Abstract

Recently, silicon optical in-phase quadrature (IQ) modulators have played an increasingly important role in coherent optical transmission networks because of their small package size and low cost. To stabilize the modulation performance of the silicon IQ optical modulator (SIQOM), the bias voltages of the SIQOM must be maintained at optimum points. Because of the nonlinear modulation characteristic of the silicon material, it is difficult to achieve high-precision closed-loop control of the bias voltage for the SIQOM. In this paper, a novel automatic bias-control scheme for the SIQOM is proposed and investigated theoretically and experimentally. First, two sinusoidal power dithers with different low frequencies are applied to the channels I and Q biases of the SIQOM. Next, a pair of orthogonal trigonometric functions with the same frequency as the power dither signal is constructed. We find that the optimum point of the bias voltage is the intersection of the orthogonal-integral curves via cross-correlation integral operations between the output signal of the SIQOM and the aforementioned trigonometric functions. The results indicate that the bias errors of the channels I/Q/P relative to the optimum point can be corrected precisely by the proposed scheme, and the jitters of the vector amplitude error caused by this scheme are <1% in 128-Gb/s dual-polarization quadrature phase-shift keying and single-polarization 16-quadrature amplitude modulation formats.

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

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References

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  2. J. P. Salvestrini, L. Guilbert, M. Fontana, M. Abarkan, and S. J. J. L. T. Gille, “Analysis and Control of the DC Drift in LiNbO3-Based Mach–Zehnder Modulators,” J. Lightwave Technol. 29(10), 1522–1534 (2011).
    [Crossref]
  3. K. Sekine, C. Hasegawa, N. Kikuchi, and S. Sasaki, “A Novel Bias Control Technique for MZ Modulator with Monitoring Power of Backward Light for Advanced Modulation Formats,” in Optical Fiber Communication and the National Fiber Optic Engineers Conference 2007 (Optical Society of America, 2007), paper OTuH5.
    [Crossref]
  4. M.-H. Kim, B.-M. Yu, and W.-Y. Choi, “A Mach-Zehnder Modulator Bias Controller Based on OMA and Average Power Monitoring,” IEEE opticals Technology Letters 29(23), 2043–2046 (2017).
    [Crossref]
  5. P. S. Cho, J. B. Khurgin, and I. Shpantzer, “Closed-Loop Bias Control of Optical Quadrature Modulator,” IEEE opticals Technology Letters 18(21), 2209–2211 (2006).
    [Crossref]
  6. H. Kawakami, T. Kobayashi, M. Yoshida, T. Kataoka, and Y. Miyamoto, “Auto bias control and bias hold circuit for IQ-modulator in flexible optical QAM transmitter with Nyquist filtering,” Opt. Express 22(23), 28163–28168 (2014).
    [Crossref] [PubMed]
  7. T. Yoshida, T. Sugihara, K. Uto, H. Bessho, K. Sawada, K. Ishida, K. Shimizu, and T. Mizuochi, “A study on automatic bias control for arbitrary optical signal generation by dual-parallel Mach-Zehnder modulator,” in 36th European Conference and Exhibition on Optical Communication, (2010), pp. 1–3.
    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  10. L. L. Wang and T. Kowalcyzk, “A Versatile Bias Control Technique for Any-Point lock in Lithium Niobate Mach–Zehnder Modulators,” J. Lightwave Technol. 28(11), 1703–1706 (2010).
    [Crossref]
  11. H. Kawakami, E. Yoshida, and Y. Miyamoto, “Auto Bias Control Technique Based on Asymmetric Bias Dithering for Optical QPSK Modulation,” J. Lightwave Technol. 30(7), 962–968 (2012).
    [Crossref]
  12. M. Sotoodeh, Y. Beaulieu, J. Harley, and D. L. McGhan, “Modulator Bias and Optical Power Control of Optical Complex E-Field Modulators,” J. Lightwave Technol. 29(15), 2235–2248 (2011).
    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
  15. X. Li, L. Deng, X. Chen, H. Song, Y. Liu, M. Cheng, S. Fu, M. Tang, M. Zhang, and D. Liu, “Arbitrary Bias Point Control Technique for Optical IQ Modulator Based on Dither-Correlation Detection,” J. Lightwave Technol. 36(18), 3824–3836 (2018).
    [Crossref]
  16. L. Chen, P. Dong, and Y.-K. Chen, “Chirp and Dispersion Tolerance of a Single-Drive Push–Pull Silicon Modulator at 28 Gb/s,” IEEE opticals Technology Letters 24(11), 936–938 (2012).
    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
  20. A. Napoli, M. M. Mezghanni, S. Calabro, R. Palmer, and B. J. J. L. T. Spinnler, “Digital Pre-Distortion Techniques for Finite Extinction Ratio IQ-Mach-Zehnder Modulators,” J. Lightwave Technol. 6(1), 1–8 (2017).
  21. Y. Wei, Y. Zhao, J. Yang, M. Wang, and X. J. J. L. T. Jiang, “Chirp Characteristics of Silicon Mach–Zehnder Modulator Under Small-Signal Modulation,” J. Lightwave Technol. 29(7), 1011–1017 (2011).
    [Crossref]

