Abstract

A dynamic noise characterization technique for measuring narrow-linewidth frequency-sweep lasers based on phase reconstruction method is proposed. The phase and the frequency fluctuation power spectral density (PSD) of the swept optical field within a specific time window are recovered mainly by demodulating the differential phase information of the 120-degree phase difference interferometer. Then the details of the laser noise characteristics and the performance evolution law of the frequency sweep process can be observed by investigating the calculated frequency fluctuation PSD. Moreover, the integration time linewidth and Lorentzian linewidth of the swept frequency field can be obtained by introducing the integral algorithm even beyond the limit of PSD physical resolution. Meanwhile, the power of this method is verified by applying it to a kHz-linewidth frequency swept laser source based on high-order modulation-sideband injection-locking. The results show many features of the laser such as specific noise peaks and the laser characteristic evolution rules which could not be measured by other traditional methods.

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

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2018 (1)

L. Liu, D.-S. Lü, W.-B. Chen, T. Li, Q.-Z. Qu, B. Wang, L. Li, W. Ren, Z.-R. Dong, J.-B. Zhao, W.-B. Xia, X. Zhao, J.-W. Ji, M.-F. Ye, Y.-G. Sun, Y.-Y. Yao, D. Song, Z.-G. Liang, S.-J. Hu, D.-H. Yu, X. Hou, W. Shi, H.-G. Zang, J.-F. Xiang, X.-K. Peng, and Y.-Z. Wang, “In-orbit operation of an atomic clock based on laser-cooled 87Rb atoms,” Nat. Commun. 9(1), 2760 (2018).
[Crossref] [PubMed]

2017 (4)

2015 (6)

2014 (1)

2013 (1)

2012 (1)

2010 (2)

2009 (1)

2007 (1)

2005 (1)

G. M. Stéphan, T. T. Tam, S. Blin, P. Besnard, and M. Têtu, “Laser line shape and spectral density of frequency noise,” Phys. Rev. A 71(4), 043809 (2005).
[Crossref]

2004 (1)

M. Osinski, R. Vicente, H. Amano, J. Mulet, M. Sciamanna, F. Henneberger, and C. R. Mirasso, “Simple interpretation of the dynamics of mutually coupled semiconductor lasers with detuning,” Proc. SPIE 5349, 307 (2004).
[Crossref]

1991 (2)

L. B. Mercer, “1/f frequency noise effects on self-heterodyne linewidth measurements,” J. Lightwave Technol. 9(4), 485–493 (1991).
[Crossref]

A. D. Kersey, M. J. Marrone, and M. A. Davis, “Polarisation-insensitive fibre optic Michelson interferometer,” Electron. Lett. 27(6), 518–520 (1991).
[Crossref]

Acef, O.

Ahn, T.-J.

Amano, H.

M. Osinski, R. Vicente, H. Amano, J. Mulet, M. Sciamanna, F. Henneberger, and C. R. Mirasso, “Simple interpretation of the dynamics of mutually coupled semiconductor lasers with detuning,” Proc. SPIE 5349, 307 (2004).
[Crossref]

Beppu, S.

Besnard, P.

G. M. Stéphan, T. T. Tam, S. Blin, P. Besnard, and M. Têtu, “Laser line shape and spectral density of frequency noise,” Phys. Rev. A 71(4), 043809 (2005).
[Crossref]

Biedermann, B. R.

Blin, S.

G. M. Stéphan, T. T. Tam, S. Blin, P. Besnard, and M. Têtu, “Laser line shape and spectral density of frequency noise,” Phys. Rev. A 71(4), 043809 (2005).
[Crossref]

Boyarsky, M.

Butler, T.

Cai, H.

Chen, D.

Chen, W.-B.

