Abstract

A novel technique is proposed and demonstrated for measuring the temporal waveforms of phase/frequency-modulated lights based on self-heterodyne interferometry with a delay time much shorter than the modulation period and on the unwrapped phase detection of heterodyne beat signals with real-time vector signal analysis. The technique makes use of an approximated relationship between the beat signal phase and the instantaneous frequency of modulated lights. The results of waveform measurements are presented for directly frequency-modulated and externally phase-modulated lights, which have been commonly employed for FWCW-LIDAR and serrodyne frequency translation, respectively. The temporal waveforms of triangular modulation are successfully measured with a frequency deviation as large as 15 GHz and the detailed investigation is presented on the deviation of measured waveform from ideal ones.

© 2017 Optical Society of America

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References

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  1. C. Laskoskie, H. Hung, T. El-Wailly, and C. L. Chang, “Ti-LiNbO3 waveguide serrodyne modulator with ultrahigh sideband suppression for fiber optic gyroscopes,” J. Lightwave Technol. 7(4), 600–606 (1989).
    [Crossref]
  2. D. Chang, G. Cardell, A. San Martin, and G. Spiers, “Coherent laser instrument would measure range and velocity,” NASA Tech Briefs 29, 9–10 (2005).
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    [Crossref]
  4. W. V. Sorin, K. W. Chang, G. A. Conrad, and P. R. Hernday, “Frequency domain analysis of an optical FM discriminator,” J. Lightwave Technol. 10(6), 787–793 (1992).
    [Crossref]
  5. X. Xie, J. Khurgin, J. Kang, and F.-S. Choa, “Ring-assisted frequency discriminator with improved linearity,” IEEE Photonics Technol. Lett. 14(8), 1136–1138 (2002).
    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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2016 (1)

2015 (1)

2012 (1)

I. Coddington, F. R. Giorgetta, E. Baumann, W. C. Swann, and N. R. Newbury, “Characterizing fast arbitrary CW waveforms with 1500 THz/s instantaneous chirps,” IEEE J. Sel. Top. Quantum Electron. 18(1), 228–238 (2012).
[Crossref]

2011 (3)

2009 (2)

2007 (1)

2005 (3)

G. Chen, J. U. Kang, and J. B. Khurgin, “Frequency discriminator based on ring-assisted fiber Sagnac filter,” IEEE Photonics Technol. Lett. 17(1), 109–111 (2005).
[Crossref]

D. Chang, G. Cardell, A. San Martin, and G. Spiers, “Coherent laser instrument would measure range and velocity,” NASA Tech Briefs 29, 9–10 (2005).

I. Y. Poberezhskiy, B. Bortnik, J. Chou, B. Jalali, and H. R. Fetterman, “Serrodyne frequency translation of continuous optical signals using ultrawide-band electrical sawtooth waveforms,” IEEE J. Quantum Electron. 41(12), 1533–1539 (2005).
[Crossref]

2002 (1)

X. Xie, J. Khurgin, J. Kang, and F.-S. Choa, “Ring-assisted frequency discriminator with improved linearity,” IEEE Photonics Technol. Lett. 14(8), 1136–1138 (2002).
[Crossref]

1996 (1)

K. Iiyama, L.-T. Wang, and K. Hayashi, “Linearizing optical frequency-sweep of a laser diode for FMCW reflectometry,” J. Lightwave Technol. 14(2), 173–178 (1996).
[Crossref]

1994 (1)

A. Dieckmann, “FMCW-LIDAR with tunable twin-guide laser diode,” Electron. Lett. 30(4), 308–309 (1994).
[Crossref]

1992 (1)

W. V. Sorin, K. W. Chang, G. A. Conrad, and P. R. Hernday, “Frequency domain analysis of an optical FM discriminator,” J. Lightwave Technol. 10(6), 787–793 (1992).
[Crossref]

1989 (1)

C. Laskoskie, H. Hung, T. El-Wailly, and C. L. Chang, “Ti-LiNbO3 waveguide serrodyne modulator with ultrahigh sideband suppression for fiber optic gyroscopes,” J. Lightwave Technol. 7(4), 600–606 (1989).
[Crossref]

Ahn, T. J.

Babbitt, W. R.

Barber, Z. W.

Barry, L. P.

Baumann, E.

I. Coddington, F. R. Giorgetta, E. Baumann, W. C. Swann, and N. R. Newbury, “Characterizing fast arbitrary CW waveforms with 1500 THz/s instantaneous chirps,” IEEE J. Sel. Top. Quantum Electron. 18(1), 228–238 (2012).
[Crossref]

Berg, T.

Bortnik, B.