2018 (1)

2017 (3)

X. Li, L. Deng, X. Chen, M. Cheng, S. Fu, M. Tang, and D. Liu, “Modulation-format-free and automatic bias control for optical IQ modulators based on dither-correlation detection,” Opt. Express 25(8), 9333–9345 (2017).
[Crossref] [PubMed]

M.-H. Kim, B.-M. Yu, and W.-Y. Choi, “A Mach-Zehnder Modulator Bias Controller Based on OMA and Average Power Monitoring,” IEEE opticals Technology Letters 29(23), 2043–2046 (2017).
[Crossref]

A. Napoli, M. M. Mezghanni, S. Calabro, R. Palmer, and B. J. J. L. T. Spinnler, “Digital Pre-Distortion Techniques for Finite Extinction Ratio IQ-Mach-Zehnder Modulators,” J. Lightwave Technol. 6(1), 1–8 (2017).

2016 (1)

2015 (1)

2014 (3)

2013 (2)

2012 (2)

H. Kawakami, E. Yoshida, and Y. Miyamoto, “Auto Bias Control Technique Based on Asymmetric Bias Dithering for Optical QPSK Modulation,” J. Lightwave Technol. 30(7), 962–968 (2012).
[Crossref]

L. Chen, P. Dong, and Y.-K. Chen, “Chirp and Dispersion Tolerance of a Single-Drive Push–Pull Silicon Modulator at 28 Gb/s,” IEEE opticals Technology Letters 24(11), 936–938 (2012).
[Crossref]

2011 (3)

2010 (1)

2006 (1)

P. S. Cho, J. B. Khurgin, and I. Shpantzer, “Closed-Loop Bias Control of Optical Quadrature Modulator,” IEEE opticals Technology Letters 18(21), 2209–2211 (2006).
[Crossref]

Abarkan, M.

Baehr-Jones, T.

Beaulieu, Y.

Bessho, H.

T. Yoshida, T. Sugihara, K. Uto, H. Bessho, K. Sawada, K. Ishida, K. Shimizu, and T. Mizuochi, “A study on automatic bias control for arbitrary optical signal generation by dual-parallel Mach-Zehnder modulator,” in 36th European Conference and Exhibition on Optical Communication, (2010), pp. 1–3.
[Crossref]

Calabro, S.

A. Napoli, M. M. Mezghanni, S. Calabro, R. Palmer, and B. J. J. L. T. Spinnler, “Digital Pre-Distortion Techniques for Finite Extinction Ratio IQ-Mach-Zehnder Modulators,” J. Lightwave Technol. 6(1), 1–8 (2017).

Chang, S. H.

Chen, J.

Chen, J. J. P. R.

Chen, L.

L. Chen, P. Dong, and Y.-K. Chen, “Chirp and Dispersion Tolerance of a Single-Drive Push–Pull Silicon Modulator at 28 Gb/s,” IEEE opticals Technology Letters 24(11), 936–938 (2012).
[Crossref]

Chen, X.

Chen, Y.-K.

L. Chen, P. Dong, and Y.-K. Chen, “Chirp and Dispersion Tolerance of a Single-Drive Push–Pull Silicon Modulator at 28 Gb/s,” IEEE opticals Technology Letters 24(11), 936–938 (2012).
[Crossref]

Chen, Z.

Cheng, M.

Cho, P. S.

P. S. Cho, J. B. Khurgin, and I. Shpantzer, “Closed-Loop Bias Control of Optical Quadrature Modulator,” IEEE opticals Technology Letters 18(21), 2209–2211 (2006).
[Crossref]

Choi, W.-Y.

M.-H. Kim, B.-M. Yu, and W.-Y. Choi, “A Mach-Zehnder Modulator Bias Controller Based on OMA and Average Power Monitoring,” IEEE opticals Technology Letters 29(23), 2043–2046 (2017).
[Crossref]

Chung, H. S.

Deng, L.

Dong, P.

L. Chen, P. Dong, and Y.-K. Chen, “Chirp and Dispersion Tolerance of a Single-Drive Push–Pull Silicon Modulator at 28 Gb/s,” IEEE opticals Technology Letters 24(11), 936–938 (2012).
[Crossref]

Englund, D.

Fontana, M.

Fu, S.

Fujita, T.

T. Fujita, T. Kawanishi, T. Sakamoto, K. Higuma, S. Mori, J. Ichikawa, T. Miyazaki, and M. Izutsu, “80 Gb/s Optical Quadrature P Shift Keying Modulation Using an Integrated LiNbO3 Modulator,” in Conference on Lasers & Electro-optics(CLEO 2006), paper CFP4.

Galland, C.

Gille, S. J. J. L. T.

Gui, T.

Guilbert, L.

Harley, J.

Harris, N. C.

Higuma, K.