L. Liu, D.-S. Lü, W.-B. Chen, T. Li, Q.-Z. Qu, B. Wang, L. Li, W. Ren, Z.-R. Dong, J.-B. Zhao, W.-B. Xia, X. Zhao, J.-W. Ji, M.-F. Ye, Y.-G. Sun, Y.-Y. Yao, D. Song, Z.-G. Liang, S.-J. Hu, D.-H. Yu, X. Hou, W. Shi, H.-G. Zang, J.-F. Xiang, X.-K. Peng, and Y.-Z. Wang, “In-orbit operation of an atomic clock based on laser-cooled 87Rb atoms,” Nat. Commun. 9(1), 2760 (2018).
[Crossref] [PubMed]

Chiodo, N.

Clairon, A.

Cui, S.

Davis, M. A.

A. D. Kersey, M. J. Marrone, and M. A. Davis, “Polarisation-insensitive fibre optic Michelson interferometer,” Electron. Lett. 27(6), 518–520 (1991).
[Crossref]

Di Domenico, G.

Djerroud, K.

Dong, Y.

Dong, Z.-R.

L. Liu, D.-S. Lü, W.-B. Chen, T. Li, Q.-Z. Qu, B. Wang, L. Li, W. Ren, Z.-R. Dong, J.-B. Zhao, W.-B. Xia, X. Zhao, J.-W. Ji, M.-F. Ye, Y.-G. Sun, Y.-Y. Yao, D. Song, Z.-G. Liang, S.-J. Hu, D.-H. Yu, X. Hou, W. Shi, H.-G. Zang, J.-F. Xiang, X.-K. Peng, and Y.-Z. Wang, “In-orbit operation of an atomic clock based on laser-cooled 87Rb atoms,” Nat. Commun. 9(1), 2760 (2018).
[Crossref] [PubMed]

Eigenwillig, C. M.

Evans, M.

Fang, Z.

Fritschel, P.

Frolov, V.

Fromenteze, T.

Goulding, D.

Hegarty, S. P.

Henneberger, F.

M. Osinski, R. Vicente, H. Amano, J. Mulet, M. Sciamanna, F. Henneberger, and C. R. Mirasso, “Simple interpretation of the dynamics of mutually coupled semiconductor lasers with detuning,” Proc. SPIE 5349, 307 (2004).
[Crossref]

Hou, X.

L. Liu, D.-S. Lü, W.-B. Chen, T. Li, Q.-Z. Qu, B. Wang, L. Li, W. Ren, Z.-R. Dong, J.-B. Zhao, W.-B. Xia, X. Zhao, J.-W. Ji, M.-F. Ye, Y.-G. Sun, Y.-Y. Yao, D. Song, Z.-G. Liang, S.-J. Hu, D.-H. Yu, X. Hou, W. Shi, H.-G. Zang, J.-F. Xiang, X.-K. Peng, and Y.-Z. Wang, “In-orbit operation of an atomic clock based on laser-cooled 87Rb atoms,” Nat. Commun. 9(1), 2760 (2018).
[Crossref] [PubMed]

Hu, S.-J.

L. Liu, D.-S. Lü, W.-B. Chen, T. Li, Q.-Z. Qu, B. Wang, L. Li, W. Ren, Z.-R. Dong, J.-B. Zhao, W.-B. Xia, X. Zhao, J.-W. Ji, M.-F. Ye, Y.-G. Sun, Y.-Y. Yao, D. Song, Z.-G. Liang, S.-J. Hu, D.-H. Yu, X. Hou, W. Shi, H.-G. Zang, J.-F. Xiang, X.-K. Peng, and Y.-Z. Wang, “In-orbit operation of an atomic clock based on laser-cooled 87Rb atoms,” Nat. Commun. 9(1), 2760 (2018).
[Crossref] [PubMed]

Hu, W.

Huber, R.

Huyet, G.

Imani, M. F.

Ji, J.-W.

