Abstract

In coherent optical communication systems, the transmitter usually employs an optical in-phase and quadrature (IQ) modulator to perform electrical-to-optical up-conversion. However, some environmental factors, such as temperature and mechanical stress, strongly influence the stability. To stabilize the quality of the transmitted signal, auto bias control (ABC) is essential to keep modulator in optimum bias. In this paper, we present a novel method of ABC for the optical orthogonal frequency division multiplexing (O-OFDM) signal. In the proposed scheme, a small cosine/sine wave dither signal is added on to the I/Q baseband signal, respectively. Based on the power monitoring of the 1st and 2nd harmonics of the dither signal, the biases of the optical IQ modulator for O-OFDM system can be adjusted very precisely. The simulation and experimental results show good performance on locating the optimum bias voltages for the IQ modulator with high precision.

©2013 Optical Society of America

1. Introduction

In the last decade, the attention of both academia and industry in high-capacity transmission shifted to coherent optical communication due to rapid advances in semiconductor technology and electronic digital signal processing (DSP) [13]. Along with the rapid development of coherent optical single carrier, coherent optical OFDM (CO-OFDM) received much attention due to its excellent performance and flexibility, and has been considered as a promising technology for the future long-haul transmission and dynamic optical networks [4]. The optical IQ modulator is a key component for generation of the optical signals in coherent optical transmission system. However, some environmental factors, such as temperature and mechanical vibration, strongly influence the stability of IQ modulator [5,6]. To maintain the long-term quality of the transmitted signal, ABC is essential to trace the optimum bias conditions. In [7,8], the ABC was based on an asymmetric dithering and has been employed to monitor and control the bias drifting of signal carriers modulated with QPSK and 16-QAM, respectively. Differential phase information could also be used to control the biases for single carrier modulation [9]. However, only a few publications on bias controlling for O-OFDM have been reported, in [10], Cho analyzed the statistics of output optical power to control the bias of OFDM modulated signal.

In this paper, we propose a novel ABC approach for O-OFDM as an extension of [10]. In [10], within a small range ( ± 10% of Vπ ) close to the optimum DC condition, the statistical analysis only offers a tiny distinguish ratio of the monitored power (< 0.5 dB). This may be a challenge for the practical implementation. In our proposed scheme, we add a small sine/cosine dither onto the OFDM I/Q signal. Based on the power monitoring of the 1st and 2nd harmonics of the dither signal, the bias of the optical IQ modulator for O-OFDM system can be finely controlled. A numerical simulation is first conducted to investigate the effect of the proposed bias control method. We then carry out a 10 Gb/s single-polarization CO-OFDM experiment to evaluate the system performance under the controlled bias condition. We will demonstrate that the proposed approach successfully enables us to control the system to the optimum bias condition with only negligible dithering penalty in the back-to-back configuration.

2. The principle of auto bias control technique

A typical ABC configuration for an optical IQ modulator is illustrated in Fig. 1. The IQ modulator comprises two parallel Mach–Zehnder modulators, with an I/Q phase shifter to define the phase difference of the two optical paths. In most of the current commercial optical IQ modulator, a photo-detector (PD) is integrated at the output end to detect a small proportion (usually ~5%) of the signal power. To monitor and control the biases, a low speed (tens of MHz) analog-to-digital converter (ADC) is employed to sample the detector signal. A digital signal processor (DSP) is then used to trace the optimum bias conditions. The calculated bias voltages are applied to the modulator after digital-to-analog conversion.

 figure: Fig. 1

Fig. 1 The auto bias control configuration.

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The output optical field Eo can be written as:

Eo=Ei2[cos(π2VI+Vbias,IVπ)+cos(π2VQ+Vbias,QVπ)ejϕIQ]
where, φIQ is the phase difference between the IQ branches, Vπ is the half-wave switching voltage, Vbias,I and Vbias,Q are the DC bias voltages for the real and imaginary components, respectively. The monitored electrical current of the coupled PD at the output end is proportional to the output optical power (ImPo = |Eo|2), given by [10]
Po=Pi8[2+cos(ϕI+ϕbias,I)+cos(ϕQ+ϕbias,Q)+4cos(ϕI+ϕbias,I)2cos(ϕQ+ϕbias,Q)2cosϕIQ]
Where φI(Q) = πVI(Q)/Vπ, φbias,I(Q) = πVbias,I(Q)/Vπ, and Pi denotes the input optical power Pi = |Ei|2.