T. Fujita, T. Kawanishi, T. Sakamoto, K. Higuma, S. Mori, J. Ichikawa, T. Miyazaki, and M. Izutsu, “80 Gb/s Optical Quadrature P Shift Keying Modulation Using an Integrated LiNbO3 Modulator,” in Conference on Lasers & Electro-optics(CLEO 2006), paper CFP4.

Hochberg, M.

Ichikawa, J.

T. Fujita, T. Kawanishi, T. Sakamoto, K. Higuma, S. Mori, J. Ichikawa, T. Miyazaki, and M. Izutsu, “80 Gb/s Optical Quadrature P Shift Keying Modulation Using an Integrated LiNbO3 Modulator,” in Conference on Lasers & Electro-optics(CLEO 2006), paper CFP4.

Ishida, K.

T. Yoshida, T. Sugihara, K. Uto, H. Bessho, K. Sawada, K. Ishida, K. Shimizu, and T. Mizuochi, “A study on automatic bias control for arbitrary optical signal generation by dual-parallel Mach-Zehnder modulator,” in 36th European Conference and Exhibition on Optical Communication, (2010), pp. 1–3.
[Crossref]

Izutsu, M.

T. Fujita, T. Kawanishi, T. Sakamoto, K. Higuma, S. Mori, J. Ichikawa, T. Miyazaki, and M. Izutsu, “80 Gb/s Optical Quadrature P Shift Keying Modulation Using an Integrated LiNbO3 Modulator,” in Conference on Lasers & Electro-optics(CLEO 2006), paper CFP4.

Jiang, X. J. J. L. T.

Jin, C.

Kataoka, T.

Kawakami, H.

Kawanishi, T.

T. Fujita, T. Kawanishi, T. Sakamoto, K. Higuma, S. Mori, J. Ichikawa, T. Miyazaki, and M. Izutsu, “80 Gb/s Optical Quadrature P Shift Keying Modulation Using an Integrated LiNbO3 Modulator,” in Conference on Lasers & Electro-optics(CLEO 2006), paper CFP4.

Khurgin, J. B.

P. S. Cho, J. B. Khurgin, and I. Shpantzer, “Closed-Loop Bias Control of Optical Quadrature Modulator,” IEEE opticals Technology Letters 18(21), 2209–2211 (2006).
[Crossref]

Kim, K.

Kim, M.-H.

M.-H. Kim, B.-M. Yu, and W.-Y. Choi, “A Mach-Zehnder Modulator Bias Controller Based on OMA and Average Power Monitoring,” IEEE opticals Technology Letters 29(23), 2043–2046 (2017).
[Crossref]

Kobayashi, T.

Kowalcyzk, T.

Lee, J. H.

Li, C.

Li, X.

Li, Z.

Liu, D.

Liu, L.

Liu, Y.

Ma, Y.

McGhan, D. L.

Meng, L.

Mezghanni, M. M.

A. Napoli, M. M. Mezghanni, S. Calabro, R. Palmer, and B. J. J. L. T. Spinnler, “Digital Pre-Distortion Techniques for Finite Extinction Ratio IQ-Mach-Zehnder Modulators,” J. Lightwave Technol. 6(1), 1–8 (2017).

Miyamoto, Y.

Miyazaki, T.

T. Fujita, T. Kawanishi, T. Sakamoto, K. Higuma, S. Mori, J. Ichikawa, T. Miyazaki, and M. Izutsu, “80 Gb/s Optical Quadrature P Shift Keying Modulation Using an Integrated LiNbO3 Modulator,” in Conference on Lasers & Electro-optics(CLEO 2006), paper CFP4.

Mizuochi, T.

T. Yoshida, T. Sugihara, K. Uto, H. Bessho, K. Sawada, K. Ishida, K. Shimizu, and T. Mizuochi, “A study on automatic bias control for arbitrary optical signal generation by dual-parallel Mach-Zehnder modulator,” in 36th European Conference and Exhibition on Optical Communication, (2010), pp. 1–3.
[Crossref]

Mori, S.

T. Fujita, T. Kawanishi, T. Sakamoto, K. Higuma, S. Mori, J. Ichikawa, T. Miyazaki, and M. Izutsu, “80 Gb/s Optical Quadrature P Shift Keying Modulation Using an Integrated LiNbO3 Modulator,” in Conference on Lasers & Electro-optics(CLEO 2006), paper CFP4.

Mower, J.

Napoli, A.

A. Napoli, M. M. Mezghanni, S. Calabro, R. Palmer, and B. J. J. L. T. Spinnler, “Digital Pre-Distortion Techniques for Finite Extinction Ratio IQ-Mach-Zehnder Modulators,” J. Lightwave Technol. 6(1), 1–8 (2017).

Palmer, R.

A. Napoli, M. M. Mezghanni, S. Calabro, R. Palmer, and B. J. J. L. T. Spinnler, “Digital Pre-Distortion Techniques for Finite Extinction Ratio IQ-Mach-Zehnder Modulators,” J. Lightwave Technol. 6(1), 1–8 (2017).