I. Y. Poberezhskiy, B. Bortnik, J. Chou, B. Jalali, and H. R. Fetterman, “Serrodyne frequency translation of continuous optical signals using ultrawide-band electrical sawtooth waveforms,” IEEE J. Quantum Electron. 41(12), 1533–1539 (2005).
[Crossref]

Bretenaker, F.

Byrne, D.

Cardell, G.

D. Chang, G. Cardell, A. San Martin, and G. Spiers, “Coherent laser instrument would measure range and velocity,” NASA Tech Briefs 29, 9–10 (2005).

Chang, C. L.

C. Laskoskie, H. Hung, T. El-Wailly, and C. L. Chang, “Ti-LiNbO3 waveguide serrodyne modulator with ultrahigh sideband suppression for fiber optic gyroscopes,” J. Lightwave Technol. 7(4), 600–606 (1989).
[Crossref]

Chang, D.

D. Chang, G. Cardell, A. San Martin, and G. Spiers, “Coherent laser instrument would measure range and velocity,” NASA Tech Briefs 29, 9–10 (2005).

Chang, K. W.

W. V. Sorin, K. W. Chang, G. A. Conrad, and P. R. Hernday, “Frequency domain analysis of an optical FM discriminator,” J. Lightwave Technol. 10(6), 787–793 (1992).
[Crossref]

Chen, G.

G. Chen, J. U. Kang, and J. B. Khurgin, “Frequency discriminator based on ring-assisted fiber Sagnac filter,” IEEE Photonics Technol. Lett. 17(1), 109–111 (2005).
[Crossref]

Choa, F.-S.

X. Xie, J. Khurgin, J. Kang, and F.-S. Choa, “Ring-assisted frequency discriminator with improved linearity,” IEEE Photonics Technol. Lett. 14(8), 1136–1138 (2002).
[Crossref]

Chou, J.

I. Y. Poberezhskiy, B. Bortnik, J. Chou, B. Jalali, and H. R. Fetterman, “Serrodyne frequency translation of continuous optical signals using ultrawide-band electrical sawtooth waveforms,” IEEE J. Quantum Electron. 41(12), 1533–1539 (2005).
[Crossref]

Coddington, I.

I. Coddington, F. R. Giorgetta, E. Baumann, W. C. Swann, and N. R. Newbury, “Characterizing fast arbitrary CW waveforms with 1500 THz/s instantaneous chirps,” IEEE J. Sel. Top. Quantum Electron. 18(1), 228–238 (2012).
[Crossref]

Conrad, G. A.

W. V. Sorin, K. W. Chang, G. A. Conrad, and P. R. Hernday, “Frequency domain analysis of an optical FM discriminator,” J. Lightwave Technol. 10(6), 787–793 (1992).
[Crossref]

Dieckmann, A.

A. Dieckmann, “FMCW-LIDAR with tunable twin-guide laser diode,” Electron. Lett. 30(4), 308–309 (1994).
[Crossref]

Dong, Y.

El-Wailly, T.

C. Laskoskie, H. Hung, T. El-Wailly, and C. L. Chang, “Ti-LiNbO3 waveguide serrodyne modulator with ultrahigh sideband suppression for fiber optic gyroscopes,” J. Lightwave Technol. 7(4), 600–606 (1989).
[Crossref]

Fetterman, H. R.

I. Y. Poberezhskiy, B. Bortnik, J. Chou, B. Jalali, and H. R. Fetterman, “Serrodyne frequency translation of continuous optical signals using ultrawide-band electrical sawtooth waveforms,” IEEE J. Quantum Electron. 41(12), 1533–1539 (2005).
[Crossref]

Giorgetta, F. R.

I. Coddington, F. R. Giorgetta, E. Baumann, W. C. Swann, and N. R. Newbury, “Characterizing fast arbitrary CW waveforms with 1500 THz/s instantaneous chirps,” IEEE J. Sel. Top. Quantum Electron. 18(1), 228–238 (2012).
[Crossref]

Hayashi, K.

K. Iiyama, L.-T. Wang, and K. Hayashi, “Linearizing optical frequency-sweep of a laser diode for FMCW reflectometry,” J. Lightwave Technol. 14(2), 173–178 (1996).
[Crossref]

Hernday, P. R.

W. V. Sorin, K. W. Chang, G. A. Conrad, and P. R. Hernday, “Frequency domain analysis of an optical FM discriminator,” J. Lightwave Technol. 10(6), 787–793 (1992).
[Crossref]

Hu, W.

Hung, H.

C. Laskoskie, H. Hung, T. El-Wailly, and C. L. Chang, “Ti-LiNbO3 waveguide serrodyne modulator with ultrahigh sideband suppression for fiber optic gyroscopes,” J. Lightwave Technol. 7(4), 600–606 (1989).
[Crossref]

Iiyama, K.

