Abstract

Forced oscillation based on self-injection locked phase-locked (SILPLL) opto-electronic oscillator (OEO) technique is the basis of highly stable and low phase noise oscillators to be used as a key component in modern communication and sensing systems. To avoid large-size modular OEO, inter-modal oscillation at X-band frequencies is achieved in a compact multi-mode multi-section semiconductor laser using InP foundry service. Self-forced oscillation technique of SILPLL is demonstrated, where a phase noise performance of −98 dBc/Hz is measured at 10 kHz offset carrier of 11 GHz, which is an improvement of 68 dB compared with the free-running condition, which corresponds with 600 times reduction in calculated timing jitters from the free-running case to reach 0.45 ps for over 1 kHz to 1 MHz bandwidth.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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    [Crossref]
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    [Crossref]
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    [Crossref]
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2017 (2)

T. Sun, L. Zhang, A. K. Poddar, U. L. Rohde, and A. S. Daryoush, “Limits in Timing Jitters of Forced Microwave Oscillator Using Optical Self-ILPLL,” IEEE Photonics Technol. Lett. 29(2), 181–184 (2017).
[Crossref]

T. Sun, L. Zhang, A. K. Poddar, U. L. Rohde, and A. S. Daryoush, “Frequency synthesis of forced opto-electronic oscillators at the X-band,” Chin. Opt. Lett. 15(1), 10009–10013 (2017).
[Crossref]

2014 (2)

L. Zhang, A. K. Poddar, U. L. Rohde, and A. S. Daryoush, “Comparison of optical self-phase locked loop techniques for frequency stabilization of oscillators,” IEEE Photonics J. 6(5), 1–15 (2014).
[Crossref]

S. Joshi, C. Calò, N. Chimot, M. Radziunas, R. Arkhipov, S. Barbet, A. Accard, A. Ramdane, and F. Lelarge, “Quantum dash based single section mode locked lasers for photonic integrated circuits,” Opt. Express 22(9), 11254–11266 (2014).
[Crossref]

2013 (2)

A. Ishizawa, T. Nishikawa, A. Mizutori, H. Takara, A. Takada, T. Sogawa, and M. Koga, “Phase-noise characteristics of a 25-GHz-spaced optical frequency comb based on a phase- and intensity-modulated laser,” Opt. Express 21(24), 29186–29194 (2013).
[Crossref]

L. Zhang, A. K. Poddar, U. L. Rohde, and A. S. Daryoush, “Analytical and experimental evaluation of SSB phase noise reduction in self-injection locked oscillators using optical delay loops,” IEEE Photonics J. 5(6), 6602217 (2013).
[Crossref]

2010 (1)

L. Hou, R. Dylewicz, M. Haji, P. Stolarz, B. Qiu, and A. C. Bryce, “Monolithic 40-GHz Passively Mode-Locked AlGaInAs–InP 1.55-um MQW Laser With Surface-Etched Distributed Bragg Reflector,” IEEE Photonics Technol. Lett. 22(20), 1503–1505 (2010).
[Crossref]

2009 (3)

G. Carpintero, M. G. Thompson, R. V. Penty, and I. H. White, “Low Noise Performance of Passively Mode-Locked 10-GHz Quantum-Dot Laser Diode,” IEEE Photonics Technol. Lett. 21(6), 389–391 (2009).
[Crossref]

F. Quinlan, S. Ozharar, S. Gee, and P. J. Delfyett, “Harmonically modelocked semiconductor based lasers as high repetition rate ultralow noise pulse train and optical frequency comb sources,” J. Opt. A: Pure Appl. Opt. 11(10), 103001 (2009).
[Crossref]

M. Chen and J. Xu, “Wideband Frequency Synthesizer at X/Ku Band by Mixing and Phase Locking of Half Frequency Output of VCO,” J. Infrared, Millimeter, Terahertz Waves 31(1), 100–110 (2009).
[Crossref]

2008 (2)

2004 (2)

S. Arahira and Y. Ogawa, “40 GHz actively mode-locked distributed bragg reflector laser diode module with an impedance-matching circuit for effi- cient RF signal injection,” Jpn. J. Appl. Phys. 43(4B), 1960–1964 (2004).
[Crossref]

L. A. Johansson, Y. A. Akulova, G. A. Fish, and L. A. Coldren, “Sampled-grating DBR laser integrated with SOA and tandem electroabsorption modulator for chirp-control,” Electron. Lett. 40(1), 70–71 (2004).
[Crossref]

2003 (1)

J. S. Barton, E. J. Skogen, M. L. Masanovic, S. P. Denbaars, and L. A. Coldren, “A widely tunable high-speed transmitter using an integrated SGDBR laser-semiconductor optical amplifier and Mach-Zehnder modulator,” IEEE J. Sel. Top. Quantum Electron. 9(5), 1113–1117 (2003).
[Crossref]

2002 (1)

S. Ye, L. Jansson, and I. Galton, “A multiple-crystal interface PLL with VCO realignment to reduce phase noise,” IEEE J. Solid-State Circuits 37(12), 1795–1803 (2002).
[Crossref]

1997 (2)

A. S. Daryoush, K. Sato, K. Horikawa, and H. Ogawa, “Electrically injection-locked intermodal oscillation in a long optical cavity laser diode,” IEEE Microw. Guid. Wave Lett. 7(7), 194–196 (1997).
[Crossref]

A. S. Daryoush, K. Sato, K. Horikawa, and H. Ogawa, “Dynamic response of long optical-cavity laser diode for Ka-band communication satellites,” IEEE Trans. Microwave Theory Tech. 45(8), 1288–1295 (1997).
[Crossref]

1996 (1)

T. Hoshida, H. Liu, M. Tsuchiya, Y. Ogawa, and T. Kamiya, “Subharmonic hybrid mode-locking of a monolithic semiconductor laser,” IEEE J. Sel. Top. Quantum Electron. 2(3), 514–522 (1996).
[Crossref]

1995 (1)

T. D. Ni, X. Zhang, and A. S. Daryoush, “Experimental Study on Close-in carrier Phase Noise of Laser Diode with Coherent Feedback,” IEEE Trans. Microwave Theory Tech. 43(9), 2277–2283 (1995).
[Crossref]

1990 (1)

A. S. Daryoush, “Optical synchronization of millimeter-wave oscillators for distributed architecture,” IEEE Trans. Microwave Theory Tech. 38(5), 467–476 (1990).
[Crossref]

Accard, A.

Akulova, Y. A.