Sakamoto, T.

T. Fujita, T. Kawanishi, T. Sakamoto, K. Higuma, S. Mori, J. Ichikawa, T. Miyazaki, and M. Izutsu, “80 Gb/s Optical Quadrature P Shift Keying Modulation Using an Integrated LiNbO3 Modulator,” in Conference on Lasers & Electro-optics(CLEO 2006), paper CFP4.

Salvestrini, J. P.

Sawada, K.

T. Yoshida, T. Sugihara, K. Uto, H. Bessho, K. Sawada, K. Ishida, K. Shimizu, and T. Mizuochi, “A study on automatic bias control for arbitrary optical signal generation by dual-parallel Mach-Zehnder modulator,” in 36th European Conference and Exhibition on Optical Communication, (2010), pp. 1–3.
[Crossref]

Shimizu, K.

T. Yoshida, T. Sugihara, K. Uto, H. Bessho, K. Sawada, K. Ishida, K. Shimizu, and T. Mizuochi, “A study on automatic bias control for arbitrary optical signal generation by dual-parallel Mach-Zehnder modulator,” in 36th European Conference and Exhibition on Optical Communication, (2010), pp. 1–3.
[Crossref]

Shpantzer, I.

P. S. Cho, J. B. Khurgin, and I. Shpantzer, “Closed-Loop Bias Control of Optical Quadrature Modulator,” IEEE opticals Technology Letters 18(21), 2209–2211 (2006).
[Crossref]

Song, H.

Sotoodeh, M.

Spinnler, B. J. J. L. T.

A. Napoli, M. M. Mezghanni, S. Calabro, R. Palmer, and B. J. J. L. T. Spinnler, “Digital Pre-Distortion Techniques for Finite Extinction Ratio IQ-Mach-Zehnder Modulators,” J. Lightwave Technol. 6(1), 1–8 (2017).

Su, F.

Sugihara, T.

T. Yoshida, T. Sugihara, K. Uto, H. Bessho, K. Sawada, K. Ishida, K. Shimizu, and T. Mizuochi, “A study on automatic bias control for arbitrary optical signal generation by dual-parallel Mach-Zehnder modulator,” in 36th European Conference and Exhibition on Optical Communication, (2010), pp. 1–3.
[Crossref]

Tang, M.

Tao, Z.

Uto, K.

T. Yoshida, T. Sugihara, K. Uto, H. Bessho, K. Sawada, K. Ishida, K. Shimizu, and T. Mizuochi, “A study on automatic bias control for arbitrary optical signal generation by dual-parallel Mach-Zehnder modulator,” in 36th European Conference and Exhibition on Optical Communication, (2010), pp. 1–3.
[Crossref]

Wang, J.

Wang, L. L.

Wang, M.

Wang, T.

Wei, Y.

Xiao, X.

Yang, J.

Yang, Q.

Yang, R.

Yi, X.

Yoshida, E.

Yoshida, M.

Yoshida, T.

T. Yoshida, T. Sugihara, K. Uto, H. Bessho, K. Sawada, K. Ishida, K. Shimizu, and T. Mizuochi, “A study on automatic bias control for arbitrary optical signal generation by dual-parallel Mach-Zehnder modulator,” in 36th European Conference and Exhibition on Optical Communication, (2010), pp. 1–3.
[Crossref]

Yu, B.-M.

M.-H. Kim, B.-M. Yu, and W.-Y. Choi, “A Mach-Zehnder Modulator Bias Controller Based on OMA and Average Power Monitoring,” IEEE opticals Technology Letters 29(23), 2043–2046 (2017).
[Crossref]

Zhang, C.

Zhang, M.

Zhao, Y.

Zheng, Z.

Zhou, L.

Zhou, Y.

Zhu, H.

Zhu, L.

Zhu, X.

IEEE opticals Technology Letters (3)

M.-H. Kim, B.-M. Yu, and W.-Y. Choi, “A Mach-Zehnder Modulator Bias Controller Based on OMA and Average Power Monitoring,” IEEE opticals Technology Letters 29(23), 2043–2046 (2017).
[Crossref]

P. S. Cho, J. B. Khurgin, and I. Shpantzer, “Closed-Loop Bias Control of Optical Quadrature Modulator,” IEEE opticals Technology Letters 18(21), 2209–2211 (2006).
[Crossref]

L. Chen, P. Dong, and Y.-K. Chen, “Chirp and Dispersion Tolerance of a Single-Drive Push–Pull Silicon Modulator at 28 Gb/s,” IEEE opticals Technology Letters 24(11), 936–938 (2012).
[Crossref]

J. Lightwave Technol. (9)

A. Napoli, M. M. Mezghanni, S. Calabro, R. Palmer, and B. J. J. L. T. Spinnler, “Digital Pre-Distortion Techniques for Finite Extinction Ratio IQ-Mach-Zehnder Modulators,” J. Lightwave Technol. 6(1), 1–8 (2017).

