M. Oldenbeuving, E. J. Klein, C. J. Lee, H. Song, M. R. H. Khan, H. L. Offerhaus, P. J. M. van der Slot, and K.-J. Boller, “A hybrid semiconductor-glass waveguide laser,” Proc. SPIE, vol.  9135, 91351B (2014).

R. M. Oldenbeuving, E. J. Klein, H. L. Offerhaus, C. J. Lee, H. Song, and K.-J. Boller, “25 kHz narrow spectral bandwidth of a wavelength tunable diode laser with a short waveguide-based external cavity,” Laser Phys. Lett. 10(1), 015804 (2013).
[Crossref]

C. G. H. Roeloffzen, L. Zhuang, C. Taddei, A. Leinse, R. G. Heideman, P. W. L. van Dijk, R. M. Oldenbeuving, D. A. I. Marpaung, M. Burla, and K.-J. Boller, “Silicon nitride microwave photonic circuits,” Opt. Express 21(19), 22937–22961 (2013).
[Crossref] [PubMed]

Y. Fan, R. M. Oldenbeuving, P. J. M. van der Slot, and K.-J. Boller, “A semiconductor-glass waveguide hybrid laser with ultra-long cavity length,” in Proceedings of the 20th Annual Symposium of the IEEE Photonics Society Benelux, (2016), pp. 121–124.

Bowers, J. E.

T. Komljenovic, S. Srinivasan, E. Norberg, M. Davenport, G. Fish, and J. E. Bowers, “Widely tunable narrow-linewidth monolithically integrated external-cavity semiconductor lasers,” IEEE J. Sel. Topics Quantum Electron. 21(6), 214–222 (2015).
[Crossref]

S. Srinivasan, M. Davenport, T. Komljenovic, J. Hulme, D. T. Spencer, and J. E. Bowers, “Coupled-ring-resonator-mirror-based heterogeneous III–V silicon tunable laser,” IEEE Photon. J. 7(3), 1–8 (2015).
[Crossref]

J. C. Hulme, J. K. Doylend, and J. E. Bowers, “Widely tunable vernier ring laser on hybrid silicon,” Opt. Express 21(17), 19718–19722 (2013).
[Crossref] [PubMed]

B. Liu, A. Shakouri, and J. E. Bowers, “Passive microring-resonator-coupled lasers,” Appl. Phys. Lett. 79(22), 3561–3563 (2001).
[Crossref]

R. Nagarajan, M. Ishikawa, T. Fukushima, R. S. Geels, and J. E. Bowers, “High speed quantum-well lasers and carrier transport effects,” IEEE J. Quantum Electron. 28(10), 1990–2008 (1992).
[Crossref]

Burla, M.

Busch, K.

Carroll, J. E.

L. M. Zhang and J. E. Carroll, “Large-signal dynamic model of the DFB laser,” IEEE J. Quantum Electron. 28(3), 604–611 (1992).
[Crossref]

Chen, J.

S. Zhang, P. Y. Kam, C. Yu, and J. Chen, “Laser linewidth tolerance of decision-aided maximum likelihood phase estimation in coherent optical M-ary PSK and QAM systems,” IEEE Photon. Technol. Lett. 21(15), 1075–1077 (2009).
[Crossref]

Chtioui, M.

M. Faugeron, M. Tran, O. Parillaud, and M. Chtioui, “High-power tunable dilute mode DFB laser with low RIN and narrow linewidth,” IEEE Photon. Technol. Lett. 25(1), 7–10 (2013).
[Crossref]

Chu, T.

Coldren, C. W.

Y. A. Akulova, G. A. Fish, P.-C. Koh, C. L. Schow, P. Kozodoy, A. P. Dahl, S. Nakagawa, M. C. Larson, M. P. Mack, T. A. Strand, C. W. Coldren, E. Hegblom, S. K. Penniman, T. Wipiejewski, and L. A. Coldren, “Widely tunable electroabsorption-modulated sampled-grating DBR laser transmitter,” IEEE J. Sel. Topics Quantum Electron. 8(6), 1349–1357 (2002).
[Crossref]

Coldren, L. A.

Y. A. Akulova, G. A. Fish, P.-C. Koh, C. L. Schow, P. Kozodoy, A. P. Dahl, S. Nakagawa, M. C. Larson, M. P. Mack, T. A. Strand, C. W. Coldren, E. Hegblom, S. K. Penniman, T. Wipiejewski, and L. A. Coldren, “Widely tunable electroabsorption-modulated sampled-grating DBR laser transmitter,” IEEE J. Sel. Topics Quantum Electron. 8(6), 1349–1357 (2002).
[Crossref]

L. A. Coldren, S. W. Corzine, and M. L. Mashanovitch, Diode Lasers and Photonic Integrated Circuits, 2nd edition (John Wiley & Sons, 2012).
[Crossref]

Corzine, S. W.