L. A. Johansson, Y. A. Akulova, G. A. Fish, and L. A. Coldren, “Sampled-grating DBR laser integrated with SOA and tandem electroabsorption modulator for chirp-control,” Electron. Lett. 40(1), 70–71 (2004).
[Crossref]

Arahira, S.

S. Arahira and Y. Ogawa, “40 GHz actively mode-locked distributed bragg reflector laser diode module with an impedance-matching circuit for effi- cient RF signal injection,” Jpn. J. Appl. Phys. 43(4B), 1960–1964 (2004).
[Crossref]

Arkhipov, R.

Barbet, S.

Barton, J. S.

J. S. Barton, E. J. Skogen, M. L. Masanovic, S. P. Denbaars, and L. A. Coldren, “A widely tunable high-speed transmitter using an integrated SGDBR laser-semiconductor optical amplifier and Mach-Zehnder modulator,” IEEE J. Sel. Top. Quantum Electron. 9(5), 1113–1117 (2003).
[Crossref]

Bretenaker, F.

Brunel, M.

Bryce, A. C.

L. Hou, R. Dylewicz, M. Haji, P. Stolarz, B. Qiu, and A. C. Bryce, “Monolithic 40-GHz Passively Mode-Locked AlGaInAs–InP 1.55-um MQW Laser With Surface-Etched Distributed Bragg Reflector,” IEEE Photonics Technol. Lett. 22(20), 1503–1505 (2010).
[Crossref]

Byrd, J.

A. A. Savchenkov, V. S. Iichenko, J. Byrd, W. Liang, D. Eliyahu, A. B. Matsko, D. Seidel, and L. Maleki, “Whispering-gallery mode based opto-electronic oscillators,” in Proceedings of IEEE Conference on International Frequency Control Symposium (IEEE, 2010), pp. 554–557.

Calò, C.

Carpintero, G.

G. Carpintero, M. G. Thompson, R. V. Penty, and I. H. White, “Low Noise Performance of Passively Mode-Locked 10-GHz Quantum-Dot Laser Diode,” IEEE Photonics Technol. Lett. 21(6), 389–391 (2009).
[Crossref]

F. Dijk, M. Lamponi, M. Chtioui, F. Lelarge, G. Kervella, E. Rouvalis, C. Renaud, M. Fice, and G. Carpintero, “Heterodyne millimeter wave source with monolithically integrated UTC photodiodes,” in Proceedings of IEEE Conference on International Topical Meeting on Microwave Photonics (IEEE, 2013), pp. 336–339.

G. Carpintero, S. Hisatake, D. Felipe, R. Guzman, T. Nagatsuma, N. Keil, and T. Gobel, “Photonics-based millimeter and terahertz wave generation using a hybrid integrated dual DBR polymer laser,” in Proceedings of IEEE Conference on International Microwave Symposium (IEEE, 2016), pp. 1–3.

Chen, M.

M. Chen and J. Xu, “Wideband Frequency Synthesizer at X/Ku Band by Mixing and Phase Locking of Half Frequency Output of VCO,” J. Infrared, Millimeter, Terahertz Waves 31(1), 100–110 (2009).
[Crossref]

Chimot, N.

Chtioui, M.

F. Dijk, M. Lamponi, M. Chtioui, F. Lelarge, G. Kervella, E. Rouvalis, C. Renaud, M. Fice, and G. Carpintero, “Heterodyne millimeter wave source with monolithically integrated UTC photodiodes,” in Proceedings of IEEE Conference on International Topical Meeting on Microwave Photonics (IEEE, 2013), pp. 336–339.

Coldren, L. A.

L. A. Johansson, Y. A. Akulova, G. A. Fish, and L. A. Coldren, “Sampled-grating DBR laser integrated with SOA and tandem electroabsorption modulator for chirp-control,” Electron. Lett. 40(1), 70–71 (2004).
[Crossref]

J. S. Barton, E. J. Skogen, M. L. Masanovic, S. P. Denbaars, and L. A. Coldren, “A widely tunable high-speed transmitter using an integrated SGDBR laser-semiconductor optical amplifier and Mach-Zehnder modulator,” IEEE J. Sel. Top. Quantum Electron. 9(5), 1113–1117 (2003).
[Crossref]

Daryoush, A. S.

T. Sun, L. Zhang, A. K. Poddar, U. L. Rohde, and A. S. Daryoush, “Limits in Timing Jitters of Forced Microwave Oscillator Using Optical Self-ILPLL,” IEEE Photonics Technol. Lett. 29(2), 181–184 (2017).
[Crossref]

T. Sun, L. Zhang, A. K. Poddar, U. L. Rohde, and A. S. Daryoush, “Frequency synthesis of forced opto-electronic oscillators at the X-band,” Chin. Opt. Lett. 15(1), 10009–10013 (2017).
[Crossref]

L. Zhang, A. K. Poddar, U. L. Rohde, and A. S. Daryoush, “Comparison of optical self-phase locked loop techniques for frequency stabilization of oscillators,” IEEE Photonics J. 6(5), 1–15 (2014).
[Crossref]

L. Zhang, A. K. Poddar, U. L. Rohde, and A. S. Daryoush, “Analytical and experimental evaluation of SSB phase noise reduction in self-injection locked oscillators using optical delay loops,” IEEE Photonics J. 5(6), 6602217 (2013).
[Crossref]

A. S. Daryoush, K. Sato, K. Horikawa, and H. Ogawa, “Electrically injection-locked intermodal oscillation in a long optical cavity laser diode,” IEEE Microw. Guid. Wave Lett. 7(7), 194–196 (1997).
[Crossref]

A. S. Daryoush, K. Sato, K. Horikawa, and H. Ogawa, “Dynamic response of long optical-cavity laser diode for Ka-band communication satellites,” IEEE Trans. Microwave Theory Tech. 45(8), 1288–1295 (1997).
[Crossref]

T. D. Ni, X. Zhang, and A. S. Daryoush, “Experimental Study on Close-in carrier Phase Noise of Laser Diode with Coherent Feedback,” IEEE Trans. Microwave Theory Tech. 43(9), 2277–2283 (1995).
[Crossref]

A. S. Daryoush, “Optical synchronization of millimeter-wave oscillators for distributed architecture,” IEEE Trans. Microwave Theory Tech. 38(5), 467–476 (1990).
[Crossref]

T. D. Ni, X. Zhang, and A. S. Daryoush, “Close-in carrier phase noise of laser with coherent feedback,” in Proceedings of IEEE Conference on International Microwave Symposium Digest (IEEE, 1994), pp. 61–64.