J. P. Salvestrini, L. Guilbert, M. Fontana, M. Abarkan, and S. J. J. L. T. Gille, “Analysis and Control of the DC Drift in LiNbO3-Based Mach–Zehnder Modulators,” J. Lightwave Technol. 29(10), 1522–1534 (2011).
[Crossref]

H. Kawakami, E. Yoshida, and Y. Miyamoto, “Auto Bias Control Technique Based on Asymmetric Bias Dithering for Optical QPSK Modulation,” J. Lightwave Technol. 30(7), 962–968 (2012).
[Crossref]

Y. Zhou, L. Zhou, F. Su, X. Li, and J. Chen, “Linearity Measurement and Pulse Amplitude Modulation in a Silicon Single-Drive Push–Pull Mach–Zehnder Modulator,” J. Lightwave Technol. 34(14), 3323–3329 (2016).
[Crossref]

Y. Wei, Y. Zhao, J. Yang, M. Wang, and X. J. J. L. T. Jiang, “Chirp Characteristics of Silicon Mach–Zehnder Modulator Under Small-Signal Modulation,” J. Lightwave Technol. 29(7), 1011–1017 (2011).
[Crossref]

M. Sotoodeh, Y. Beaulieu, J. Harley, and D. L. McGhan, “Modulator Bias and Optical Power Control of Optical Complex E-Field Modulators,” J. Lightwave Technol. 29(15), 2235–2248 (2011).
[Crossref]

X. Zhu, Z. Zheng, C. Zhang, L. Zhu, Z. Tao, and Z. Chen, “Coherent Detection-Based Automatic Bias Control of Mach–Zehnder Modulators for Various Modulation Formats,” J. Lightwave Technol. 32(14), 2502–2509 (2014).
[Crossref]

L. L. Wang and T. Kowalcyzk, “A Versatile Bias Control Technique for Any-Point lock in Lithium Niobate Mach–Zehnder Modulators,” J. Lightwave Technol. 28(11), 1703–1706 (2010).
[Crossref]

X. Li, L. Deng, X. Chen, H. Song, Y. Liu, M. Cheng, S. Fu, M. Tang, M. Zhang, and D. Liu, “Arbitrary Bias Point Control Technique for Optical IQ Modulator Based on Dither-Correlation Detection,” J. Lightwave Technol. 36(18), 3824–3836 (2018).
[Crossref]

Opt. Express (5)

Photon. Res. (1)

Other (3)

T. Yoshida, T. Sugihara, K. Uto, H. Bessho, K. Sawada, K. Ishida, K. Shimizu, and T. Mizuochi, “A study on automatic bias control for arbitrary optical signal generation by dual-parallel Mach-Zehnder modulator,” in 36th European Conference and Exhibition on Optical Communication, (2010), pp. 1–3.
[Crossref]

T. Fujita, T. Kawanishi, T. Sakamoto, K. Higuma, S. Mori, J. Ichikawa, T. Miyazaki, and M. Izutsu, “80 Gb/s Optical Quadrature P Shift Keying Modulation Using an Integrated LiNbO3 Modulator,” in Conference on Lasers & Electro-optics(CLEO 2006), paper CFP4.

K. Sekine, C. Hasegawa, N. Kikuchi, and S. Sasaki, “A Novel Bias Control Technique for MZ Modulator with Monitoring Power of Backward Light for Advanced Modulation Formats,” in Optical Fiber Communication and the National Fiber Optic Engineers Conference 2007 (Optical Society of America, 2007), paper OTuH5.
[Crossref]

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Figures (13)

