Abstract

We propose a self-calibrating method for high-frequency response measurement of electro-optic phase modulators based on two-tone modulation. The method utilizes the electrical domain measurement of heterodyning spectrum between the two-tone modulation optical signal and the frequency-shifted optical carrier, and eliminates the need to correct the responsivity fluctuation in the photodetection. High-frequency modulation depth and half-wave voltages are measured and compared to those with the traditional optical spectrum analysis method in the experimental demonstration. The proposed method enables calibration-free and accurate frequency response measurement of electro-optic phase modulators by using high-resolution electrical spectrum analysis.

© 2014 Optical Society of America

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2012 (3)

S. Zhang, X. Zhang, S. Liu, and Y. Liu, Opt. Commun. 285, 5089 (2012).
[CrossRef]

X. M. Wu, J. W. Man, L. Xie, Y. Liu, X. Q. Qi, L. X. Wang, J. G. Liu, and N. H. Zhu, IEEE Photon. Technol. Lett. 24, 575 (2012).
[CrossRef]

J. Lloret, R. Kumar, S. Sales, F. Ramos, G. Morthier, P. Mechet, T. Spuesens, D. Van Thourhout, N. Olivier, J.-M. Fédéli, and J. Capmany, Opt. Lett. 37, 2379 (2012).
[CrossRef]

2011 (1)

2009 (2)

2008 (2)

2006 (1)

2003 (3)

Y. Shi, L. Yan, and A. E. Willner, J. Lightwave Technol. 21, 2358 (2003).
[CrossRef]

S. Oikawa, T. Kawanishi, and M. Izutsu, IEEE Photon. Technol. Lett. 15, 682 (2003).
[CrossRef]

P. Hale and D. Williams, IEEE Trans. Microwave Theory Tech. 51, 1422 (2003).
[CrossRef]

2002 (2)

F. P. Romstad, D. Birkedal, J. Mørk, and J. M. Hvam, IEEE Photon. Technol. Lett. 14, 621 (2002).
[CrossRef]

J. A. Campbell, A. Knoesen, and D. R. Yankelevich, IEEE Photon. Technol. Lett. 14, 1330 (2002).
[CrossRef]

Andrew, G. E.

G. E. Andrew, R. Askey, and R. Roy, Special Functions (Cambridge University, 2001).

Askey, R.

G. E. Andrew, R. Askey, and R. Roy, Special Functions (Cambridge University, 2001).

Birkedal, D.

F. P. Romstad, D. Birkedal, J. Mørk, and J. M. Hvam, IEEE Photon. Technol. Lett. 14, 621 (2002).
[CrossRef]

Bowers, J.

Campbell, J. A.

J. A. Campbell, A. Knoesen, and D. R. Yankelevich, IEEE Photon. Technol. Lett. 14, 1330 (2002).
[CrossRef]

Capmany, J.

Chan, E. H. W.

Chi, H.

Chou, H.-F.

Coldren, L.

Fédéli, J.-M.

Haas, B. M.

Hale, P.

P. Hale and D. Williams, IEEE Trans. Microwave Theory Tech. 51, 1422 (2003).
[CrossRef]

Hvam, J. M.

F. P. Romstad, D. Birkedal, J. Mørk, and J. M. Hvam, IEEE Photon. Technol. Lett. 14, 621 (2002).
[CrossRef]

Izutsu, M.

S. Oikawa, T. Kawanishi, and M. Izutsu, IEEE Photon. Technol. Lett. 15, 682 (2003).
[CrossRef]

Johansson, L. A.

Kawanishi, T.

S. Oikawa, T. Kawanishi, and M. Izutsu, IEEE Photon. Technol. Lett. 15, 682 (2003).
[CrossRef]

Klamkin, J.

Knoesen, A.

J. A. Campbell, A. Knoesen, and D. R. Yankelevich, IEEE Photon. Technol. Lett. 14, 1330 (2002).
[CrossRef]

Kumar, R.

Liu, J. G.