L. A. Coldren, S. W. Corzine, and M. L. Mashanovitch, Diode Lasers and Photonic Integrated Circuits, 2nd edition (John Wiley & Sons, 2012).
[Crossref]

Dahl, A. P.

Y. A. Akulova, G. A. Fish, P.-C. Koh, C. L. Schow, P. Kozodoy, A. P. Dahl, S. Nakagawa, M. C. Larson, M. P. Mack, T. A. Strand, C. W. Coldren, E. Hegblom, S. K. Penniman, T. Wipiejewski, and L. A. Coldren, “Widely tunable electroabsorption-modulated sampled-grating DBR laser transmitter,” IEEE J. Sel. Topics Quantum Electron. 8(6), 1349–1357 (2002).
[Crossref]

Davenport, M.

S. Srinivasan, M. Davenport, T. Komljenovic, J. Hulme, D. T. Spencer, and J. E. Bowers, “Coupled-ring-resonator-mirror-based heterogeneous III–V silicon tunable laser,” IEEE Photon. J. 7(3), 1–8 (2015).
[Crossref]

T. Komljenovic, S. Srinivasan, E. Norberg, M. Davenport, G. Fish, and J. E. Bowers, “Widely tunable narrow-linewidth monolithically integrated external-cavity semiconductor lasers,” IEEE J. Sel. Topics Quantum Electron. 21(6), 214–222 (2015).
[Crossref]

del Alamo, J.

B. Bennett, R. A. Soref, and J. del Alamo, “Carrier-induced change in refractive index of InP, GaAs and InGaAsP,” IEEE J. Quant. Electron. 26(1), 113–122 (1990).
[Crossref]

Domenico, G. D.

Doylend, J. K.

Duan, G.-H.

F. Girardin, G.-H. Duan, and P. Gallion, “Linewidth rebroadening due to nonlinear gain and index induced by carrier heating in strained quantum-well lasers,” IEEE Photon. Technol. Lett. 8(3), 334–336 (1996).
[Crossref]

Fan, Y.

Y. Fan, R. M. Oldenbeuving, E. J. Klein, C. J. Lee, H. Song, M. R. H. Khan, H. L. Offerhaus, P. J. M. van der Slot, and K.-J. Boller, “A hybrid semiconductor-glass waveguide laser,” Proc. SPIE, vol.  9135, 91351B (2014).

Y. Fan, R. M. Oldenbeuving, P. J. M. van der Slot, and K.-J. Boller, “A semiconductor-glass waveguide hybrid laser with ultra-long cavity length,” in Proceedings of the 20th Annual Symposium of the IEEE Photonics Society Benelux, (2016), pp. 121–124.

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Y. Fan, R. M. Oldenbeuving, E. J. Klein, C. J. Lee, H. Song, M. R. H. Khan, H. L. Offerhaus, P. J. M. van der Slot, and K.-J. Boller, “A hybrid semiconductor-glass waveguide laser,” Proc. SPIE, vol.  9135, 91351B (2014).

R. M. Oldenbeuving, E. J. Klein, H. L. Offerhaus, C. J. Lee, H. Song, and K.-J. Boller, “25 kHz narrow spectral bandwidth of a wavelength tunable diode laser with a short waveguide-based external cavity,” Laser Phys. Lett. 10(1), 015804 (2013).
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T. Komljenovic, S. Srinivasan, E. Norberg, M. Davenport, G. Fish, and J. E. Bowers, “Widely tunable narrow-linewidth monolithically integrated external-cavity semiconductor lasers,” IEEE J. Sel. Topics Quantum Electron. 21(6), 214–222 (2015).
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Y. Fan, R. M. Oldenbeuving, E. J. Klein, C. J. Lee, H. Song, M. R. H. Khan, H. L. Offerhaus, P. J. M. van der Slot, and K.-J. Boller, “A hybrid semiconductor-glass waveguide laser,” Proc. SPIE, vol.  9135, 91351B (2014).