L. Liu, D.-S. Lü, W.-B. Chen, T. Li, Q.-Z. Qu, B. Wang, L. Li, W. Ren, Z.-R. Dong, J.-B. Zhao, W.-B. Xia, X. Zhao, J.-W. Ji, M.-F. Ye, Y.-G. Sun, Y.-Y. Yao, D. Song, Z.-G. Liang, S.-J. Hu, D.-H. Yu, X. Hou, W. Shi, H.-G. Zang, J.-F. Xiang, X.-K. Peng, and Y.-Z. Wang, “In-orbit operation of an atomic clock based on laser-cooled 87Rb atoms,” Nat. Commun. 9(1), 2760 (2018).
[Crossref] [PubMed]

Jiang, X.

Karnowski, K.

Kasai, K.

Ke, C.

Kelleher, B.

Kersey, A. D.

A. D. Kersey, M. J. Marrone, and M. A. Davis, “Polarisation-insensitive fibre optic Michelson interferometer,” Electron. Lett. 27(6), 518–520 (1991).
[Crossref]

Kikuchi, K.

Kim, D. Y.

Klein, T.

Li, L.

L. Liu, D.-S. Lü, W.-B. Chen, T. Li, Q.-Z. Qu, B. Wang, L. Li, W. Ren, Z.-R. Dong, J.-B. Zhao, W.-B. Xia, X. Zhao, J.-W. Ji, M.-F. Ye, Y.-G. Sun, Y.-Y. Yao, D. Song, Z.-G. Liang, S.-J. Hu, D.-H. Yu, X. Hou, W. Shi, H.-G. Zang, J.-F. Xiang, X.-K. Peng, and Y.-Z. Wang, “In-orbit operation of an atomic clock based on laser-cooled 87Rb atoms,” Nat. Commun. 9(1), 2760 (2018).
[Crossref] [PubMed]

Li, T.

L. Liu, D.-S. Lü, W.-B. Chen, T. Li, Q.-Z. Qu, B. Wang, L. Li, W. Ren, Z.-R. Dong, J.-B. Zhao, W.-B. Xia, X. Zhao, J.-W. Ji, M.-F. Ye, Y.-G. Sun, Y.-Y. Yao, D. Song, Z.-G. Liang, S.-J. Hu, D.-H. Yu, X. Hou, W. Shi, H.-G. Zang, J.-F. Xiang, X.-K. Peng, and Y.-Z. Wang, “In-orbit operation of an atomic clock based on laser-cooled 87Rb atoms,” Nat. Commun. 9(1), 2760 (2018).
[Crossref] [PubMed]

Liang, Z.-G.

L. Liu, D.-S. Lü, W.-B. Chen, T. Li, Q.-Z. Qu, B. Wang, L. Li, W. Ren, Z.-R. Dong, J.-B. Zhao, W.-B. Xia, X. Zhao, J.-W. Ji, M.-F. Ye, Y.-G. Sun, Y.-Y. Yao, D. Song, Z.-G. Liang, S.-J. Hu, D.-H. Yu, X. Hou, W. Shi, H.-G. Zang, J.-F. Xiang, X.-K. Peng, and Y.-Z. Wang, “In-orbit operation of an atomic clock based on laser-cooled 87Rb atoms,” Nat. Commun. 9(1), 2760 (2018).
[Crossref] [PubMed]

Liu, D.

Liu, L.

L. Liu, D.-S. Lü, W.-B. Chen, T. Li, Q.-Z. Qu, B. Wang, L. Li, W. Ren, Z.-R. Dong, J.-B. Zhao, W.-B. Xia, X. Zhao, J.-W. Ji, M.-F. Ye, Y.-G. Sun, Y.-Y. Yao, D. Song, Z.-G. Liang, S.-J. Hu, D.-H. Yu, X. Hou, W. Shi, H.-G. Zang, J.-F. Xiang, X.-K. Peng, and Y.-Z. Wang, “In-orbit operation of an atomic clock based on laser-cooled 87Rb atoms,” Nat. Commun. 9(1), 2760 (2018).
[Crossref] [PubMed]

Liu, Z.

Lu, B.

Lu, H.

Lü, D.-S.