K. Iiyama, L.-T. Wang, and K. Hayashi, “Linearizing optical frequency-sweep of a laser diode for FMCW reflectometry,” J. Lightwave Technol. 14(2), 173–178 (1996).
[Crossref]

Jalali, B.

I. Y. Poberezhskiy, B. Bortnik, J. Chou, B. Jalali, and H. R. Fetterman, “Serrodyne frequency translation of continuous optical signals using ultrawide-band electrical sawtooth waveforms,” IEEE J. Quantum Electron. 41(12), 1533–1539 (2005).
[Crossref]

Kang, J.

X. Xie, J. Khurgin, J. Kang, and F.-S. Choa, “Ring-assisted frequency discriminator with improved linearity,” IEEE Photonics Technol. Lett. 14(8), 1136–1138 (2002).
[Crossref]

Kang, J. U.

G. Chen, J. U. Kang, and J. B. Khurgin, “Frequency discriminator based on ring-assisted fiber Sagnac filter,” IEEE Photonics Technol. Lett. 17(1), 109–111 (2005).
[Crossref]

Kaylor, B.

Kelly, B.

Khurgin, J.

X. Xie, J. Khurgin, J. Kang, and F.-S. Choa, “Ring-assisted frequency discriminator with improved linearity,” IEEE Photonics Technol. Lett. 14(8), 1136–1138 (2002).
[Crossref]

Khurgin, J. B.

G. Chen, J. U. Kang, and J. B. Khurgin, “Frequency discriminator based on ring-assisted fiber Sagnac filter,” IEEE Photonics Technol. Lett. 17(1), 109–111 (2005).
[Crossref]

Kim, D. Y.

Laskoskie, C.

C. Laskoskie, H. Hung, T. El-Wailly, and C. L. Chang, “Ti-LiNbO3 waveguide serrodyne modulator with ultrahigh sideband suppression for fiber optic gyroscopes,” J. Lightwave Technol. 7(4), 600–606 (1989).
[Crossref]

Leyva, V.

Liu, Z.

Newbury, N. R.

I. Coddington, F. R. Giorgetta, E. Baumann, W. C. Swann, and N. R. Newbury, “Characterizing fast arbitrary CW waveforms with 1500 THz/s instantaneous chirps,” IEEE J. Sel. Top. Quantum Electron. 18(1), 228–238 (2012).
[Crossref]

O’Carroll, J.

O’Gorman, J.

Phelan, R.

Poberezhskiy, I. Y.

I. Y. Poberezhskiy, B. Bortnik, J. Chou, B. Jalali, and H. R. Fetterman, “Serrodyne frequency translation of continuous optical signals using ultrawide-band electrical sawtooth waveforms,” IEEE J. Quantum Electron. 41(12), 1533–1539 (2005).
[Crossref]

Qin, J.

Rakuljic, G.

Reibel, R. R.

Roos, P. A.

San Martin, A.

D. Chang, G. Cardell, A. San Martin, and G. Spiers, “Coherent laser instrument would measure range and velocity,” NASA Tech Briefs 29, 9–10 (2005).

Satyan, N.

Shi, H.

Sorin, W. V.

W. V. Sorin, K. W. Chang, G. A. Conrad, and P. R. Hernday, “Frequency domain analysis of an optical FM discriminator,” J. Lightwave Technol. 10(6), 787–793 (1992).
[Crossref]

Spiers, G.

D. Chang, G. Cardell, A. San Martin, and G. Spiers, “Coherent laser instrument would measure range and velocity,” NASA Tech Briefs 29, 9–10 (2005).

Swann, W. C.

I. Coddington, F. R. Giorgetta, E. Baumann, W. C. Swann, and N. R. Newbury, “Characterizing fast arbitrary CW waveforms with 1500 THz/s instantaneous chirps,” IEEE J. Sel. Top. Quantum Electron. 18(1), 228–238 (2012).
[Crossref]

Tong, Y.

Tsuchida, H.

H. Tsuchida, “Laser frequency modulation noise measurement by recirculating delayed self-heterodyne method,” Opt. Lett. 36(5), 681–683 (2011).
[Crossref] [PubMed]

H. Tsuchida, “Characterization of white and flicker frequency modulation noise in narrow-linewidth laser diodes,” IEEE Photonics Technol. Lett. 23(11), 727–729 (2011).
[Crossref]

Vasilyev, A.

Wang, L.-T.

K. Iiyama, L.-T. Wang, and K. Hayashi, “Linearizing optical frequency-sweep of a laser diode for FMCW reflectometry,” J. Lightwave Technol. 14(2), 173–178 (1996).
[Crossref]

Xia, Z.

Xie, W.

Xie, X.

X. Xie, J. Khurgin, J. Kang, and F.-S. Choa, “Ring-assisted frequency discriminator with improved linearity,” IEEE Photonics Technol. Lett. 14(8), 1136–1138 (2002).
[Crossref]

Xu, Y.