R. M. Oldenbeuving, E. J. Klein, H. L. Offerhaus, C. J. Lee, H. Song, and K.-J. Boller, “25 kHz narrow spectral bandwidth of a wavelength tunable diode laser with a short waveguide-based external cavity,” Laser Phys. Lett. 10(1), 015804 (2013).
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Y. Jiang, A. Ludlow, N. Lemke, R. Fox, J. Sherman, L.-S. Ma, and C. Oates, “Making optical atomic clocks more stable with 10−16-level laser stabilization,” Nat. Photonics 5(3), 158–161 (2011).
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Y. A. Akulova, G. A. Fish, P.-C. Koh, C. L. Schow, P. Kozodoy, A. P. Dahl, S. Nakagawa, M. C. Larson, M. P. Mack, T. A. Strand, C. W. Coldren, E. Hegblom, S. K. Penniman, T. Wipiejewski, and L. A. Coldren, “Widely tunable electroabsorption-modulated sampled-grating DBR laser transmitter,” IEEE J. Sel. Topics Quantum Electron. 8(6), 1349–1357 (2002).
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A. Hemmerich, D. McIntyre, D. Schropp, D. Meschede, and T. Hänsch, “Optically stabilized narrow linewidth semiconductor laser for high resolution spectroscopy,” Opt. Commun. 75(2), 118–122 (1990).
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A. Hemmerich, D. McIntyre, D. Schropp, D. Meschede, and T. Hänsch, “Optically stabilized narrow linewidth semiconductor laser for high resolution spectroscopy,” Opt. Commun. 75(2), 118–122 (1990).
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Y. A. Akulova, G. A. Fish, P.-C. Koh, C. L. Schow, P. Kozodoy, A. P. Dahl, S. Nakagawa, M. C. Larson, M. P. Mack, T. A. Strand, C. W. Coldren, E. Hegblom, S. K. Penniman, T. Wipiejewski, and L. A. Coldren, “Widely tunable electroabsorption-modulated sampled-grating DBR laser transmitter,” IEEE J. Sel. Topics Quantum Electron. 8(6), 1349–1357 (2002).
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T. Kita, K. Nemoto, and H. Yamada, “Silicon photonic wavelength-tunable laser diode with asymmetric Mach-Zehnder interferometer,” IEEE J. Sel. Topics Quantum Electron. 20(4), 344–349 (2014).
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Y. Jiang, A. Ludlow, N. Lemke, R. Fox, J. Sherman, L.-S. Ma, and C. Oates, “Making optical atomic clocks more stable with 10−16-level laser stabilization,” Nat. Photonics 5(3), 158–161 (2011).
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Y. Fan, R. M. Oldenbeuving, E. J. Klein, C. J. Lee, H. Song, M. R. H. Khan, H. L. Offerhaus, P. J. M. van der Slot, and K.-J. Boller, “A hybrid semiconductor-glass waveguide laser,” Proc. SPIE, vol.  9135, 91351B (2014).

R. M. Oldenbeuving, E. J. Klein, H. L. Offerhaus, C. J. Lee, H. Song, and K.-J. Boller, “25 kHz narrow spectral bandwidth of a wavelength tunable diode laser with a short waveguide-based external cavity,” Laser Phys. Lett. 10(1), 015804 (2013).
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Y. Fan, R. M. Oldenbeuving, E. J. Klein, C. J. Lee, H. Song, M. R. H. Khan, H. L. Offerhaus, P. J. M. van der Slot, and K.-J. Boller, “A hybrid semiconductor-glass waveguide laser,” Proc. SPIE, vol.  9135, 91351B (2014).

R. M. Oldenbeuving, E. J. Klein, H. L. Offerhaus, C. J. Lee, H. Song, and K.-J. Boller, “25 kHz narrow spectral bandwidth of a wavelength tunable diode laser with a short waveguide-based external cavity,” Laser Phys. Lett. 10(1), 015804 (2013).
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Özdemir, S.

L. He, Ş. Özdemir, J. Zhu, W. Kim, and L. Yang, “Detecting single viruses and nanoparticles using whispering gallery microlasers,” Nat. Nanotech. 6(7), 428–432 (2011).
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Parillaud, O.