L. Liu, D.-S. Lü, W.-B. Chen, T. Li, Q.-Z. Qu, B. Wang, L. Li, W. Ren, Z.-R. Dong, J.-B. Zhao, W.-B. Xia, X. Zhao, J.-W. Ji, M.-F. Ye, Y.-G. Sun, Y.-Y. Yao, D. Song, Z.-G. Liang, S.-J. Hu, D.-H. Yu, X. Hou, W. Shi, H.-G. Zang, J.-F. Xiang, X.-K. Peng, and Y.-Z. Wang, “In-orbit operation of an atomic clock based on laser-cooled 87Rb atoms,” Nat. Commun. 9(1), 2760 (2018).
[Crossref] [PubMed]

Lyu, H. C.

Ma, J.

Marrone, M. J.

A. D. Kersey, M. J. Marrone, and M. A. Davis, “Polarisation-insensitive fibre optic Michelson interferometer,” Electron. Lett. 27(6), 518–520 (1991).
[Crossref]

Mercer, L. B.

L. B. Mercer, “1/f frequency noise effects on self-heterodyne linewidth measurements,” J. Lightwave Technol. 9(4), 485–493 (1991).
[Crossref]

Mirasso, C. R.

M. Osinski, R. Vicente, H. Amano, J. Mulet, M. Sciamanna, F. Henneberger, and C. R. Mirasso, “Simple interpretation of the dynamics of mutually coupled semiconductor lasers with detuning,” Proc. SPIE 5349, 307 (2004).
[Crossref]

Mulet, J.

M. Osinski, R. Vicente, H. Amano, J. Mulet, M. Sciamanna, F. Henneberger, and C. R. Mirasso, “Simple interpretation of the dynamics of mutually coupled semiconductor lasers with detuning,” Proc. SPIE 5349, 307 (2004).
[Crossref]

Nakazawa, M.

O’Shaughnessy, B.

Osinski, M.

M. Osinski, R. Vicente, H. Amano, J. Mulet, M. Sciamanna, F. Henneberger, and C. R. Mirasso, “Simple interpretation of the dynamics of mutually coupled semiconductor lasers with detuning,” Proc. SPIE 5349, 307 (2004).
[Crossref]

Pan, Z.

Pedross-Engel, A.

Peng, X.-K.

L. Liu, D.-S. Lü, W.-B. Chen, T. Li, Q.-Z. Qu, B. Wang, L. Li, W. Ren, Z.-R. Dong, J.-B. Zhao, W.-B. Xia, X. Zhao, J.-W. Ji, M.-F. Ye, Y.-G. Sun, Y.-Y. Yao, D. Song, Z.-G. Liang, S.-J. Hu, D.-H. Yu, X. Hou, W. Shi, H.-G. Zang, J.-F. Xiang, X.-K. Peng, and Y.-Z. Wang, “In-orbit operation of an atomic clock based on laser-cooled 87Rb atoms,” Nat. Commun. 9(1), 2760 (2018).
[Crossref] [PubMed]

Pulido-Mancera, L.

Qin, J.

Qu, Q.-Z.

L. Liu, D.-S. Lü, W.-B. Chen, T. Li, Q.-Z. Qu, B. Wang, L. Li, W. Ren, Z.-R. Dong, J.-B. Zhao, W.-B. Xia, X. Zhao, J.-W. Ji, M.-F. Ye, Y.-G. Sun, Y.-Y. Yao, D. Song, Z.-G. Liang, S.-J. Hu, D.-H. Yu, X. Hou, W. Shi, H.-G. Zang, J.-F. Xiang, X.-K. Peng, and Y.-Z. Wang, “In-orbit operation of an atomic clock based on laser-cooled 87Rb atoms,” Nat. Commun. 9(1), 2760 (2018).
[Crossref] [PubMed]

Qu, R.

Ren, W.