X. M. Wu, J. W. Man, L. Xie, Y. Liu, X. Q. Qi, L. X. Wang, J. G. Liu, and N. H. Zhu, IEEE Photon. Technol. Lett. 24, 575 (2012).
[CrossRef]

Liu, S.

S. Zhang, X. Zhang, S. Liu, and Y. Liu, Opt. Commun. 285, 5089 (2012).
[CrossRef]

Liu, Y.

S. Zhang, X. Zhang, S. Liu, and Y. Liu, Opt. Commun. 285, 5089 (2012).
[CrossRef]

X. M. Wu, J. W. Man, L. Xie, Y. Liu, X. Q. Qi, L. X. Wang, J. G. Liu, and N. H. Zhu, IEEE Photon. Technol. Lett. 24, 575 (2012).
[CrossRef]

Lloret, J.

Man, J. W.

X. M. Wu, J. W. Man, L. Xie, Y. Liu, X. Q. Qi, L. X. Wang, J. G. Liu, and N. H. Zhu, IEEE Photon. Technol. Lett. 24, 575 (2012).
[CrossRef]

Mechet, P.

Minasian, R. A.

Mørk, J.

F. P. Romstad, D. Birkedal, J. Mørk, and J. M. Hvam, IEEE Photon. Technol. Lett. 14, 621 (2002).
[CrossRef]

Morthier, G.

Murphy, T. E.

Oikawa, S.

S. Oikawa, T. Kawanishi, and M. Izutsu, IEEE Photon. Technol. Lett. 15, 682 (2003).
[CrossRef]

Olivier, N.

Pagan, V. R.

Qi, X. Q.

X. M. Wu, J. W. Man, L. Xie, Y. Liu, X. Q. Qi, L. X. Wang, J. G. Liu, and N. H. Zhu, IEEE Photon. Technol. Lett. 24, 575 (2012).
[CrossRef]

Ramaswamy, A.

Ramos, F.

Rodwell, M.

Romstad, F. P.

F. P. Romstad, D. Birkedal, J. Mørk, and J. M. Hvam, IEEE Photon. Technol. Lett. 14, 621 (2002).
[CrossRef]

Roy, R.

G. E. Andrew, R. Askey, and R. Roy, Special Functions (Cambridge University, 2001).

Sales, S.

Seeds, A. J.

Sheldon, C.

Shi, Y.

Spuesens, T.

Van Thourhout, D.

Wang, L. X.

X. M. Wu, J. W. Man, L. Xie, Y. Liu, X. Q. Qi, L. X. Wang, J. G. Liu, and N. H. Zhu, IEEE Photon. Technol. Lett. 24, 575 (2012).
[CrossRef]

Williams, D.

P. Hale and D. Williams, IEEE Trans. Microwave Theory Tech. 51, 1422 (2003).
[CrossRef]

Williams, K. J.

Willner, A. E.

Wu, X. M.

X. M. Wu, J. W. Man, L. Xie, Y. Liu, X. Q. Qi, L. X. Wang, J. G. Liu, and N. H. Zhu, IEEE Photon. Technol. Lett. 24, 575 (2012).
[CrossRef]

Xie, L.

X. M. Wu, J. W. Man, L. Xie, Y. Liu, X. Q. Qi, L. X. Wang, J. G. Liu, and N. H. Zhu, IEEE Photon. Technol. Lett. 24, 575 (2012).
[CrossRef]

Yan, L.

Yankelevich, D. R.

J. A. Campbell, A. Knoesen, and D. R. Yankelevich, IEEE Photon. Technol. Lett. 14, 1330 (2002).
[CrossRef]

Yao, J.

Zhang, S.

S. Zhang, X. Zhang, S. Liu, and Y. Liu, Opt. Commun. 285, 5089 (2012).
[CrossRef]

Zhang, X.

S. Zhang, X. Zhang, S. Liu, and Y. Liu, Opt. Commun. 285, 5089 (2012).
[CrossRef]

Zhu, N. H.