Yariv, A.

Yu, S.

Zhou, Q.

Appl. Opt. (1)

Electron. Lett. (1)

A. Dieckmann, “FMCW-LIDAR with tunable twin-guide laser diode,” Electron. Lett. 30(4), 308–309 (1994).
[Crossref]

IEEE J. Quantum Electron. (1)

I. Y. Poberezhskiy, B. Bortnik, J. Chou, B. Jalali, and H. R. Fetterman, “Serrodyne frequency translation of continuous optical signals using ultrawide-band electrical sawtooth waveforms,” IEEE J. Quantum Electron. 41(12), 1533–1539 (2005).
[Crossref]

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

I. Coddington, F. R. Giorgetta, E. Baumann, W. C. Swann, and N. R. Newbury, “Characterizing fast arbitrary CW waveforms with 1500 THz/s instantaneous chirps,” IEEE J. Sel. Top. Quantum Electron. 18(1), 228–238 (2012).
[Crossref]

IEEE Photonics Technol. Lett. (3)

H. Tsuchida, “Characterization of white and flicker frequency modulation noise in narrow-linewidth laser diodes,” IEEE Photonics Technol. Lett. 23(11), 727–729 (2011).
[Crossref]

X. Xie, J. Khurgin, J. Kang, and F.-S. Choa, “Ring-assisted frequency discriminator with improved linearity,” IEEE Photonics Technol. Lett. 14(8), 1136–1138 (2002).
[Crossref]

G. Chen, J. U. Kang, and J. B. Khurgin, “Frequency discriminator based on ring-assisted fiber Sagnac filter,” IEEE Photonics Technol. Lett. 17(1), 109–111 (2005).
[Crossref]

J. Lightwave Technol. (3)

K. Iiyama, L.-T. Wang, and K. Hayashi, “Linearizing optical frequency-sweep of a laser diode for FMCW reflectometry,” J. Lightwave Technol. 14(2), 173–178 (1996).
[Crossref]

W. V. Sorin, K. W. Chang, G. A. Conrad, and P. R. Hernday, “Frequency domain analysis of an optical FM discriminator,” J. Lightwave Technol. 10(6), 787–793 (1992).
[Crossref]

C. Laskoskie, H. Hung, T. El-Wailly, and C. L. Chang, “Ti-LiNbO3 waveguide serrodyne modulator with ultrahigh sideband suppression for fiber optic gyroscopes,” J. Lightwave Technol. 7(4), 600–606 (1989).
[Crossref]

NASA Tech Briefs (1)

D. Chang, G. Cardell, A. San Martin, and G. Spiers, “Coherent laser instrument would measure range and velocity,” NASA Tech Briefs 29, 9–10 (2005).

Opt. Express (2)

Opt. Lett. (4)

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Figures (6)

Fig. 1
Fig. 1 (a) Schematic of the modulation waveform measurement technique. (b) FM noise power spectral density (FMPSD) of the discrete mode laser in the absence of modulation. The resolution bandwidth is 30 kHz.
Fig. 2
Fig. 2 (a) Measured waveforms for the directly modulated laser diodes with the 12-kHz triangular signal. The DC bias current is 160 mA. (b) Peak-to-peak frequency deviation plotted as a function of the modulation current.
Fig. 3
Fig. 3 (a) Measured waveforms for various bias currents. The modulation frequency and current are 12 kHz and 6.8 mApp, respectively. (b) Peak-to-peak frequency deviation plotted as a function of the bias current.
Fig. 4
Fig. 4 Comparison of the measured waveforms with the ideal triangular waves for the modulation currents (a) 6.8 and (b) 68 mApp, where the green lines represents the errors between the measured and ideal waveforms.
Fig. 5
Fig. 5 FMPSDs for the modulation currents (a) 6.8 and (b) 68 mApp, where the green lines represents the results in the absence of modulation.
Fig. 6
Fig. 6 Waveforms for the driver amplifier output and measured phase obtained with (a) sawtooth and (b) pseudo-random binary sequence modulations.

Equations (8)

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E(t)= E 0 exp{ i ω 0 t+iϕ(t) },
ν(t)= ( 2π ) 1 dϕ(t) / dt.
I B (t)=η E 0 2 cos[ 2π f S t ω 0 τ D +ϕ(t)ϕ(t τ D ) ],
ν(t) ( 2π ) 1 { ϕ(t)ϕ(t τ D ) } / τ D ,
ϕ(t)=2π 0 t ν( t ) d t .
S B (t)=2{ 1cos( 2πf τ D ) } S ν (f).
ν(t)= 4 ν m π 2 k=1 sin( kπ /2 ) k 2 sin( 2πk f m t ) ,
ϕ(t)= ϕ m π k=1 sin( 2πk f m t ) k ,

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