L. Liu, D.-S. Lü, W.-B. Chen, T. Li, Q.-Z. Qu, B. Wang, L. Li, W. Ren, Z.-R. Dong, J.-B. Zhao, W.-B. Xia, X. Zhao, J.-W. Ji, M.-F. Ye, Y.-G. Sun, Y.-Y. Yao, D. Song, Z.-G. Liang, S.-J. Hu, D.-H. Yu, X. Hou, W. Shi, H.-G. Zang, J.-F. Xiang, X.-K. Peng, and Y.-Z. Wang, “In-orbit operation of an atomic clock based on laser-cooled 87Rb atoms,” Nat. Commun. 9(1), 2760 (2018).
[Crossref] [PubMed]

Reynolds, M. S.

Schilt, S.

Sciamanna, M.

M. Osinski, R. Vicente, H. Amano, J. Mulet, M. Sciamanna, F. Henneberger, and C. R. Mirasso, “Simple interpretation of the dynamics of mutually coupled semiconductor lasers with detuning,” Proc. SPIE 5349, 307 (2004).
[Crossref]

Shi, W.

L. Liu, D.-S. Lü, W.-B. Chen, T. Li, Q.-Z. Qu, B. Wang, L. Li, W. Ren, Z.-R. Dong, J.-B. Zhao, W.-B. Xia, X. Zhao, J.-W. Ji, M.-F. Ye, Y.-G. Sun, Y.-Y. Yao, D. Song, Z.-G. Liang, S.-J. Hu, D.-H. Yu, X. Hou, W. Shi, H.-G. Zang, J.-F. Xiang, X.-K. Peng, and Y.-Z. Wang, “In-orbit operation of an atomic clock based on laser-cooled 87Rb atoms,” Nat. Commun. 9(1), 2760 (2018).
[Crossref] [PubMed]

Sleasman, T.

Slepneva, S.

Smith, D. R.

Song, D.

L. Liu, D.-S. Lü, W.-B. Chen, T. Li, Q.-Z. Qu, B. Wang, L. Li, W. Ren, Z.-R. Dong, J.-B. Zhao, W.-B. Xia, X. Zhao, J.-W. Ji, M.-F. Ye, Y.-G. Sun, Y.-Y. Yao, D. Song, Z.-G. Liang, S.-J. Hu, D.-H. Yu, X. Hou, W. Shi, H.-G. Zang, J.-F. Xiang, X.-K. Peng, and Y.-Z. Wang, “In-orbit operation of an atomic clock based on laser-cooled 87Rb atoms,” Nat. Commun. 9(1), 2760 (2018).
[Crossref] [PubMed]

Stéphan, G. M.

G. M. Stéphan, T. T. Tam, S. Blin, P. Besnard, and M. Têtu, “Laser line shape and spectral density of frequency noise,” Phys. Rev. A 71(4), 043809 (2005).
[Crossref]

Sun, Y.-G.

L. Liu, D.-S. Lü, W.-B. Chen, T. Li, Q.-Z. Qu, B. Wang, L. Li, W. Ren, Z.-R. Dong, J.-B. Zhao, W.-B. Xia, X. Zhao, J.-W. Ji, M.-F. Ye, Y.-G. Sun, Y.-Y. Yao, D. Song, Z.-G. Liang, S.-J. Hu, D.-H. Yu, X. Hou, W. Shi, H.-G. Zang, J.-F. Xiang, X.-K. Peng, and Y.-Z. Wang, “In-orbit operation of an atomic clock based on laser-cooled 87Rb atoms,” Nat. Commun. 9(1), 2760 (2018).
[Crossref] [PubMed]

Tam, T. T.

G. M. Stéphan, T. T. Tam, S. Blin, P. Besnard, and M. Têtu, “Laser line shape and spectral density of frequency noise,” Phys. Rev. A 71(4), 043809 (2005).
[Crossref]

Têtu, M.

G. M. Stéphan, T. T. Tam, S. Blin, P. Besnard, and M. Têtu, “Laser line shape and spectral density of frequency noise,” Phys. Rev. A 71(4), 043809 (2005).
[Crossref]

Thomann, P.

Tong, Y.

Vicente, R.

