Abstract

A laser phase and frequency noise measurement method by an unbalanced Michelson interferometer composed of a 3 × 3 optical fiber coupler is proposed. The relations and differences of the power spectral density (PSD) of differential phase and frequency fluctuation, PSD of instantaneous phase and frequency fluctuation, phase noise and linewidth are derived strictly and discussed carefully. The method obtains the noise features of a narrow linewidth laser conveniently without any specific assumptions or noise models. The technique is also used to characterize the noise features of a narrow linewidth external-cavity semiconductor laser, which confirms the correction and robustness of the method.

© 2015 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
  3. H. Lee, M. G. Suh, T. Chen, J. Li, S. A. Diddams, and K. J. Vahala, “Spiral resonators for on-chip laser frequency stabilization,” Nat. Commun. 4, 2468 (2013).
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    [Crossref]
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2015 (2)

2013 (1)

H. Lee, M. G. Suh, T. Chen, J. Li, S. A. Diddams, and K. J. Vahala, “Spiral resonators for on-chip laser frequency stabilization,” Nat. Commun. 4, 2468 (2013).
[Crossref] [PubMed]

2012 (1)

F. Yang, Q. Ye, Z. Pan, D. Chen, H. Cai, R. Qu, Z. Yang, and Q. Zhang, “100-mW linear polarization single-frequency all-fiber seed laser for coherent Doppler lidar application,” Opt. Commun. 285(2), 149–152 (2012).
[Crossref]

2011 (2)

2010 (1)

2009 (1)

2007 (1)

F. Lienhart, S. Boussen, O. Carraz, N. Zahzam, Y. Bidel, and A. Bresson, “Compact and robust laser system for rubidium laser cooling based on the frequency doubling of a fiber bench at 1560 nm,” Appl. Phys. B 89(2–3), 177–180 (2007).
[Crossref]

2001 (1)

R. P. Scott, C. Langrock, and B. H. Kolner, “High-dynamic-range laser amplitude and phase noise measurement techniques,” IEEE J. Sel. Top. Quantum Electron. 7(4), 641–655 (2001).
[Crossref]

1982 (1)

S. Piazzolla, P. Spano, and M. Tamburrini, “Characterization of phase noise in semiconductor lasers,” Appl. Phys. Lett. 41(8), 695–696 (1982).
[Crossref]

1981 (1)

S. K. Sheem, “Optical fiber interferometers with [3×3] directional couplers: Analysis,” J. Appl. Phys. 52(6), 3865–3872 (1981).
[Crossref]

1980 (1)

T. Okoshi, K. Kikuchi, and A. Nakayama, “Novel method for high resolution measurement of laser output spectrum,” Electron. Lett. 16(16), 630–631 (1980).
[Crossref]

1967 (1)

P. D. Welch, “The use of fast Fourier transform for the estimation of power spectra: a method based on time averaging over short, modified periodograms,” IEEE Trans. Audio Electroacoust. 15(2), 70–73 (1967).
[Crossref]

Bidel, Y.

F. Lienhart, S. Boussen, O. Carraz, N. Zahzam, Y. Bidel, and A. Bresson, “Compact and robust laser system for rubidium laser cooling based on the frequency doubling of a fiber bench at 1560 nm,” Appl. Phys. B 89(2–3), 177–180 (2007).
[Crossref]

Boussen, S.

F. Lienhart, S. Boussen, O. Carraz, N. Zahzam, Y. Bidel, and A. Bresson, “Compact and robust laser system for rubidium laser cooling based on the frequency doubling of a fiber bench at 1560 nm,” Appl. Phys. B 89(2–3), 177–180 (2007).
[Crossref]

Brahimi, H.

Bresson, A.

F. Lienhart, S. Boussen, O. Carraz, N. Zahzam, Y. Bidel, and A. Bresson, “Compact and robust laser system for rubidium laser cooling based on the frequency doubling of a fiber bench at 1560 nm,” Appl. Phys. B 89(2–3), 177–180 (2007).
[Crossref]

Butler, T.

Cai, H.

F. Wei, B. Lu, J. Wang, D. Xu, Z. Pan, D. Chen, H. Cai, and R. Qu, “Precision and broadband frequency swept laser source based on high-order modulation-sideband injection-locking,” Opt. Express 23(4), 4970–4980 (2015).
[Crossref] [PubMed]

F. Yang, Q. Ye, Z. Pan, D. Chen, H. Cai, R. Qu, Z. Yang, and Q. Zhang, “100-mW linear polarization single-frequency all-fiber seed laser for coherent Doppler lidar application,” Opt. Commun. 285(2), 149–152 (2012).
[Crossref]

Carraz, O.