M. Faugeron, M. Tran, O. Parillaud, and M. Chtioui, “High-power tunable dilute mode DFB laser with low RIN and narrow linewidth,” IEEE Photon. Technol. Lett. 25(1), 7–10 (2013).
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Y. A. Akulova, G. A. Fish, P.-C. Koh, C. L. Schow, P. Kozodoy, A. P. Dahl, S. Nakagawa, M. C. Larson, M. P. Mack, T. A. Strand, C. W. Coldren, E. Hegblom, S. K. Penniman, T. Wipiejewski, and L. A. Coldren, “Widely tunable electroabsorption-modulated sampled-grating DBR laser transmitter,” IEEE J. Sel. Topics Quantum Electron. 8(6), 1349–1357 (2002).
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A. Hemmerich, D. McIntyre, D. Schropp, D. Meschede, and T. Hänsch, “Optically stabilized narrow linewidth semiconductor laser for high resolution spectroscopy,” Opt. Commun. 75(2), 118–122 (1990).
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B. Liu, A. Shakouri, and J. E. Bowers, “Passive microring-resonator-coupled lasers,” Appl. Phys. Lett. 79(22), 3561–3563 (2001).
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Y. Jiang, A. Ludlow, N. Lemke, R. Fox, J. Sherman, L.-S. Ma, and C. Oates, “Making optical atomic clocks more stable with 10−16-level laser stabilization,” Nat. Photonics 5(3), 158–161 (2011).
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Y. Fan, R. M. Oldenbeuving, E. J. Klein, C. J. Lee, H. Song, M. R. H. Khan, H. L. Offerhaus, P. J. M. van der Slot, and K.-J. Boller, “A hybrid semiconductor-glass waveguide laser,” Proc. SPIE, vol.  9135, 91351B (2014).

R. M. Oldenbeuving, E. J. Klein, H. L. Offerhaus, C. J. Lee, H. Song, and K.-J. Boller, “25 kHz narrow spectral bandwidth of a wavelength tunable diode laser with a short waveguide-based external cavity,” Laser Phys. Lett. 10(1), 015804 (2013).
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S. Srinivasan, M. Davenport, T. Komljenovic, J. Hulme, D. T. Spencer, and J. E. Bowers, “Coupled-ring-resonator-mirror-based heterogeneous III–V silicon tunable laser,” IEEE Photon. J. 7(3), 1–8 (2015).
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T. Komljenovic, S. Srinivasan, E. Norberg, M. Davenport, G. Fish, and J. E. Bowers, “Widely tunable narrow-linewidth monolithically integrated external-cavity semiconductor lasers,” IEEE J. Sel. Topics Quantum Electron. 21(6), 214–222 (2015).
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C. T. Santis, S. T. Steger, Y. Vilenchik, A. Vasilyev, and A. Yariv, “High-coherence semiconductor lasers based on integral high-Q resonators in hybrid Si/III–V platforms,” Proc. Natl. Acad. Sci. U.S.A. 111(8), 2879–2884 (2014).
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K. A. Williams, M. G. Thompson, and I. H. White, “Long-wavelength monolithic mode-locked diode lasers,” New J. Phys. 6(1), 179 (2004).
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M. Faugeron, M. Tran, O. Parillaud, and M. Chtioui, “High-power tunable dilute mode DFB laser with low RIN and narrow linewidth,” IEEE Photon. Technol. Lett. 25(1), 7–10 (2013).
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Y. Fan, R. M. Oldenbeuving, P. J. M. van der Slot, and K.-J. Boller, “A semiconductor-glass waveguide hybrid laser with ultra-long cavity length,” in Proceedings of the 20th Annual Symposium of the IEEE Photonics Society Benelux, (2016), pp. 121–124.

van Dijk, P. W. L.

Vasilyev, A.

C. T. Santis, S. T. Steger, Y. Vilenchik, A. Vasilyev, and A. Yariv, “High-coherence semiconductor lasers based on integral high-Q resonators in hybrid Si/III–V platforms,” Proc. Natl. Acad. Sci. U.S.A. 111(8), 2879–2884 (2014).
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Figures (8)