M. Osinski, R. Vicente, H. Amano, J. Mulet, M. Sciamanna, F. Henneberger, and C. R. Mirasso, “Simple interpretation of the dynamics of mutually coupled semiconductor lasers with detuning,” Proc. SPIE 5349, 307 (2004).
[Crossref]

Wang, B.

L. Liu, D.-S. Lü, W.-B. Chen, T. Li, Q.-Z. Qu, B. Wang, L. Li, W. Ren, Z.-R. Dong, J.-B. Zhao, W.-B. Xia, X. Zhao, J.-W. Ji, M.-F. Ye, Y.-G. Sun, Y.-Y. Yao, D. Song, Z.-G. Liang, S.-J. Hu, D.-H. Yu, X. Hou, W. Shi, H.-G. Zang, J.-F. Xiang, X.-K. Peng, and Y.-Z. Wang, “In-orbit operation of an atomic clock based on laser-cooled 87Rb atoms,” Nat. Commun. 9(1), 2760 (2018).
[Crossref] [PubMed]

Wang, J.

Wang, Y.-Z.

L. Liu, D.-S. Lü, W.-B. Chen, T. Li, Q.-Z. Qu, B. Wang, L. Li, W. Ren, Z.-R. Dong, J.-B. Zhao, W.-B. Xia, X. Zhao, J.-W. Ji, M.-F. Ye, Y.-G. Sun, Y.-Y. Yao, D. Song, Z.-G. Liang, S.-J. Hu, D.-H. Yu, X. Hou, W. Shi, H.-G. Zang, J.-F. Xiang, X.-K. Peng, and Y.-Z. Wang, “In-orbit operation of an atomic clock based on laser-cooled 87Rb atoms,” Nat. Commun. 9(1), 2760 (2018).
[Crossref] [PubMed]

Wang, Z.

Watts, C. M.

Wei, F.

Wieser, W.

Wojtkowski, M.

Wolf, P.

Xia, W.-B.

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L. Liu, D.-S. Lü, W.-B. Chen, T. Li, Q.-Z. Qu, B. Wang, L. Li, W. Ren, Z.-R. Dong, J.-B. Zhao, W.-B. Xia, X. Zhao, J.-W. Ji, M.-F. Ye, Y.-G. Sun, Y.-Y. Yao, D. Song, Z.-G. Liang, S.-J. Hu, D.-H. Yu, X. Hou, W. Shi, H.-G. Zang, J.-F. Xiang, X.-K. Peng, and Y.-Z. Wang, “In-orbit operation of an atomic clock based on laser-cooled 87Rb atoms,” Nat. Commun. 9(1), 2760 (2018).
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L. Liu, D.-S. Lü, W.-B. Chen, T. Li, Q.-Z. Qu, B. Wang, L. Li, W. Ren, Z.-R. Dong, J.-B. Zhao, W.-B. Xia, X. Zhao, J.-W. Ji, M.-F. Ye, Y.-G. Sun, Y.-Y. Yao, D. Song, Z.-G. Liang, S.-J. Hu, D.-H. Yu, X. Hou, W. Shi, H.-G. Zang, J.-F. Xiang, X.-K. Peng, and Y.-Z. Wang, “In-orbit operation of an atomic clock based on laser-cooled 87Rb atoms,” Nat. Commun. 9(1), 2760 (2018).
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L. Liu, D.-S. Lü, W.-B. Chen, T. Li, Q.-Z. Qu, B. Wang, L. Li, W. Ren, Z.-R. Dong, J.-B. Zhao, W.-B. Xia, X. Zhao, J.-W. Ji, M.-F. Ye, Y.-G. Sun, Y.-Y. Yao, D. Song, Z.-G. Liang, S.-J. Hu, D.-H. Yu, X. Hou, W. Shi, H.-G. Zang, J.-F. Xiang, X.-K. Peng, and Y.-Z. Wang, “In-orbit operation of an atomic clock based on laser-cooled 87Rb atoms,” Nat. Commun. 9(1), 2760 (2018).
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L. Liu, D.-S. Lü, W.-B. Chen, T. Li, Q.-Z. Qu, B. Wang, L. Li, W. Ren, Z.-R. Dong, J.-B. Zhao, W.-B. Xia, X. Zhao, J.-W. Ji, M.-F. Ye, Y.-G. Sun, Y.-Y. Yao, D. Song, Z.-G. Liang, S.-J. Hu, D.-H. Yu, X. Hou, W. Shi, H.-G. Zang, J.-F. Xiang, X.-K. Peng, and Y.-Z. Wang, “In-orbit operation of an atomic clock based on laser-cooled 87Rb atoms,” Nat. Commun. 9(1), 2760 (2018).
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Figures (8)