T. Sun, A. S. Daryoush, A. Poddar, L. Zhang, and U. Rohde, “High-resolution frequency synthesizers over X-band using SILPLL opto-electronic oscillators,” in Proceedings of Joint Conference of the European Frequency and Time Forum and IEEE International Frequency Control Symposium (IEEE, 2017), pp. 484–485.

T. Sun, L. Zhang, A. K. Poddar, U. L. Rohde, and A. S. Daryoush, “Forced SILPLL oscillation of X- and K-band frequency synthesized opto-electronic oscillators,” in Proceedings of IEEE Conference on International Topical Meeting on Microwave Photonics (IEEE, 2016), pp. 91–94.

A. S. Daryoush, Microwave Photonics from Components to Applications and Systems (Springer Science & Business Media, 2003), Chap. 6.

A. K. Poddar, U. L. Rohde, and A. S. Daryoush, “Self-Injection Locked Phase Locked Loop Optoelectronic Oscillator,” WO Patent, WO2014105707A1, (2014).

Delfyett, P. J.

F. Quinlan, S. Ozharar, S. Gee, and P. J. Delfyett, “Harmonically modelocked semiconductor based lasers as high repetition rate ultralow noise pulse train and optical frequency comb sources,” J. Opt. A: Pure Appl. Opt. 11(10), 103001 (2009).
[Crossref]

Denbaars, S. P.

J. S. Barton, E. J. Skogen, M. L. Masanovic, S. P. Denbaars, and L. A. Coldren, “A widely tunable high-speed transmitter using an integrated SGDBR laser-semiconductor optical amplifier and Mach-Zehnder modulator,” IEEE J. Sel. Top. Quantum Electron. 9(5), 1113–1117 (2003).
[Crossref]

Dijk, F.

F. Dijk, M. Lamponi, M. Chtioui, F. Lelarge, G. Kervella, E. Rouvalis, C. Renaud, M. Fice, and G. Carpintero, “Heterodyne millimeter wave source with monolithically integrated UTC photodiodes,” in Proceedings of IEEE Conference on International Topical Meeting on Microwave Photonics (IEEE, 2013), pp. 336–339.

Dolfi, D.

G. Pillet, L. Morvan, M. Brunel, F. Bretenaker, D. Dolfi, M. Vallet, J. P. Huignard, and A. L. Floch, “Dual-Frequency Laser at 1.5 µm for Optical Distribution and Generation of High-Purity Microwave Signals,” J. Lightwave Technol. 26(15), 2764–2773 (2008).
[Crossref]

G. Pillet, L. Morvan, D. Dolfi, J. Schiellein, and T. Merlet, “Stabilization of new generation solid-state dual-frequency laser at 1.5 µm for optical distribution of high purity microwave signals,” in Proceedings of IEEE Conference on International Topical Meeting on Microwave Photonics (IEEE, 2010), pp. 163–166.

Dylewicz, R.

L. Hou, R. Dylewicz, M. Haji, P. Stolarz, B. Qiu, and A. C. Bryce, “Monolithic 40-GHz Passively Mode-Locked AlGaInAs–InP 1.55-um MQW Laser With Surface-Etched Distributed Bragg Reflector,” IEEE Photonics Technol. Lett. 22(20), 1503–1505 (2010).
[Crossref]

Eliyahu, D.

A. A. Savchenkov, V. S. Iichenko, J. Byrd, W. Liang, D. Eliyahu, A. B. Matsko, D. Seidel, and L. Maleki, “Whispering-gallery mode based opto-electronic oscillators,” in Proceedings of IEEE Conference on International Frequency Control Symposium (IEEE, 2010), pp. 554–557.

Felipe, D.

G. Carpintero, S. Hisatake, D. Felipe, R. Guzman, T. Nagatsuma, N. Keil, and T. Gobel, “Photonics-based millimeter and terahertz wave generation using a hybrid integrated dual DBR polymer laser,” in Proceedings of IEEE Conference on International Microwave Symposium (IEEE, 2016), pp. 1–3.

Fice, M.

F. Dijk, M. Lamponi, M. Chtioui, F. Lelarge, G. Kervella, E. Rouvalis, C. Renaud, M. Fice, and G. Carpintero, “Heterodyne millimeter wave source with monolithically integrated UTC photodiodes,” in Proceedings of IEEE Conference on International Topical Meeting on Microwave Photonics (IEEE, 2013), pp. 336–339.

Fish, G. A.

L. A. Johansson, Y. A. Akulova, G. A. Fish, and L. A. Coldren, “Sampled-grating DBR laser integrated with SOA and tandem electroabsorption modulator for chirp-control,” Electron. Lett. 40(1), 70–71 (2004).
[Crossref]

Floch, A. L.

Galton, I.

S. Ye, L. Jansson, and I. Galton, “A multiple-crystal interface PLL with VCO realignment to reduce phase noise,” IEEE J. Solid-State Circuits 37(12), 1795–1803 (2002).
[Crossref]

Gee, S.

F. Quinlan, S. Ozharar, S. Gee, and P. J. Delfyett, “Harmonically modelocked semiconductor based lasers as high repetition rate ultralow noise pulse train and optical frequency comb sources,” J. Opt. A: Pure Appl. Opt. 11(10), 103001 (2009).
[Crossref]

Gobel, T.

G. Carpintero, S. Hisatake, D. Felipe, R. Guzman, T. Nagatsuma, N. Keil, and T. Gobel, “Photonics-based millimeter and terahertz wave generation using a hybrid integrated dual DBR polymer laser,” in Proceedings of IEEE Conference on International Microwave Symposium (IEEE, 2016), pp. 1–3.

Guzman, R.

G. Carpintero, S. Hisatake, D. Felipe, R. Guzman, T. Nagatsuma, N. Keil, and T. Gobel, “Photonics-based millimeter and terahertz wave generation using a hybrid integrated dual DBR polymer laser,” in Proceedings of IEEE Conference on International Microwave Symposium (IEEE, 2016), pp. 1–3.

Haji, M.

L. Hou, R. Dylewicz, M. Haji, P. Stolarz, B. Qiu, and A. C. Bryce, “Monolithic 40-GHz Passively Mode-Locked AlGaInAs–InP 1.55-um MQW Laser With Surface-Etched Distributed Bragg Reflector,” IEEE Photonics Technol. Lett. 22(20), 1503–1505 (2010).
[Crossref]

Hisatake, S.