Fig. 1
Fig. 1 Schematic representation of the hybrid laser with an active gain section with length L1 coupled, with power coupling coefficient β, to a passive waveguide section with physical length L2 (excluding the MRRs). The left facet of the laser diode is highly reflective, R1, and the right facet is anti-reflection coated combined with a tilt angle of 5°, resulting in an extremely low facet reflectivity (R2 ≈ 0). The two MRRs provide an effective power reflectivity R3 which is frequency dependent.
Fig. 2
Fig. 2 Schematic representation of the transmission line model (TLM) for the hybrid laser. In the TLM applied here, the semiconductor gain medium is divided in sections. The passive external resonator section is modeled in the frequency domain based on the scattering-matrix method. reff(ω) is complex-valued and frequency dependent to include all frequency dependencies and phase shifts.
Fig. 3
Fig. 3 (a) Calculated amplitude reflectivity as a function of frequency detuning (with respect to the Vernier peak frequency) for three different values of the chip-to-chip coupling efficiency, β; (b) Calculated coefficients A, B and linewidth reduction factor F as a function of frequency detuning. The values of A, B, and F are independent of the chip-to-chip coupling efficiencies.
Fig. 4
Fig. 4 Calculated output power vs drive current for three different values of the power coupling efficiency, β. The curves resemble the typical output power characteristic of diode lasers and the observed discontinuities are due to mode hopping. The values of the output power within the gray area (drive currents between 20 mA and 60 mA) were chosen for calculations of the linewidth (Fig. 7 and 8).
Fig. 5
Fig. 5 Calculated laser frequency detuning Δf from the Vernier peak frequency (f0) vs drive current for three different values of power coupling efficiency β. The frequency detuning and mode hops vs increasing drive currents are caused by index changes within the gain section.
Fig. 6
Fig. 6 Two examples of the calculated power spectral density (PSD) of frequency noise for power coupling efficiency β = 0.7 at 20 mA and 60 mA drive current. For each PSD curve, two spectral peaks can be seen, which correspond to relaxation oscillations (between 2 and 3 GHz) and beating between two adjacent longitudinal modes (at about 14 GHz) respectively. The laser spectral linewidth is retrieved via multiplying the mean values of the PSD at low frequencies by π, in this case obtaining about 32.2 kHz at 20 mA and 7.4 kHz at 60 mA.
Fig. 7
Fig. 7 Calculated laser spectral linewidth plotted vs 1/P for a chip-to-chip coupling efficiency β = 0.7, as an example. The symbols represent the values calculated with the transmission line model and the error bars represent the standard deviation of the PSD levels at low frequencies from the average PSD level in that range. The dashed line is a linear least mean square fit. The good agreement confirms the expected overall trend of linewidth narrowing with increasing output power. .
Fig. 8
Fig. 8 Ratio between laser spectral linewidths obtained with the transmission line model and the modified mean-field model for the full range of power coupling efficiencies β (0.1 to 1) and drive currents (20 mA to 60 mA). Due to the different amount of laser frequency detuning caused by different drive currents, |r(ω)| varies with drive current for each value of β. A systematic decrease of |r(ω)| can be seen as β decreases from unity (1) to a low value of 0.1, which can be understood by Eq. (1) where β enters |r(ω)| as a multiplicative factor. The red solid curve is a simple exponential fitting curve. A clear trend of increasing error in the mean-field model is seen when β approaches smaller values.

Tables (3)

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Table 1 Configuration parameters used for numerical modeling

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Table 2 Semiconductor chip parameters

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Table 3 Feedback waveguide chip parameters

Equations (18)

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r ( ω ) = β exp ( α 2 L 2 ) r 3 ( ω ) .
Δ ν = Δ ν ST F 2 .
Δ ν ST = 1 4 π v g 2 h ν n sp γ tot γ m ( 1 + α 2 ) P 0 ( 1 + r 1 r ( ω ) 1 r ( ω ) 2 1 R 1 ) ,
F = 1 + A + B ,
A = 1 τ LD ( d d ω φ eff ( ω ) ) ,
B = α τ LD ( d d ω ln r ( ω ) ) .
B = α τ LD ( d d ω ln r 3 ( ω ) ) .
F R = [ ( r 1 + r 2 ) ( 1 r 1 r 2 ) 2 r 1 r 2 ln ( r 1 r 2 ) ] 2 ,
F c = 0.94 + 1.06 exp ( 3.06 r ( ω ) )
E ( z , t ) = f ( z , t ) + b ( z , t ) ,
f ( z , t ) = F ( z , t ) e q z i ω 0 t ,
b ( z , t ) = B ( z , t ) e + q z i ω 0 t ,
( 1 v g + z ) f ( z , t ) = ( 1 2 g 1 2 α i ) f ( z , t ) + Q spf ,
( 1 v g + z ) b ( z , t ) = ( 1 2 g 1 2 α i ) b ( z , t ) + Q spb ,
g = Γ g 0 ln ( N MQW / N tr ) 1 + S .
d N SCH d t = η i I ew L 1 d SCH N SCH τ cap + N MQW τ em d MQW d SCH ,
d N MQW d t = N SCH τ cap d SCH d MQW N MQW τ em v g g S R ( N MQW ) .
R ( N MQW ) = A d N MQW + B d N MQW 2 + C d N MQW 3 .

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