To locate the optimum biases of the two MZM branches, we make the following obversions: biasing at the null point will suppress the optical carrier, and drive the RF signal in the most linear region of the IQ modulator; any drift from the null point will result a DC offset coupled onto the monitored electrical signal Im. Thus, we can monitor the power of the monitoring signal Im including both RF and DC components using an electrical low-pass filter, which we call ‘current power’ for brevity. Minimizing the current power by tuning the two biases suppresses the optical carrier, and forces the bias to the null point. Figure 2(a) shows the monitored current power as a function of both φbias,I and φbias,Q under the optimum φIQ. As shown in Fig. 2(a), for any given φbias,Q, we can minimize the current power to find the optimum φbias,I. Similarly, we can then find the optimum φbias,Q under the optimum φbias,I. With a few rounds of tracing, the current power can achieve the minimum value, which indicates the two bias voltages are optimized. To observe the detailed simulation results, we plot the relative current power as a function of φbias,I with varying φIQ and φbias,Q in the Fig. 2(b). Here, we define the distinguish ratio (DR) as the maximum current power variation in a specified range of biases. Within the range of |△φbias,I|≤0.1π, the DR is only 0.5 dB, where △φbias,I = φbias,I-φbias,I_optimum. As a result, φbias,I(Q) would be easily affected by the electrical noise or resolution inaccuracy of sampling [10]. also analyzed the bias voltage for φIQ using the variance of Im as a function of the phase shifter. Similarly, the optimum φIQ is hard to be precisely controlled.

 figure: Fig. 2

Fig. 2 The relative power as a function of (a)φbias,I and φbias,Q, (b)φbias,I with differentφbias,Q andφIQ.

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In order to achieve precisely bias control, a small cosine/sine dither signal is added onto the OFDM signal. Note that the frequency of dither signal fdith should be much smaller than the bandwidth of OFDM subcarriers. The detailed procedure of proposed ABC technique is described as following: I) We first monitor the minimum current power based on [10] to locate the biases in the range of ~0.1π. II) The optimum bias of φIQ is indicated by monitoring the overall minimum current power at the frequency of 2nd harmonic of dither signal. III) With numbers of iterations, the optimum bias ofφbias,I/Q can be estimated by monitoring the minimum current power at the frequency of 1st harmonic of dither signal. Next the fundamental and simulation results of proposed scheme will be introduced. The dither signal is expressed as Vdithcos(2πfditht) and Vdithsin(2πfditht) for the real and imaginary branches respectively, where Vdrift, I and Vdrift, Q are relatively small compared to Vπ. In such a configuration, the biased signal can be expressed as:

Vbias,I=Vπ+Vdrift,I+Vdithcos(ωditht)Vbias,Q=Vπ+Vdrift,Q+Vdithsin(ωditht)

In the practical implementation, the OFDM subcarriers close to DC are commonly padded with zero to avoid DC interference [11].The OFDM RF signal VI and VQ can be written as Eq. (4), note that 2fdith << fs:

VI(t)=2NscRe{ck}cos(2πfs(k1)t)VQ(t)=2NscIm{ck}sin(2πfs(k1)t)
First we set F1, F2 as following:
F1=2+cos(ϕI+ϕbias,I)+cos(ϕQ+ϕbias,Q)F2=4cos(ϕI+ϕbias,I2)cos(ϕQ+ϕbias,Q2)cosϕIQ
Then we substitute Eq. (3), Eq. (4) into F1, F2 and expand using a Taylor series expansion to second order, respectively:

F1(t)21+(ϕI+ϕbias,I+π)221+(ϕQ+ϕbias,Q+π)22=π2Vπ2(VI(t)+Vdrift,I+Vdithcos(2πfditht))22+π2Vπ2(VQ(t)+Vdrift,Q+Vdithsin(2πfditht))22=π22Vπ2(2Vdith[Vdrift,Icos(2πfditht)+Vdrift,Qsin(2πfditht)]+Vdith2+Vdrift,I2+Vdrift,Q2)+π22Vπ2(VI2(t)+VQ2(t)+2VI(t)(Vdrift,I+Vdithcos(2πfditht))+2VQ(t)(Vdrift,Q+Vdithsin(2πfditht)))
F2(t)=4sin(ϕI+ϕbias,I+π2)sin(ϕQ+ϕbias,Q+π2)cosϕIQ4(ϕI+ϕbias,I+π2)(ϕQ+ϕbias,Q+π2)cosϕIQ=π2(VI(t)+Vdrift,I+Vdithcos(2πfditht)VπVQ(t)+Vdrift,Q+Vdithsin(2πfditht)Vπ)cosϕIQ=π2Vπ2{Vdrift,IVdrift,Q+Vdith[Vdrift,Qcos(ωditht)+Vdrift,Isin(ωditht)]+0.5Vdith2cos(2ωditht)}cosϕIQ+π2Vπ2{VI(t)VQ(t)+VI(t)Vdithcos(2πfditht)+VI(t)Vdrift,I+VQ(t)Vdrift,Q+VQ(t)Vdithsin(2πfditht)}cosϕIQ