F. Lienhart, S. Boussen, O. Carraz, N. Zahzam, Y. Bidel, and A. Bresson, “Compact and robust laser system for rubidium laser cooling based on the frequency doubling of a fiber bench at 1560 nm,” Appl. Phys. B 89(2–3), 177–180 (2007).
[Crossref]

Chen, D.

F. Wei, B. Lu, J. Wang, D. Xu, Z. Pan, D. Chen, H. Cai, and R. Qu, “Precision and broadband frequency swept laser source based on high-order modulation-sideband injection-locking,” Opt. Express 23(4), 4970–4980 (2015).
[Crossref] [PubMed]

F. Yang, Q. Ye, Z. Pan, D. Chen, H. Cai, R. Qu, Z. Yang, and Q. Zhang, “100-mW linear polarization single-frequency all-fiber seed laser for coherent Doppler lidar application,” Opt. Commun. 285(2), 149–152 (2012).
[Crossref]

Chen, T.

H. Lee, M. G. Suh, T. Chen, J. Li, S. A. Diddams, and K. J. Vahala, “Spiral resonators for on-chip laser frequency stabilization,” Nat. Commun. 4, 2468 (2013).
[Crossref] [PubMed]

Choi, H. Y.

Chung, Y. C.

Di Domenico, G.

Diddams, S. A.

H. Lee, M. G. Suh, T. Chen, J. Li, S. A. Diddams, and K. J. Vahala, “Spiral resonators for on-chip laser frequency stabilization,” Nat. Commun. 4, 2468 (2013).
[Crossref] [PubMed]

Goulding, D.

Hegarty, S. P.

Huyet, G.

Karnowski, K.

Kelleher, B.

Kikuchi, K.

T. Okoshi, K. Kikuchi, and A. Nakayama, “Novel method for high resolution measurement of laser output spectrum,” Electron. Lett. 16(16), 630–631 (1980).
[Crossref]

Kolner, B. H.

R. P. Scott, C. Langrock, and B. H. Kolner, “High-dynamic-range laser amplitude and phase noise measurement techniques,” IEEE J. Sel. Top. Quantum Electron. 7(4), 641–655 (2001).
[Crossref]

Lacroix, P.

Langrock, C.

R. P. Scott, C. Langrock, and B. H. Kolner, “High-dynamic-range laser amplitude and phase noise measurement techniques,” IEEE J. Sel. Top. Quantum Electron. 7(4), 641–655 (2001).
[Crossref]

Lee, H.

H. Lee, M. G. Suh, T. Chen, J. Li, S. A. Diddams, and K. J. Vahala, “Spiral resonators for on-chip laser frequency stabilization,” Nat. Commun. 4, 2468 (2013).
[Crossref] [PubMed]

Li, J.

H. Lee, M. G. Suh, T. Chen, J. Li, S. A. Diddams, and K. J. Vahala, “Spiral resonators for on-chip laser frequency stabilization,” Nat. Commun. 4, 2468 (2013).
[Crossref] [PubMed]

Lienhart, F.

F. Lienhart, S. Boussen, O. Carraz, N. Zahzam, Y. Bidel, and A. Bresson, “Compact and robust laser system for rubidium laser cooling based on the frequency doubling of a fiber bench at 1560 nm,” Appl. Phys. B 89(2–3), 177–180 (2007).
[Crossref]

Llopis, O.

Lu, B.

Lyu, H. C.

Merrer, P. H.

Nakayama, A.

T. Okoshi, K. Kikuchi, and A. Nakayama, “Novel method for high resolution measurement of laser output spectrum,” Electron. Lett. 16(16), 630–631 (1980).
[Crossref]

O’shaughnessy, B.

Okoshi, T.

T. Okoshi, K. Kikuchi, and A. Nakayama, “Novel method for high resolution measurement of laser output spectrum,” Electron. Lett. 16(16), 630–631 (1980).
[Crossref]

Pan, Z.

F. Wei, B. Lu, J. Wang, D. Xu, Z. Pan, D. Chen, H. Cai, and R. Qu, “Precision and broadband frequency swept laser source based on high-order modulation-sideband injection-locking,” Opt. Express 23(4), 4970–4980 (2015).
[Crossref] [PubMed]

F. Yang, Q. Ye, Z. Pan, D. Chen, H. Cai, R. Qu, Z. Yang, and Q. Zhang, “100-mW linear polarization single-frequency all-fiber seed laser for coherent Doppler lidar application,” Opt. Commun. 285(2), 149–152 (2012).
[Crossref]

Piazzolla, S.