Fig. 1
Fig. 1 Model diagram of the DP_MZ SIQOM.
Fig. 2
Fig. 2 Simulated curves of the 1st harmonic component (210 Hz) versus the channel-I bias and channel-P bias when the (a) sine voltage dither and (b) sine power dither are applied to channel I.
Fig. 3
Fig. 3 (a) Simulated curves of the normalized amplitude spectra with different noise spectral densities after the sine power dither is applied to channel I. (b) Simulated curves of the channel-I in-phase integral error ( C I_SIN ) and quadrature integral error ( C I_COS ) with different noise spectral densities after different voltages are applied to channel I.
Fig. 4
Fig. 4 (a) Simulated curves of the maximum noise power distinguished by the proposed ABC scheme with different power dither amplitudes applied to the channel I bias and the bias deviation degree relative to the optimum point with different power dither amplitudes applied to the channel-I bias. (b) Simulated curves of C I _SIN and C I _COS with different RF signal amplitudes.
Fig. 5
Fig. 5 Simulated curves of the sum frequency harmonic component (820 Hz) with different channel-I, -Q, and -P biases when (a) the sine voltage dither is applied to channel I and (b) the sine power dither is applied to channel I.
Fig. 6
Fig. 6 (a)Simulated curves of the normalized amplitude spectra with different noise spectral densities after sine power dithers are applied to channels I and Q, (b) Simulated curves of the channel-P in-phase integral error ( C P_SIN ) and quadrature integral error ( C P_COS ) with different noise spectral densities after different voltages are applied to channel P.
Fig. 7
Fig. 7 (a)Simulated curve of the maximum noise spectral density distinguished by the proposed ABC scheme with different power dither amplitudes applied to the channel-I and channel-Q biases simultaneously, and simulated curve of the bias deviation degree relative to the optimum point caused by the power dither signal. (b) Simulated curves of C P _SIN and C P _COS with different RF signal amplitudes.
Fig. 8
Fig. 8 Experimental setup for implementing the ABC scheme in 128-Gb/s DP-QPSK and SP-16-QAM modulation.
Fig. 9
Fig. 9 Measurements of (a) amplitude spectra versus the channel-I bias after the sine power dither was applied to channel I and (b) the channel-I in-phase integral error ( C I_SIN ) and quadrature integral error ( C I_COS ).
Fig. 10
Fig. 10 Measurements of (a) the normalized amplitude spectra with different channel-P biases after channel I and channel Q applied the sine power dither and (b) the channel-P in-phase integral error ( C P_SIN ) and quadrature integral error ( C P_COS ).
Fig. 11
Fig. 11 Constellation diagrams of the optical signal in QPSK modulation after the application of different bias voltages to channels I/Q/P. (a) Bias voltages of channels I, Q, and P were 0.95 Vπ, 0.95 Vπ, and 0.95 Vπ/2, respectively; (b) bias voltages of channels I, Q, and P were 1.05 Vπ, 0.95 Vπ, and 0.95 Vπ/2, respectively; (c) bias voltages of channels I, Q, and P were 0.95 Vπ, 1.05 Vπ, and 0.95 Vπ/2, respectively; (d) bias voltages of channels I, Q, and P were 1.05 Vπ, 1.05 Vπ, and 0.95 Vπ/2, respectively; (e) bias voltages of channels I, Q, and P were 0.95 Vπ, 0.95 Vπ, and 1.05 Vπ/2, respectively; (f) bias voltages of channels I, Q, and P were 0.95 Vπ, 0.95 Vπ, and 1.05 Vπ/2, respectively; (g) bias voltages of channels I, Q, and P were 1.05 Vπ, 1.05 Vπ, and 1.05 Vπ/2, respectively; (h) bias voltages of channels I, Q, and P were 1.05 Vπ, 0.95 Vπ, and 1.05 Vπ/2, respectively; (i) ABC was on.
Fig. 12
Fig. 12 Measured EVM performance in (a) QPSK modulation and (b) 16-QAM modulation when the ABC was on and off.
Fig. 13
Fig. 13 Measured EVM performance versus temperature(a) and wavelength(b) when ABC was on and off, and the BER performance of 128 Gb/s optical DP-QPSK signal(c) when the proposed ABC and the manual control mode were applied respectively.

Tables (1)

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Table 1 Comparison of the proposed ABC scheme and other ABC schemes

Equations (40)