It can be proved that the cross terms including OFDM in Eq. (6) and Eq. (7) has negligible impact in the range of DC to fs-fdither. Because the frequency of dither signal fdither is much smaller than the subcarrier bandwidth fs, those cross terms can be digitally or electrically removed by employing a low-pass filter. Therefore, the F1 can be approximately express as:

F1(t)π22Vπ2{Vdrift,I2+Vdrift,Q2+Vdith2DCharmoniccomponent+2Vdith[Vdrift,Icos(2πfditht)+Vdrift,Qsin(2πfditht)]1stharmoniccomponent}
Analogously, the summation of the F2 can be also expressed as:

F2(t)π2Vπ2{Vdith[Vdrift,Qcos(2πfditht)+Vdrift,Isin(2πfditht)]1stharmoniccomponent+0.5Vdith2cos(4πfditht)2ndharmoniccomponent}cosϕIQ

Then we monitor the signal power of dither harmonics applying a low speed ADC operated at tens of megahertz. From Eq. (9), the signal contains 1st and 2nd harmonics of dither frequency at φIQ≠90°. The 2nd harmonic component only vanishes when φIQ equals to 90°. Similarly, according to the Eq. (8) the 1st harmonic component vanishes when Vdrift, I and Vdrift, Q equal to zero. Thus, within the 0.1π range based on [10], we are able to control the three bias voltages just by monitoring the RF power of 1st and 2nd harmonic components. The first step is to tuneφIQ to the optimum, which can be achieved by monitoring the power of 2nd harmonic component of dither signal using a narrow band pass filter. Minimizing this power will lead φIQ to 90°.

Figure 3 shows the power of the 2nd harmonic component at the frequency of 2fdith versusφIQ of differentφbias,I(Q). As shown in the figure, the 2nd harmonic component power reaches the minimum value whenφIQ equals to π/2 with any settings of φbias,I(Q). The DR within the range of |△φIQ|≤0.1π is larger than 15dB. Such a high DR signifies that the optimum bias can be accurately set.

 figure: Fig. 3

Fig. 3 The power of the 2nd harmonic vs.φIQ with differentφbias,I andφbias,Q;

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Figure 4(a) shows the power of the 1st harmonic component as a function ofφbias,I and φbias,Q, whereφIQ = π/2. The power of 1st harmonic component reaches the minimum when both ofφbias,Q andφbias,I are optimum. Figure 4(b) shows the power of the 1st harmonic component as a function ofφbias,I with certain values of △φbias,Q. From the Fig. 4(b) we find that the performance of proposed technique is dependent on the resolution of the adjusted bias votages provided by the DACs. For instance, DR is only 5 dB with resolution of 0.02π whereas DR of 17 dB can be achieved with resolution of 0.001π. Currently many commercialized DACs have a resolution up to 16 bits, which can give a tracking resolution of 2π/2^16 = 0.00003π. With such resolution the DR within range of |△φbias,I|≤0.1π is more than 20 dB. With a few iterations of tracing the minimum power, we can readily find and control the biasφbias,I(Q) to be close to the optimum.

 figure: Fig. 4

Fig. 4 The power of (a) the 1st harmonic versusφbias,I andφbias,Q, (b) the 1st harmonic component versusφbias,I.

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3. Experimental setup and results

A coherent optical OFDM back-to-back experiment is conducted to evaluate proposed ABC scheme. Figure 5 shows the experimental setup. The OFDM signal with 4-QAM mapping along with the dither signal (10MHz) is first offline generated with 4-QAM mapping, and then uploaded into a Tektronix arbitrary waveform generator (AWG) 7122B, operated at 10GS/s. The OFDM baseband signal is constructed with 80 subcarriers. The fast Fourier transform (FFT) size is 128. Two subcarriers are used to estimate the phase noise. 1/8 of the symbol period is used for cyclic prefix. The information rate is 10.6 Gb/s. The middle two sub-carriers are set to zero to avoid DC interference. The RF signal is fed into an optical IQ modulator (Suimitomo, T.SBX1.5-10-P-FA) to perform electrical-to-optical up-conversion. The half-wave switching voltage for the modulator used in the experiment is 5.8V. A typical coherent receiver is used to detect the optical signal. The received base band signal is digitized by a real-time scope operated at 12.5 GS/s. In the digital signal processing, we use a digital band-pass filter with a bandwidth of 1MHz to remove other frequency components, in order to monitor the RF power which only includes the 1st or 2nd harmonic component.

 figure: Fig. 5

Fig. 5 Experimental setup for evaluation the proposed auto bias control technique.