S. Piazzolla, P. Spano, and M. Tamburrini, “Characterization of phase noise in semiconductor lasers,” Appl. Phys. Lett. 41(8), 695–696 (1982).
[Crossref]

Qu, R.

F. Wei, B. Lu, J. Wang, D. Xu, Z. Pan, D. Chen, H. Cai, and R. Qu, “Precision and broadband frequency swept laser source based on high-order modulation-sideband injection-locking,” Opt. Express 23(4), 4970–4980 (2015).
[Crossref] [PubMed]

F. Yang, Q. Ye, Z. Pan, D. Chen, H. Cai, R. Qu, Z. Yang, and Q. Zhang, “100-mW linear polarization single-frequency all-fiber seed laser for coherent Doppler lidar application,” Opt. Commun. 285(2), 149–152 (2012).
[Crossref]

Saleh, K.

Schilt, S.

Scott, R. P.

R. P. Scott, C. Langrock, and B. H. Kolner, “High-dynamic-range laser amplitude and phase noise measurement techniques,” IEEE J. Sel. Top. Quantum Electron. 7(4), 641–655 (2001).
[Crossref]

Sheem, S. K.

S. K. Sheem, “Optical fiber interferometers with [3×3] directional couplers: Analysis,” J. Appl. Phys. 52(6), 3865–3872 (1981).
[Crossref]

Slepneva, S.

Spano, P.

S. Piazzolla, P. Spano, and M. Tamburrini, “Characterization of phase noise in semiconductor lasers,” Appl. Phys. Lett. 41(8), 695–696 (1982).
[Crossref]

Suh, M. G.

H. Lee, M. G. Suh, T. Chen, J. Li, S. A. Diddams, and K. J. Vahala, “Spiral resonators for on-chip laser frequency stabilization,” Nat. Commun. 4, 2468 (2013).
[Crossref] [PubMed]

Takushima, Y.

Tamburrini, M.

S. Piazzolla, P. Spano, and M. Tamburrini, “Characterization of phase noise in semiconductor lasers,” Appl. Phys. Lett. 41(8), 695–696 (1982).
[Crossref]

Thomann, P.

Tsuchida, H.

Vahala, K. J.

H. Lee, M. G. Suh, T. Chen, J. Li, S. A. Diddams, and K. J. Vahala, “Spiral resonators for on-chip laser frequency stabilization,” Nat. Commun. 4, 2468 (2013).
[Crossref] [PubMed]

Wang, J.

Wei, F.

Welch, P. D.

P. D. Welch, “The use of fast Fourier transform for the estimation of power spectra: a method based on time averaging over short, modified periodograms,” IEEE Trans. Audio Electroacoust. 15(2), 70–73 (1967).
[Crossref]

Wojtkowski, M.

Xu, D.

Yang, F.

F. Yang, Q. Ye, Z. Pan, D. Chen, H. Cai, R. Qu, Z. Yang, and Q. Zhang, “100-mW linear polarization single-frequency all-fiber seed laser for coherent Doppler lidar application,” Opt. Commun. 285(2), 149–152 (2012).
[Crossref]

Yang, Z.

F. Yang, Q. Ye, Z. Pan, D. Chen, H. Cai, R. Qu, Z. Yang, and Q. Zhang, “100-mW linear polarization single-frequency all-fiber seed laser for coherent Doppler lidar application,” Opt. Commun. 285(2), 149–152 (2012).
[Crossref]

Ye, Q.

F. Yang, Q. Ye, Z. Pan, D. Chen, H. Cai, R. Qu, Z. Yang, and Q. Zhang, “100-mW linear polarization single-frequency all-fiber seed laser for coherent Doppler lidar application,” Opt. Commun. 285(2), 149–152 (2012).
[Crossref]

Zahzam, N.

F. Lienhart, S. Boussen, O. Carraz, N. Zahzam, Y. Bidel, and A. Bresson, “Compact and robust laser system for rubidium laser cooling based on the frequency doubling of a fiber bench at 1560 nm,” Appl. Phys. B 89(2–3), 177–180 (2007).
[Crossref]

Zhang, Q.