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E OUT_I/Q = 1 2 [ E IN_I/Q exp(j Δ ψ RF_I/Q 2 )+ E IN_I/Q exp(j Δ ψ RF_I/Q 2 )exp(jΔ ψ DC_I/Q ) ],
E OUT = 1 2 [ E OUT_I + E OUT_Q exp(jΔ ψ DC_P ) ],
Δ ψ DC_I/Q/P = V I/Q/P_SET 2 / R I/Q/P_SET V I/Q/P_πDC 2 / R I/Q/P_πDC π,
Δ ψ RF_I/Q =Δ ψ RF_I/Q_upper Δ ψ RF_I/Q_lower ,
Δ ψ NoneRF_I/Q_upper/lower = φ RF_I/Q_1 + φ RF_I/Q_2 V PN + φ RF_I/Q_3 V PN 2 + φ RF_I/Q_4 V PN 3 , Δ ψ RF_I/Q_upper = φ RF_I/Q_1 + φ RF_I/Q_2 ( V PN 1 2 V I/Q_RFSET )+ φ RF_I/Q_3 ( V PN 1 2 V I/Q_RFSET ) 2 + φ RF_I/Q_4 ( V PN 1 2 V I/Q_RFSET ) 3 Δ ψ NoneRF_I/Q_upper/lower ,
Δ ψ RF_I/Q_lower = φ RF_I/Q_1 + φ RF_I/Q_2 ( V PN + 1 2 V I/Q_RFSET )+ φ RF_I/Q_3 ( V PN + 1 2 V I/Q_RFSET ) 2 + φ RF_I/Q_4 ( V PN + 1 2 V I/Q_RFSET ) 3 Δ ψ NoneRF_I/Q_upper/lower .
Δ ψ RF_I/Q =( φ RF_I/Q_2 +2 φ RF_I/Q_3 V PN 3 φ RF_I/Q_4 V PN 2 ) V I/Q_RFSET 1 4 φ RF_I/Q_4 V I/Q_RFSET 3 .
E OUT_I/Q = E IN_I/Q exp[ -j πf( V I/Q_RFSET ) 2f( V I/Q_πRF ) ]+exp[ j( πf( V I/Q_RFSET ) 2f( V I/Q_πRF ) +π V I/Q_SET 2 V I/Q_πDC 2 ) ] 2 .
P OUT P max = 1 8 { 2+cos{ π[ V I_SET 2 / R I_SET V I_πDC 2 / R I_πDC + f( V I_RFSET ) f( V I_πRF ) ] }+cos{ π[ V Q_SET 2 / R Q_SET V Q_πDC 2 / R Q_πDC + f( V Q_RFSET ) f( V Q_πRF ) ] }+cos{ π[ V P_SET 2 / R P_SET V P_πDC 2 / R P_πDC + f( V I_RFSET ) 2f( V I_πRF ) f( V Q_RFSET ) 2f( V Q_πRF ) ] }+\ +cos{ π[ V Q_SET 2 / R Q_SET V Q_πDC 2 / R Q_πDC + V P_SET 2 / R P_SET V P_πDC 2 / R P_πDC + f( V I_RFSET ) 2f( V I_πRF ) + f( V Q_RFSET ) 2f( V Q_πRF ) ] }+cos{ π[ V P_SET 2 / R P_SET V P_πDC 2 / R P_πDC V I_SET 2 / R I_SET V I_πDC 2 / R I_πDC f( V I_RFSET ) 2f( V I_πRF ) f( V Q_RFSET ) 2f( V Q_πRF ) ] }+\ cos{ π[ V Q_SET 2 / R Q_SET V Q_πDC 2 / R Q_πDC V I_SET 2 / R I_SET V I_πDC 2 / R I_πDC + V P_SET 2 / R P_SET V P_πDC 2 / R P_πDC f( V I_RFSET ) 2f( V I_πRF ) + f( V Q_RFSET ) 2f( V Q_πRF ) ] } }.
sin[ f( V I/Q_RFSET ) f( V I/Q_πRF ) π ] = sin[ f( V I/Q_RFSET ) 2f( V I/Q_πRF ) π ] =0,
I OUT I max = 1 8 [ 2+cos(π V I_SET 2 V I_πDC 2 ) cos[ f( V I_RFSET ) f( V I_πRF ) π ] +cos(π V Q_SET 2 V Q_πDC 2 ) cos[ f( V Q_RFSET ) f( V Q_πRF ) π ] +\ { cos(π V P_SET 2 V P_πDC 2 )+cos(π V P_SET 2 V P_πDC 2 +π V Q_SET 2 V Q_πDC 2 )+cos(π V P_SET 2 V P_πDC 2 π V I_SET 2 V I_πDC 2 )+cos(π V P_SET 2 V P_πDC 2 +π V Q_SET 2 V Q_πDC 2 π V I_SET 2 V I_πDC 2 ) } cos[ f( V I_RFSET ) 2f( V I_πRF ) π ] cos[ f( V Q_RFSET ) 2f( V Q_πRF ) π ] ].
I OUT I max = 1 4 + I OUT_I I max + I OUT_Q I max + I OUT_P I max ,
F I ( V I_RFSET )= cos[ f( V I_RFSET ) f( V I_πRF ) π ] ,
F Q ( V Q_RFSET )= cos[ f( V Q_RFSET ) f( V Q_πRF ) π ] ,
F P ( V I_RFSET , V Q_RFSET )= cos[ f( V I_RFSET ) f( V I_πRF ) π 2 ] cos[ f( V Q_RFSET ) f( V Q_πRF ) π 2 ] ,
I OUT I max = 1 8 { 2+cos(π V I_SET 2 V I_πDC 2 ) F I ( V I_RFSET )+cos(π V Q_SET 2 V Q_πDC 2 ) F Q ( V Q_RFSET )+ F P ( V I_RFSET , V Q_RFSET )\ [ cos(π V P_SET 2 V P_πDC 2 )+cos(π V P_SET 2 V P_πDC 2 +π V Q_SET 2 V Q_πDC 2 )+cos(π V P_SET 2 V P_πDC 2 π V I_SET 2 V I_πDC 2 )+cos(π V P_SET 2 V P_πDC 2 +π V Q_SET 2 V Q_πDC 2 π V I_SET 2 V I_πDC 2 ) ] }.