G. Carpintero, S. Hisatake, D. Felipe, R. Guzman, T. Nagatsuma, N. Keil, and T. Gobel, “Photonics-based millimeter and terahertz wave generation using a hybrid integrated dual DBR polymer laser,” in Proceedings of IEEE Conference on International Microwave Symposium (IEEE, 2016), pp. 1–3.

Horikawa, K.

A. S. Daryoush, K. Sato, K. Horikawa, and H. Ogawa, “Dynamic response of long optical-cavity laser diode for Ka-band communication satellites,” IEEE Trans. Microwave Theory Tech. 45(8), 1288–1295 (1997).
[Crossref]

A. S. Daryoush, K. Sato, K. Horikawa, and H. Ogawa, “Electrically injection-locked intermodal oscillation in a long optical cavity laser diode,” IEEE Microw. Guid. Wave Lett. 7(7), 194–196 (1997).
[Crossref]

Hosako, I.

Hoshida, T.

T. Hoshida, H. Liu, M. Tsuchiya, Y. Ogawa, and T. Kamiya, “Subharmonic hybrid mode-locking of a monolithic semiconductor laser,” IEEE J. Sel. Top. Quantum Electron. 2(3), 514–522 (1996).
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Hou, L.

L. Hou, R. Dylewicz, M. Haji, P. Stolarz, B. Qiu, and A. C. Bryce, “Monolithic 40-GHz Passively Mode-Locked AlGaInAs–InP 1.55-um MQW Laser With Surface-Etched Distributed Bragg Reflector,” IEEE Photonics Technol. Lett. 22(20), 1503–1505 (2010).
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Iichenko, V. S.

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Jansson, L.

S. Ye, L. Jansson, and I. Galton, “A multiple-crystal interface PLL with VCO realignment to reduce phase noise,” IEEE J. Solid-State Circuits 37(12), 1795–1803 (2002).
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Johansson, L. A.

L. A. Johansson, Y. A. Akulova, G. A. Fish, and L. A. Coldren, “Sampled-grating DBR laser integrated with SOA and tandem electroabsorption modulator for chirp-control,” Electron. Lett. 40(1), 70–71 (2004).
[Crossref]

Joshi, S.

Kamiya, T.

T. Hoshida, H. Liu, M. Tsuchiya, Y. Ogawa, and T. Kamiya, “Subharmonic hybrid mode-locking of a monolithic semiconductor laser,” IEEE J. Sel. Top. Quantum Electron. 2(3), 514–522 (1996).
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G. Carpintero, S. Hisatake, D. Felipe, R. Guzman, T. Nagatsuma, N. Keil, and T. Gobel, “Photonics-based millimeter and terahertz wave generation using a hybrid integrated dual DBR polymer laser,” in Proceedings of IEEE Conference on International Microwave Symposium (IEEE, 2016), pp. 1–3.

Kervella, G.

F. Dijk, M. Lamponi, M. Chtioui, F. Lelarge, G. Kervella, E. Rouvalis, C. Renaud, M. Fice, and G. Carpintero, “Heterodyne millimeter wave source with monolithically integrated UTC photodiodes,” in Proceedings of IEEE Conference on International Topical Meeting on Microwave Photonics (IEEE, 2013), pp. 336–339.

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V. Kroeze, “SmartPhotonics Introduction,” https://smartphotonics.nl/ .

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F. Dijk, M. Lamponi, M. Chtioui, F. Lelarge, G. Kervella, E. Rouvalis, C. Renaud, M. Fice, and G. Carpintero, “Heterodyne millimeter wave source with monolithically integrated UTC photodiodes,” in Proceedings of IEEE Conference on International Topical Meeting on Microwave Photonics (IEEE, 2013), pp. 336–339.

Lelarge, F.

S. Joshi, C. Calò, N. Chimot, M. Radziunas, R. Arkhipov, S. Barbet, A. Accard, A. Ramdane, and F. Lelarge, “Quantum dash based single section mode locked lasers for photonic integrated circuits,” Opt. Express 22(9), 11254–11266 (2014).
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F. Dijk, M. Lamponi, M. Chtioui, F. Lelarge, G. Kervella, E. Rouvalis, C. Renaud, M. Fice, and G. Carpintero, “Heterodyne millimeter wave source with monolithically integrated UTC photodiodes,” in Proceedings of IEEE Conference on International Topical Meeting on Microwave Photonics (IEEE, 2013), pp. 336–339.

Liang, W.

A. A. Savchenkov, V. S. Iichenko, J. Byrd, W. Liang, D. Eliyahu, A. B. Matsko, D. Seidel, and L. Maleki, “Whispering-gallery mode based opto-electronic oscillators,” in Proceedings of IEEE Conference on International Frequency Control Symposium (IEEE, 2010), pp. 554–557.

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J. Lin, Study of Digital Fiber-Optic Link and Clock Recovery Circuit at 1.25Gb/s, (Ph.D. Dissertation, 1995).

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T. Hoshida, H. Liu, M. Tsuchiya, Y. Ogawa, and T. Kamiya, “Subharmonic hybrid mode-locking of a monolithic semiconductor laser,” IEEE J. Sel. Top. Quantum Electron. 2(3), 514–522 (1996).
[Crossref]

Maleki, L.

A. A. Savchenkov, V. S. Iichenko, J. Byrd, W. Liang, D. Eliyahu, A. B. Matsko, D. Seidel, and L. Maleki, “Whispering-gallery mode based opto-electronic oscillators,” in Proceedings of IEEE Conference on International Frequency Control Symposium (IEEE, 2010), pp. 554–557.

Masanovic, M. L.

J. S. Barton, E. J. Skogen, M. L. Masanovic, S. P. Denbaars, and L. A. Coldren, “A widely tunable high-speed transmitter using an integrated SGDBR laser-semiconductor optical amplifier and Mach-Zehnder modulator,” IEEE J. Sel. Top. Quantum Electron. 9(5), 1113–1117 (2003).
[Crossref]

Matsko, A. B.

A. A. Savchenkov, V. S. Iichenko, J. Byrd, W. Liang, D. Eliyahu, A. B. Matsko, D. Seidel, and L. Maleki, “Whispering-gallery mode based opto-electronic oscillators,” in Proceedings of IEEE Conference on International Frequency Control Symposium (IEEE, 2010), pp. 554–557.