Fig. 1
Fig. 1 Schematic diagram of dynamic phase noise characteristics measurement system for swept lasers. RIO: Master laser; EOM: Intensity electro-optic modulator; DFB: Slave laser, distributed feedback diode laser, a single-mode DFB-type butterfly-package diode laser; RF: Radio frequency; PS: Power splitter; Ref: 100 MHz reference; VCO: Voltage controlled oscillator; LPF: Loop filter; Cir: Circulator; OC: 3 × 3 optical coupler; FRM: Faraday rotation mirror; PD: Photodiode; DAC: Data to analog card; Scope: Oscilloscope. The blue frame is a frequency swept laser source based on high-order modulation-sideband injection-locking, the pink frame is the phase noise measurement system, and the green frame is a 120-degree phase differential interferometer.
Fig. 2
Fig. 2 Frequency tuning characteristics in time domain. Green: measured tunable frequency; red: linear-fitting frequency; Grey: residual frequency error.
Fig. 3
Fig. 3 Frequency fluctuation PSD of different processes: (a) master laser is RIO, inset shows the results of SDHI; (b) master laser is NKT-X15.
Fig. 4
Fig. 4 Evolution of frequency fluctuation PSD at five different time bands in 0.5–2 ms time period.
Fig. 5
Fig. 5 Diagram of frequency with greatly varying sweep characteristics in the time domain. The blue and the red curves correspond to the left Y-axis, while the green curve corresponds to the right Y-axis.
Fig. 6
Fig. 6 Diagram of frequency with greatly varying sweep characteristics in the frequency domain.
Fig. 7
Fig. 7 Diagram of different fitting curves in the time domain. The blue and the red curves correspond to the left Y-axis, while the green curve corresponds to the right Y-axis.
Fig. 8
Fig. 8 Comparison of results of frequency fluctuation PSD values obtained from different fitting curves.

Equations (7)

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{ Spectral sampling rate: Δ T 0 = T 0 / N 0 Spectral frequency range: f s 0 = N 0 / T 0 Spectral physical resolution: Δ f p = f s 0 / N 0 = 1 / T 0 Spectral calculation resolution: Δ f c = f s 0 / N f f t 0 = ( 1 / T 0 ) × ( N 0 / N f f t 0 )
  Δ φ ( t ) = φ ( t ) φ ( t τ ) = arc tan ( X 2 ' ( t ) X 1 ' ( t ) ) arc tan ( X 2 ' ( t ) X 1 ' ( t ) ) ¯ ,
( X 1 ' ( t ) X 2 ' ( t ) X 3 ' ( t ) ) = ( η 1 ς 1 ξ 1 η 2 ς 2 ξ 2 η 3 ς 3 ξ 3 ) 1 ( I 1 ( t ) I 2 ( t ) I 3 ( t ) ) ,
{ φ ( t ) = φ ( t τ ) + τ φ ( t τ ) φ ( t τ ) = φ ( t ) τ φ ( t ) { Δ φ ( t ) = φ ( t ) φ ( t τ ) = τ φ ( t τ ) Δ φ ( t ) = φ ( t ) φ ( t τ ) = τ φ ( t )
φ ( t ) = 1 τ Δ φ ( t ) + 1 2 Δ φ ( t ) = 2 π ν ( t ) ,
ν tunable ( t ) = A + A 1 t
ν niose ( t ) = ν ( t ) ν tunable ( t )

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