X. M. Wu, J. W. Man, L. Xie, Y. Liu, X. Q. Qi, L. X. Wang, J. G. Liu, and N. H. Zhu, IEEE Photon. Technol. Lett. 24, 575 (2012).
[CrossRef]

Zou, X.

IEEE Photon. Technol. Lett. (4)

S. Oikawa, T. Kawanishi, and M. Izutsu, IEEE Photon. Technol. Lett. 15, 682 (2003).
[CrossRef]

F. P. Romstad, D. Birkedal, J. Mørk, and J. M. Hvam, IEEE Photon. Technol. Lett. 14, 621 (2002).
[CrossRef]

J. A. Campbell, A. Knoesen, and D. R. Yankelevich, IEEE Photon. Technol. Lett. 14, 1330 (2002).
[CrossRef]

X. M. Wu, J. W. Man, L. Xie, Y. Liu, X. Q. Qi, L. X. Wang, J. G. Liu, and N. H. Zhu, IEEE Photon. Technol. Lett. 24, 575 (2012).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

P. Hale and D. Williams, IEEE Trans. Microwave Theory Tech. 51, 1422 (2003).
[CrossRef]

J. Lightwave Technol. (6)

Opt. Commun. (1)

S. Zhang, X. Zhang, S. Liu, and Y. Liu, Opt. Commun. 285, 5089 (2012).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Other (1)

G. E. Andrew, R. Askey, and R. Roy, Special Functions (Cambridge University, 2001).

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Figures (6)

Fig. 1.
Fig. 1.

Schematic setup to measure a phase modulator based on two-tone modulation. ESA, electrical spectrum analyzer; OSA, optical spectrum analyzer.

Fig. 2.
Fig. 2.

Measured frequency spectrum of the output electrical signal after photodetection in the case of f1=20GHz, f2=20.02GHz and fs=70MHz, where the left inset shows a zoom-in of the spectrum lines at f1f2±fs and fs, and the right inset shows that at f1±fs and f2±fs.

Fig. 3.
Fig. 3.

Measured frequency spectra of the output electrical signals after photodetection at different two-tone frequencies, where (a) shows the components at f1f2±fs and fs, and (b) shows those at f1±fs and f2±fs.

Fig. 4.
Fig. 4.

Measured modulation depths with our method (red and blue lines) and with OSA method (open squares and circles), where the inset shows the electrical driving amplitude in the measurement.

Fig. 5.
Fig. 5.

Error transfer factors as a function of the modulation depth.

Fig. 6.
Fig. 6.

Measured half-wave voltages as functions of modulation frequency with our method (red lines and blue lines), and the optical spectrum analysis (open squares and circles).

Equations (12)

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Ep(t)=ej2πfct+jm1sin2πf1t+jm2sin2πf2t,
mi=πVi/Vπi=π2PiZL/Vπi,(i=1,2),
Es(t)=ej2π(fcfs)t.
ir(t)=R|Ep(t)+Es(t)|2=2R[1+cos(m1sin2πf1t+m2sin2πf2t+2πfst)].
ir(t)=2R{1+p=+q=+Jp(m1)Jq(m2)cos[2π(pf1+qf2+fs)t]},
ir(f1f2±fs)=2R(f1f2±fs)·J1(m1)J1(m2),
ir(fs)=2R(fs)·J0(m1)J0(m2),
ir(f1±fs)=2R(f1±fs)·J1(m1)J0(m2)
ir(f2±fs)=2R(f2±fs)·J0(m1)J1(m2).
H1(m1)=ir(f1±fs)ir(f2±fs)·ir(f1f2±fs)ir(fs)=J12(m1)J02(m1)
H2(m2)=ir(f2±fs)ir(f1±fs)·ir(f1f2±fs)ir(fs)=J12(m2)J02(m2).
F=δm/mδH/H=1m[2J1(m)J0(m)J0(m)J2(m)J1(m)],(m=m1,m2),

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