E R m = ( 1+ G m 1- G m ) 2 , m{ I,Q,P },
α m = Δ ψ RF_m_upper +Δ ψ RF_m_lower Δ ψ RF_m_upper Δ ψ RF_m_lower ,m{ I,Q },
E OUT_I/Q = E IN_I/Q exp[ -j πf( V I/Q_RFSET )(1+ α I/Q ) 2f( V I/Q_πRF ) ]+ G I/Q exp[ j( πf( V I/Q_RFSET )(1- α I/Q ) 2f( V I/Q_πRF ) +π V I/Q_SET 2 V I/Q_πDC 2 ) ] 1+ G I/Q ,
E OUT = 1 1+ G P [ E OUT_I + G P E OUT_Q exp(jπ V P_SET 2 V P_πDC 2 ) ],
I OUT_I I max = 1 [ ( 1+G P ) 2 ( 1+G I ) 2 ] [ 1+ G I 2 +2G I cos(π V I_SET 2 V I_πDC 2 ) F I ( V I_RFSET ) ],
I OUT_Q I max = G P 2 [ ( 1+G P ) 2 ( 1+G Q ) 2 ] [ 1+ G Q 2 +2G Q cos(π V Q_SET 2 V Q_πDC 2 ) F Q ( V Q_RFSET ) ],
I OUT_P I max = 2 G P ( 1+G P ) 2 ( 1+G I )( 1+G Q ) [ F P ( V I_RFSET (1+ α I ), V Q_RFSET (1+ α Q ) )cos(π V P_SET 2 V P_πDC 2 )+\ G I F P ( V I_RFSET (1 α I ), V Q_RFSET (1+ α Q ) )cos(π V P_SET 2 V P_πDC 2 π V I_SET 2 V I_πDC 2 )+\ G Q F P ( V I_RFSET (1+ α I ), V Q_RFSET (1 α Q ) )cos(π V P_SET 2 V P_πDC 2 V Q_SET 2 V Q_πDC 2 )+\ G I G Q F P ( V I_RFSET (1 α I ), V Q_RFSET (1 α Q ) )cos(π V P_SET 2 V P_πDC 2 +π V Q_SET 2 V Q_πDC 2 π V I_SET 2 V I_πDC 2 ) ].
V I_null 2 k I +1+arcsin( G P (1+ G I )( cos[ f( V Q_RFSET ) f( V Q_πRF ) π 2 ] G Q cos[ f( V Q_RFSET ) f( V Q_πRF ) π 2 ] ) (1+ G Q ) G I cos[ f( V I_RFSET ) f( V I_πRF ) π 2 ] π ) V I_πDC ,
V Q_null 2 k Q +1+arcsin( (1+ G Q )( G I cos[ f( V I_RFSET ) f( V I_πRF ) π 2 ] - cos[ f( V I_RFSET ) f( V I_πRF ) π 2 ] ) G P G Q (1+ G I ) cos[ f( V Q_RFSET ) f( V Q_πRF ) π 2 ] π ) V Q_πDC ,
V P_quad = ( k P + 1 2 ) V P_πDC ,
V I_null 2 k I +1+arcsin( 2(1 G Q ) ( G Q +1)π ) V I_πDC ,
V Q_null 2 k Q +1+arcsin( 2( G I 1) ( G I +1)π ) V Q_πDC ,
V P_quad = ( k P + 1 2 ) V P_πDC .
V I/Q_Dither = V I/Q_SET 2 + P Dither sin( w I/Q t) ,
Δ V I/Q = V I/Q_SET V I/Q_πDC ,
Δ V P = V P_SET 2 2 V P_πDC .
I RFE1 =sin( w I (t+Δt)),
I REF2 =cos( w I (t+Δt)),
C I _SIN = 0 T ( F I ( V I_RFSET )cos(π ( V I_SET 2 + P Dither sin( w I t) ) 2 V I_πDC 2 )+{ cos[ π V P_SET 2 V P_πDC 2 π ( V I_SET 2 + P Dither sin( w I t) ) 2 V I_πDC 2 ]+\ cos[ π V P_SET 2 V P_πDC 2 V Q_SET 2 V Q_πDC 2 π ( V I_SET 2 + P Dither sin( w I t) ) 2 V I_πDC 2 ] } F P ( V I_RFSET , V Q_RFSET ) ) I REF1 dt ,
C I _COS = 0 T ( F I ( V I_RFSET )cos(π ( V I_SET 2 + P Dither sin( w I t) ) 2 V I_πDC 2 )+{ cos[ π V P_SET 2 V P_πDC 2 π ( V I_SET 2 + P Dither sin( w I t) ) 2 V I_πDC 2 ]+\ cos[ π V P_SET 2 V P_πDC 2 V Q_SET 2 V Q_πDC 2 π ( V I_SET 2 + P Dither sin( w I t) ) 2 V I_πDC 2 ] } F P ( V I_RFSET , V Q_RFSET ) ) I REF2 dt ,
P RFE1 =sin(2π( f I + f Q )(t+Δt)),
P RFE2 =cos(2π( f I + f Q )(t+Δt)).
C P_SIN = 0 T F P ( V I_RFSET , V Q_RFSET )cos[ π ( V Q_SET 2 + P Dither sin( w Q t) ) 2 V Q_πDC 2 +π V P_SET 2 V P_πDC 2 π ( V I_SET 2 + P Dither sin( w I t) ) 2 V I_πDC 2 ] P REF1 dt,
C P_COS = 0 T F P ( V I_RFSET , V Q_RFSET )cos[ π ( V Q_SET 2 + P Dither sin( w Q t) ) 2 V Q_πDC 2 +π V P_SET 2 V P_πDC 2 π ( V I_SET 2 + P Dither sin( w I t) ) 2 V I_πDC 2 ] P REF2 dt.

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