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G. Pillet, L. Morvan, D. Dolfi, J. Schiellein, and T. Merlet, “Stabilization of new generation solid-state dual-frequency laser at 1.5 µm for optical distribution of high purity microwave signals,” in Proceedings of IEEE Conference on International Topical Meeting on Microwave Photonics (IEEE, 2010), pp. 163–166.

Mizutori, A.

Morohashi, I.

Morvan, L.

G. Pillet, L. Morvan, M. Brunel, F. Bretenaker, D. Dolfi, M. Vallet, J. P. Huignard, and A. L. Floch, “Dual-Frequency Laser at 1.5 µm for Optical Distribution and Generation of High-Purity Microwave Signals,” J. Lightwave Technol. 26(15), 2764–2773 (2008).
[Crossref]

G. Pillet, L. Morvan, D. Dolfi, J. Schiellein, and T. Merlet, “Stabilization of new generation solid-state dual-frequency laser at 1.5 µm for optical distribution of high purity microwave signals,” in Proceedings of IEEE Conference on International Topical Meeting on Microwave Photonics (IEEE, 2010), pp. 163–166.

Nagatsuma, T.

G. Carpintero, S. Hisatake, D. Felipe, R. Guzman, T. Nagatsuma, N. Keil, and T. Gobel, “Photonics-based millimeter and terahertz wave generation using a hybrid integrated dual DBR polymer laser,” in Proceedings of IEEE Conference on International Microwave Symposium (IEEE, 2016), pp. 1–3.

Ni, T. D.

T. D. Ni, X. Zhang, and A. S. Daryoush, “Experimental Study on Close-in carrier Phase Noise of Laser Diode with Coherent Feedback,” IEEE Trans. Microwave Theory Tech. 43(9), 2277–2283 (1995).
[Crossref]

T. D. Ni, X. Zhang, and A. S. Daryoush, “Close-in carrier phase noise of laser with coherent feedback,” in Proceedings of IEEE Conference on International Microwave Symposium Digest (IEEE, 1994), pp. 61–64.

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Ogawa, H.

A. S. Daryoush, K. Sato, K. Horikawa, and H. Ogawa, “Electrically injection-locked intermodal oscillation in a long optical cavity laser diode,” IEEE Microw. Guid. Wave Lett. 7(7), 194–196 (1997).
[Crossref]

A. S. Daryoush, K. Sato, K. Horikawa, and H. Ogawa, “Dynamic response of long optical-cavity laser diode for Ka-band communication satellites,” IEEE Trans. Microwave Theory Tech. 45(8), 1288–1295 (1997).
[Crossref]

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S. Arahira and Y. Ogawa, “40 GHz actively mode-locked distributed bragg reflector laser diode module with an impedance-matching circuit for effi- cient RF signal injection,” Jpn. J. Appl. Phys. 43(4B), 1960–1964 (2004).
[Crossref]

T. Hoshida, H. Liu, M. Tsuchiya, Y. Ogawa, and T. Kamiya, “Subharmonic hybrid mode-locking of a monolithic semiconductor laser,” IEEE J. Sel. Top. Quantum Electron. 2(3), 514–522 (1996).
[Crossref]

Ozharar, S.

F. Quinlan, S. Ozharar, S. Gee, and P. J. Delfyett, “Harmonically modelocked semiconductor based lasers as high repetition rate ultralow noise pulse train and optical frequency comb sources,” J. Opt. A: Pure Appl. Opt. 11(10), 103001 (2009).
[Crossref]

Penty, R. V.

G. Carpintero, M. G. Thompson, R. V. Penty, and I. H. White, “Low Noise Performance of Passively Mode-Locked 10-GHz Quantum-Dot Laser Diode,” IEEE Photonics Technol. Lett. 21(6), 389–391 (2009).
[Crossref]

Pillet, G.

G. Pillet, L. Morvan, M. Brunel, F. Bretenaker, D. Dolfi, M. Vallet, J. P. Huignard, and A. L. Floch, “Dual-Frequency Laser at 1.5 µm for Optical Distribution and Generation of High-Purity Microwave Signals,” J. Lightwave Technol. 26(15), 2764–2773 (2008).
[Crossref]

G. Pillet, L. Morvan, D. Dolfi, J. Schiellein, and T. Merlet, “Stabilization of new generation solid-state dual-frequency laser at 1.5 µm for optical distribution of high purity microwave signals,” in Proceedings of IEEE Conference on International Topical Meeting on Microwave Photonics (IEEE, 2010), pp. 163–166.

Poddar, A.

T. Sun, A. S. Daryoush, A. Poddar, L. Zhang, and U. Rohde, “High-resolution frequency synthesizers over X-band using SILPLL opto-electronic oscillators,” in Proceedings of Joint Conference of the European Frequency and Time Forum and IEEE International Frequency Control Symposium (IEEE, 2017), pp. 484–485.

Poddar, A. K.

T. Sun, L. Zhang, A. K. Poddar, U. L. Rohde, and A. S. Daryoush, “Frequency synthesis of forced opto-electronic oscillators at the X-band,” Chin. Opt. Lett. 15(1), 10009–10013 (2017).
[Crossref]

T. Sun, L. Zhang, A. K. Poddar, U. L. Rohde, and A. S. Daryoush, “Limits in Timing Jitters of Forced Microwave Oscillator Using Optical Self-ILPLL,” IEEE Photonics Technol. Lett. 29(2), 181–184 (2017).
[Crossref]

L. Zhang, A. K. Poddar, U. L. Rohde, and A. S. Daryoush, “Comparison of optical self-phase locked loop techniques for frequency stabilization of oscillators,” IEEE Photonics J. 6(5), 1–15 (2014).
[Crossref]

L. Zhang, A. K. Poddar, U. L. Rohde, and A. S. Daryoush, “Analytical and experimental evaluation of SSB phase noise reduction in self-injection locked oscillators using optical delay loops,” IEEE Photonics J. 5(6), 6602217 (2013).
[Crossref]

A. K. Poddar, U. L. Rohde, and A. S. Daryoush, “Self-Injection Locked Phase Locked Loop Optoelectronic Oscillator,” WO Patent, WO2014105707A1, (2014).

T. Sun, L. Zhang, A. K. Poddar, U. L. Rohde, and A. S. Daryoush, “Forced SILPLL oscillation of X- and K-band frequency synthesized opto-electronic oscillators,” in Proceedings of IEEE Conference on International Topical Meeting on Microwave Photonics (IEEE, 2016), pp. 91–94.

Qiu, B.