F. Yang, Q. Ye, Z. Pan, D. Chen, H. Cai, R. Qu, Z. Yang, and Q. Zhang, “100-mW linear polarization single-frequency all-fiber seed laser for coherent Doppler lidar application,” Opt. Commun. 285(2), 149–152 (2012).
[Crossref]

Appl. Opt. (1)

Appl. Phys. B (1)

F. Lienhart, S. Boussen, O. Carraz, N. Zahzam, Y. Bidel, and A. Bresson, “Compact and robust laser system for rubidium laser cooling based on the frequency doubling of a fiber bench at 1560 nm,” Appl. Phys. B 89(2–3), 177–180 (2007).
[Crossref]

Appl. Phys. Lett. (1)

S. Piazzolla, P. Spano, and M. Tamburrini, “Characterization of phase noise in semiconductor lasers,” Appl. Phys. Lett. 41(8), 695–696 (1982).
[Crossref]

Electron. Lett. (1)

T. Okoshi, K. Kikuchi, and A. Nakayama, “Novel method for high resolution measurement of laser output spectrum,” Electron. Lett. 16(16), 630–631 (1980).
[Crossref]

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

R. P. Scott, C. Langrock, and B. H. Kolner, “High-dynamic-range laser amplitude and phase noise measurement techniques,” IEEE J. Sel. Top. Quantum Electron. 7(4), 641–655 (2001).
[Crossref]

IEEE Trans. Audio Electroacoust. (1)

P. D. Welch, “The use of fast Fourier transform for the estimation of power spectra: a method based on time averaging over short, modified periodograms,” IEEE Trans. Audio Electroacoust. 15(2), 70–73 (1967).
[Crossref]

J. Appl. Phys. (1)

S. K. Sheem, “Optical fiber interferometers with [3×3] directional couplers: Analysis,” J. Appl. Phys. 52(6), 3865–3872 (1981).
[Crossref]

J. Lightwave Technol. (1)

Nat. Commun. (1)

H. Lee, M. G. Suh, T. Chen, J. Li, S. A. Diddams, and K. J. Vahala, “Spiral resonators for on-chip laser frequency stabilization,” Nat. Commun. 4, 2468 (2013).
[Crossref] [PubMed]

Opt. Commun. (1)

F. Yang, Q. Ye, Z. Pan, D. Chen, H. Cai, R. Qu, Z. Yang, and Q. Zhang, “100-mW linear polarization single-frequency all-fiber seed laser for coherent Doppler lidar application,” Opt. Commun. 285(2), 149–152 (2012).
[Crossref]

Opt. Express (1)

Opt. Lett. (3)

Other (1)

Rio Orion, “Laser Module,” http://www.rio-inc.com/_products/orion.html .

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Figures (6)

Fig. 1
Fig. 1 Experimental setup used to measure the laser phase and frequency noise, and the output interference fringe of the PD1, PD2, PD3 (inset). LUT: laser under test, C: circulator, OC: optical fiber coupler, FRM: Faraday rotation mirror, PD: photodetector, DAC: data acquisition board
Fig. 2
Fig. 2 Demodulation principle of the setup for triangle waveforms with different modulation periods (a)T≠2τ and (b)T = 2τ.
Fig. 3
Fig. 3 Modulated and demodulated (a) triangle phase amplitude and (b) waveform at different modulated voltage amplitudes.
Fig. 4
Fig. 4 Output voltages of (b) PD1, (c) PD2, (d) PD3 and (a) corresponding demodulated phase waveforms at a fixed modulated voltage Vm = 3 V. The red and black line represent the first and second test respectively.
Fig. 5
Fig. 5 PSD of the differential phase fluctuation (SΔφ(f) @ 1m), differential frequency fluctuation (SΔν(f) @ 1m), instantaneous phase fluctuation Sφ(f), instantaneous frequency fluctuation Sν(f) and phase noise L(f) of the RIO laser
Fig. 6
Fig. 6 PSD of instantaneous frequency fluctuation of the RIO laser and the β – separation line given by Sν(f) = 8ln2f2 [15] (left axis), laser linewidth (FWHM) obtained by the method in [15] (right axis) and by the SDH method (inset).

Equations (5)

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Δφ( t )=φ( t )φ( tτ )=arctan( X 2 (t) X 1 (t) ) arctan( X 2 (t) X 1 (t) ) ¯ ,
( X 1 (t) X 2 (t) X 3 (t) )= ( η 1 η 2 η 3 ς 1 ς 2 ς 3 ξ 1 ξ 2 ξ 3 ) 1 ( I 1 (t) I 2 (t) I 3 (t) ),
Δν(t)= Δφ(t) / ( τ ) .
S Δν (f)= ( 1 τ ) 2 S Δφ (f) .
S φ (f)= 1 4 ( sin(πfτ) ) 2 S Δφ (f) S ν (f)= f 2 4 ( sin(πfτ) ) 2 S Δφ (f)= 1 ( sinc(πfτ) ) 2 S Δν (f) S ν (f) S Δν (f), for τ=5 ns (1 m delay fiber), f<5 MHz.

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