L. Hou, R. Dylewicz, M. Haji, P. Stolarz, B. Qiu, and A. C. Bryce, “Monolithic 40-GHz Passively Mode-Locked AlGaInAs–InP 1.55-um MQW Laser With Surface-Etched Distributed Bragg Reflector,” IEEE Photonics Technol. Lett. 22(20), 1503–1505 (2010).
[Crossref]

Quinlan, F.

F. Quinlan, S. Ozharar, S. Gee, and P. J. Delfyett, “Harmonically modelocked semiconductor based lasers as high repetition rate ultralow noise pulse train and optical frequency comb sources,” J. Opt. A: Pure Appl. Opt. 11(10), 103001 (2009).
[Crossref]

Radziunas, M.

Ramdane, A.

Renaud, C.

F. Dijk, M. Lamponi, M. Chtioui, F. Lelarge, G. Kervella, E. Rouvalis, C. Renaud, M. Fice, and G. Carpintero, “Heterodyne millimeter wave source with monolithically integrated UTC photodiodes,” in Proceedings of IEEE Conference on International Topical Meeting on Microwave Photonics (IEEE, 2013), pp. 336–339.

Rohde, U.

T. Sun, A. S. Daryoush, A. Poddar, L. Zhang, and U. Rohde, “High-resolution frequency synthesizers over X-band using SILPLL opto-electronic oscillators,” in Proceedings of Joint Conference of the European Frequency and Time Forum and IEEE International Frequency Control Symposium (IEEE, 2017), pp. 484–485.

Rohde, U. L.

T. Sun, L. Zhang, A. K. Poddar, U. L. Rohde, and A. S. Daryoush, “Frequency synthesis of forced opto-electronic oscillators at the X-band,” Chin. Opt. Lett. 15(1), 10009–10013 (2017).
[Crossref]

T. Sun, L. Zhang, A. K. Poddar, U. L. Rohde, and A. S. Daryoush, “Limits in Timing Jitters of Forced Microwave Oscillator Using Optical Self-ILPLL,” IEEE Photonics Technol. Lett. 29(2), 181–184 (2017).
[Crossref]

L. Zhang, A. K. Poddar, U. L. Rohde, and A. S. Daryoush, “Comparison of optical self-phase locked loop techniques for frequency stabilization of oscillators,” IEEE Photonics J. 6(5), 1–15 (2014).
[Crossref]

L. Zhang, A. K. Poddar, U. L. Rohde, and A. S. Daryoush, “Analytical and experimental evaluation of SSB phase noise reduction in self-injection locked oscillators using optical delay loops,” IEEE Photonics J. 5(6), 6602217 (2013).
[Crossref]

T. Sun, L. Zhang, A. K. Poddar, U. L. Rohde, and A. S. Daryoush, “Forced SILPLL oscillation of X- and K-band frequency synthesized opto-electronic oscillators,” in Proceedings of IEEE Conference on International Topical Meeting on Microwave Photonics (IEEE, 2016), pp. 91–94.

A. K. Poddar, U. L. Rohde, and A. S. Daryoush, “Self-Injection Locked Phase Locked Loop Optoelectronic Oscillator,” WO Patent, WO2014105707A1, (2014).

Rouvalis, E.

F. Dijk, M. Lamponi, M. Chtioui, F. Lelarge, G. Kervella, E. Rouvalis, C. Renaud, M. Fice, and G. Carpintero, “Heterodyne millimeter wave source with monolithically integrated UTC photodiodes,” in Proceedings of IEEE Conference on International Topical Meeting on Microwave Photonics (IEEE, 2013), pp. 336–339.

Sakamoto, T.

Sato, K.

A. S. Daryoush, K. Sato, K. Horikawa, and H. Ogawa, “Dynamic response of long optical-cavity laser diode for Ka-band communication satellites,” IEEE Trans. Microwave Theory Tech. 45(8), 1288–1295 (1997).
[Crossref]

A. S. Daryoush, K. Sato, K. Horikawa, and H. Ogawa, “Electrically injection-locked intermodal oscillation in a long optical cavity laser diode,” IEEE Microw. Guid. Wave Lett. 7(7), 194–196 (1997).
[Crossref]

Savchenkov, A. A.

A. A. Savchenkov, V. S. Iichenko, J. Byrd, W. Liang, D. Eliyahu, A. B. Matsko, D. Seidel, and L. Maleki, “Whispering-gallery mode based opto-electronic oscillators,” in Proceedings of IEEE Conference on International Frequency Control Symposium (IEEE, 2010), pp. 554–557.

Schiellein, J.

G. Pillet, L. Morvan, D. Dolfi, J. Schiellein, and T. Merlet, “Stabilization of new generation solid-state dual-frequency laser at 1.5 µm for optical distribution of high purity microwave signals,” in Proceedings of IEEE Conference on International Topical Meeting on Microwave Photonics (IEEE, 2010), pp. 163–166.

Seidel, D.

A. A. Savchenkov, V. S. Iichenko, J. Byrd, W. Liang, D. Eliyahu, A. B. Matsko, D. Seidel, and L. Maleki, “Whispering-gallery mode based opto-electronic oscillators,” in Proceedings of IEEE Conference on International Frequency Control Symposium (IEEE, 2010), pp. 554–557.

Skogen, E. J.

J. S. Barton, E. J. Skogen, M. L. Masanovic, S. P. Denbaars, and L. A. Coldren, “A widely tunable high-speed transmitter using an integrated SGDBR laser-semiconductor optical amplifier and Mach-Zehnder modulator,” IEEE J. Sel. Top. Quantum Electron. 9(5), 1113–1117 (2003).
[Crossref]

Sogawa, T.

Sotobayashi, H.

Stolarz, P.

L. Hou, R. Dylewicz, M. Haji, P. Stolarz, B. Qiu, and A. C. Bryce, “Monolithic 40-GHz Passively Mode-Locked AlGaInAs–InP 1.55-um MQW Laser With Surface-Etched Distributed Bragg Reflector,” IEEE Photonics Technol. Lett. 22(20), 1503–1505 (2010).
[Crossref]

Sun, T.

T. Sun, L. Zhang, A. K. Poddar, U. L. Rohde, and A. S. Daryoush, “Frequency synthesis of forced opto-electronic oscillators at the X-band,” Chin. Opt. Lett. 15(1), 10009–10013 (2017).
[Crossref]

T. Sun, L. Zhang, A. K. Poddar, U. L. Rohde, and A. S. Daryoush, “Limits in Timing Jitters of Forced Microwave Oscillator Using Optical Self-ILPLL,” IEEE Photonics Technol. Lett. 29(2), 181–184 (2017).
[Crossref]

T. Sun, A. S. Daryoush, A. Poddar, L. Zhang, and U. Rohde, “High-resolution frequency synthesizers over X-band using SILPLL opto-electronic oscillators,” in Proceedings of Joint Conference of the European Frequency and Time Forum and IEEE International Frequency Control Symposium (IEEE, 2017), pp. 484–485.

T. Sun, L. Zhang, A. K. Poddar, U. L. Rohde, and A. S. Daryoush, “Forced SILPLL oscillation of X- and K-band frequency synthesized opto-electronic oscillators,” in Proceedings of IEEE Conference on International Topical Meeting on Microwave Photonics (IEEE, 2016), pp. 91–94.

Takada, A.

Takara, H.

Thompson, M. G.

G. Carpintero, M. G. Thompson, R. V. Penty, and I. H. White, “Low Noise Performance of Passively Mode-Locked 10-GHz Quantum-Dot Laser Diode,” IEEE Photonics Technol. Lett. 21(6), 389–391 (2009).
[Crossref]

Tsuchiya, M.

Vallet, M.

White, I. H.

G. Carpintero, M. G. Thompson, R. V. Penty, and I. H. White, “Low Noise Performance of Passively Mode-Locked 10-GHz Quantum-Dot Laser Diode,” IEEE Photonics Technol. Lett. 21(6), 389–391 (2009).
[Crossref]

Xu, J.

M. Chen and J. Xu, “Wideband Frequency Synthesizer at X/Ku Band by Mixing and Phase Locking of Half Frequency Output of VCO,” J. Infrared, Millimeter, Terahertz Waves 31(1), 100–110 (2009).
[Crossref]

Yao, J.

W. Zhang and J. Yao, “A silicon photonic integrated frequency-tunable optoelectronic oscillator,” in Proceedings of IEEE Conference on International Topical Meeting on Microwave Photonics (IEEE, 2017), pp. 1–4.

Ye, S.

S. Ye, L. Jansson, and I. Galton, “A multiple-crystal interface PLL with VCO realignment to reduce phase noise,” IEEE J. Solid-State Circuits 37(12), 1795–1803 (2002).
[Crossref]

Zhang, L.

T. Sun, L. Zhang, A. K. Poddar, U. L. Rohde, and A. S. Daryoush, “Frequency synthesis of forced opto-electronic oscillators at the X-band,” Chin. Opt. Lett. 15(1), 10009–10013 (2017).
[Crossref]

T. Sun, L. Zhang, A. K. Poddar, U. L. Rohde, and A. S. Daryoush, “Limits in Timing Jitters of Forced Microwave Oscillator Using Optical Self-ILPLL,” IEEE Photonics Technol. Lett. 29(2), 181–184 (2017).
[Crossref]

L. Zhang, A. K. Poddar, U. L. Rohde, and A. S. Daryoush, “Comparison of optical self-phase locked loop techniques for frequency stabilization of oscillators,” IEEE Photonics J. 6(5), 1–15 (2014).
[Crossref]

L. Zhang, A. K. Poddar, U. L. Rohde, and A. S. Daryoush, “Analytical and experimental evaluation of SSB phase noise reduction in self-injection locked oscillators using optical delay loops,” IEEE Photonics J. 5(6), 6602217 (2013).
[Crossref]

L. Zhang, Optoelectronic frequency stabilization techniques in forced oscillators (Ph.D. Dissertation, 2014).

T. Sun, A. S. Daryoush, A. Poddar, L. Zhang, and U. Rohde, “High-resolution frequency synthesizers over X-band using SILPLL opto-electronic oscillators,” in Proceedings of Joint Conference of the European Frequency and Time Forum and IEEE International Frequency Control Symposium (IEEE, 2017), pp. 484–485.

T. Sun, L. Zhang, A. K. Poddar, U. L. Rohde, and A. S. Daryoush, “Forced SILPLL oscillation of X- and K-band frequency synthesized opto-electronic oscillators,” in Proceedings of IEEE Conference on International Topical Meeting on Microwave Photonics (IEEE, 2016), pp. 91–94.

Zhang, W.

W. Zhang and J. Yao, “A silicon photonic integrated frequency-tunable optoelectronic oscillator,” in Proceedings of IEEE Conference on International Topical Meeting on Microwave Photonics (IEEE, 2017), pp. 1–4.

Zhang, X.

T. D. Ni, X. Zhang, and A. S. Daryoush, “Experimental Study on Close-in carrier Phase Noise of Laser Diode with Coherent Feedback,” IEEE Trans. Microwave Theory Tech. 43(9), 2277–2283 (1995).
[Crossref]

T. D. Ni, X. Zhang, and A. S. Daryoush, “Close-in carrier phase noise of laser with coherent feedback,” in Proceedings of IEEE Conference on International Microwave Symposium Digest (IEEE, 1994), pp. 61–64.

Chin. Opt. Lett. (1)

T. Sun, L. Zhang, A. K. Poddar, U. L. Rohde, and A. S. Daryoush, “Frequency synthesis of forced opto-electronic oscillators at the X-band,” Chin. Opt. Lett. 15(1), 10009–10013 (2017).
[Crossref]

Electron. Lett. (1)

L. A. Johansson, Y. A. Akulova, G. A. Fish, and L. A. Coldren, “Sampled-grating DBR laser integrated with SOA and tandem electroabsorption modulator for chirp-control,” Electron. Lett. 40(1), 70–71 (2004).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (2)

J. S. Barton, E. J. Skogen, M. L. Masanovic, S. P. Denbaars, and L. A. Coldren, “A widely tunable high-speed transmitter using an integrated SGDBR laser-semiconductor optical amplifier and Mach-Zehnder modulator,” IEEE J. Sel. Top. Quantum Electron. 9(5), 1113–1117 (2003).
[Crossref]

T. Hoshida, H. Liu, M. Tsuchiya, Y. Ogawa, and T. Kamiya, “Subharmonic hybrid mode-locking of a monolithic semiconductor laser,” IEEE J. Sel. Top. Quantum Electron. 2(3), 514–522 (1996).
[Crossref]

IEEE J. Solid-State Circuits (1)

S. Ye, L. Jansson, and I. Galton, “A multiple-crystal interface PLL with VCO realignment to reduce phase noise,” IEEE J. Solid-State Circuits 37(12), 1795–1803 (2002).
[Crossref]

IEEE Microw. Guid. Wave Lett. (1)

A. S. Daryoush, K. Sato, K. Horikawa, and H. Ogawa, “Electrically injection-locked intermodal oscillation in a long optical cavity laser diode,” IEEE Microw. Guid. Wave Lett. 7(7), 194–196 (1997).
[Crossref]

IEEE Photonics J. (2)

L. Zhang, A. K. Poddar, U. L. Rohde, and A. S. Daryoush, “Analytical and experimental evaluation of SSB phase noise reduction in self-injection locked oscillators using optical delay loops,” IEEE Photonics J. 5(6), 6602217 (2013).
[Crossref]

L. Zhang, A. K. Poddar, U. L. Rohde, and A. S. Daryoush, “Comparison of optical self-phase locked loop techniques for frequency stabilization of oscillators,” IEEE Photonics J. 6(5), 1–15 (2014).
[Crossref]

IEEE Photonics Technol. Lett. (3)

T. Sun, L. Zhang, A. K. Poddar, U. L. Rohde, and A. S. Daryoush, “Limits in Timing Jitters of Forced Microwave Oscillator Using Optical Self-ILPLL,” IEEE Photonics Technol. Lett. 29(2), 181–184 (2017).
[Crossref]

G. Carpintero, M. G. Thompson, R. V. Penty, and I. H. White, “Low Noise Performance of Passively Mode-Locked 10-GHz Quantum-Dot Laser Diode,” IEEE Photonics Technol. Lett. 21(6), 389–391 (2009).
[Crossref]

L. Hou, R. Dylewicz, M. Haji, P. Stolarz, B. Qiu, and A. C. Bryce, “Monolithic 40-GHz Passively Mode-Locked AlGaInAs–InP 1.55-um MQW Laser With Surface-Etched Distributed Bragg Reflector,” IEEE Photonics Technol. Lett. 22(20), 1503–1505 (2010).
[Crossref]

IEEE Trans. Microwave Theory Tech. (3)

A. S. Daryoush, “Optical synchronization of millimeter-wave oscillators for distributed architecture,” IEEE Trans. Microwave Theory Tech. 38(5), 467–476 (1990).
[Crossref]

A. S. Daryoush, K. Sato, K. Horikawa, and H. Ogawa, “Dynamic response of long optical-cavity laser diode for Ka-band communication satellites,” IEEE Trans. Microwave Theory Tech. 45(8), 1288–1295 (1997).
[Crossref]

T. D. Ni, X. Zhang, and A. S. Daryoush, “Experimental Study on Close-in carrier Phase Noise of Laser Diode with Coherent Feedback,” IEEE Trans. Microwave Theory Tech. 43(9), 2277–2283 (1995).
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J. Infrared, Millimeter, Terahertz Waves (1)

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Figures (15)

Fig. 1.
Fig. 1. Block diagram of inter-modal laser based RF synthesizer on a microchip structure.
Fig. 2.
Fig. 2. Fabricated DBR based multi-mode multi-section semiconductor laser on InP chip with DC bias control gold pads in rectangular patterns.
Fig. 3.
Fig. 3. Testing environment of the DBR based multi-mode multi-section semiconductor laser.
Fig. 4.
Fig. 4. Free-running performance of inter-modal RF output: center frequency of 11.5496 GHz with output power of −10.59 dBm, frequency span of 400 kHz, resolution bandwidth (RBW) of 50 Hz and video bandwidth (VBW) of 50 Hz.
Fig. 5.
Fig. 5. Close-in to carrier phase noise over 1kHz to 1 MHz offset carrier frequency. A time averaging of 10 is used.
Fig. 6.
Fig. 6. Conceptual block diagram of SIL using control theory representation with a self-feedback after a delay of Td with coupling factor of ρ integrated to system [27].
Fig. 7.
Fig. 7. Control theory representation of SPLL [28].
Fig. 8.
Fig. 8. Control theory representation of SILPLL [32].
Fig. 9.
Fig. 9. Block diagram of self-injection locking system with electrical system designated in red color, while optical system is in blue color.
Fig. 10.
Fig. 10. Phase noise performance comparison of self-injection locking with free-running inter-modal oscillation, a) different injection power levels, b) different fiber delay line lengths.
Fig. 11.
Fig. 11. External phase locking set-up using external frequency reference from RF synthesizer by detection of phase error is detected and used to control PM section of multi-section laser.
Fig. 12.
Fig. 12. Phase noise performance using external phase locking circuit (RF frequency of 11.54 GHz, RF output Power of 5.39 dBm).
Fig. 13.
Fig. 13. Simulation and measurement results of pull-in time of PLL and ILPLL using the external frequency reference.
Fig. 14.
Fig. 14. Block diagram of inter-modal oscillation stabilization using a combination of self-injection locking (SIL) and triple self-phase locking (TSPLL).
Fig. 15.
Fig. 15. Phase noise performance of SILPLL based inter-modal RF output and comparison to simulated results under different PM bias while free-running is depicted for comparison (RF = 11.54 GHz, RF Power = 3.59 dBm).

Tables (3)

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Table 1. Multi-mode laser output wavelength and related power level

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Table 2. PM tuning sensitivity and RF output frequency versus DC bias of DBR laser PM section

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Table 3. PLL board locking range testing using external RF synthesizer source for loop bandwith of 50 MHz

Equations (8)

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S SIL ( ω m ) = | H SIL ( s ) | 2 S n i ( ω m ) + | H E SIL ( s ) | 2 S n o ( ω m ) ,
H SIL ( S ) = G IL ( 1 e s τ d ) G IL + 1 , H E SIL ( S ) = 1 ( 1 e s τ d ) G IL + 1 .
S SPLL ( ω m ) = | H SPLL ( s ) | 2 S n i ( ω m ) + | H E SPLL ( s ) | 2 S n o ( ω m ) ,
H SPLL ( S ) = G PLL ( 1 e s τ d ) G PLL + 1 , H E SPLL ( S ) = 1 ( 1 e s τ d ) G PLL + 1 .
S Φ 0 = | G IL + G PLL 1 + K IL G IL + K PLL G PLL | 2 S n i + | 1 1 + K IL G IL + K PLL G PLL | 2 S n 0 ,
K IL = 1 e s τ d i , K PLL = 1 e s τ dp .
( Δ ω 0 ) 2 ω n 2 K ,
Δ ω 0 2 ( Δ ω i ) 2 ω n 2 Δ ω i .

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