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Figure 6 shows the electrical current power as a function of one MZM bias voltage (△φbias,I). The φIQ is set to π/2. There exists a power floor of the monitored RF power in the region close to the optimum bias, which matches well with the simulation results in Fig. 2. Some local minimum points can be found in the experiment, which is mainly due to the electrical/optical noise and the quantization error of ADC when detecting the small signal. However, by tracking the minimum current power in large variation range ofφbias,I and φbias,Q with sufficient DAC resolution we can locate the biases in the range of 0.1π close to optimum.

 figure: Fig. 6

Fig. 6 The current power as a function of △φbias,I.

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Then, we add the dither signal onto transmitted signal, in which the frequency is 10 MHz, and the amplitude is 10% to the OFDM subcarrier. The insets of Fig. 7 show the electrical spectrum after PD. WhenφIQ = π/2, the 2nd harmonic component (~20MHz) vanishes. Hence, minimizing the 2nd harmonic component power will directly lead φIQ to π/2. The DR is as high as ~13 dB.

 figure: Fig. 7

Fig. 7 The 2nd harmonic component power as a function of △φIQ

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Figure 8 shows the power of the 1st harmonic component as a function of φbias,I, where φbias,Q and φIQ are set to optimum voltages. Similarly, the 1st harmonic component vanishes when φbias,I reaches to the optimum point. The DR is up to 16 dB when |△φbias,I|≤0.05π (where the range of 0.29 V). The experimental results are well in agreement with the simulation results discussed in section 2.

 figure: Fig. 8

Fig. 8 The 1st harmonic power as a function of φbias,I

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Furthermore, to evaluate the influence of the dither signal, we conduct a bit error ratio (BER) against OSNR measurement with and without dither signal in a back-to-back measurement, which is shown in Fig. 9. The theoretical required OSNR for the BER of 10−3 is ~3 dB. The required OSNRs with and without dither signal are 5.0 dB and 4.8 dB, respectively. The tiny difference is mainly due to additional power of the dithering signal. The inset shows 4-QAM constellation measured at high OSNR (~6 dB/0.1nm) under the dynamically tracked optimum biases.

 figure: Fig. 9

Fig. 9 The BER performance of a 10.6 Gb/s OFDM signals with and without dither signal

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4. Conclusions

In this paper, we propose a novel ABC technique for O-OFDM based on power monitoring of 1st and 2nd harmonics of dither signals. The proposed scheme is easy to be implemented with low-speed optoelectronic devices. The theoretical analysis is given to illustrate the principle of the proposed scheme. The simulation and experiment results show good performance of an I/Q modulator with its biases set optimally according to the proposed scheme.

Acknowledgment

This work was supported by the National Basic Research (973) Program of China (2010CB328300), and 863 Program of China (2012AA011302). We also thank Dr. Henning Buelow from Bell Labs in Stuttgart for helpful discussion.

References and links

1. G. Li, “Recent advances in coherent optical communication,” Adv. Opt. Photon. 1(2), 279–307 (2009). [CrossRef]  

2. I. B. Djordjevic and B. Vasic, “Orthogonal frequency division multiplexing for high-speed optical transmission,” Opt. Express 14(9), 3767–3775 (2006). [CrossRef]   [PubMed]  

3. W. Shieh and C. Athaudage, “Coherent optical orthogonal frequency division multiplexing,” Electron. Lett. 42(10), 587–589 (2006). [CrossRef]  

4. W. Shieh, H. Bao, and Y. Tang, “Coherent optical OFDM: theory and design,” Opt. Express 16(2), 841–859 (2008). [CrossRef]   [PubMed]  

5. T. Sugihara, T. Yoshida, and K. Ishida, “Effect of Modulator Bias Control in the Presence of a Finite Extinction Ratio in DQPSK Pre-equalization Systems,” J. Lightwave Technol. 29(15), 2235–2248 (2011).

6. 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 Proc. of OFC (2007), Paper. OTuH5.

7. H. Kawakami, E. Yoshida, and Y. Miyamoto, “Asymmetric dithering technique for bias condition monitoring in optical QPSK modulator,” Electron. Lett. 46(6), 430–431 (2010). [CrossRef]  

8. H. Kawakami, T. Kobayashi, E. Yoshida, and Y. Miyamoto, “Auto bias control technique for optical 16-QAM transmitter with asymmetric bias dithering,” Opt. Express 19(26), B308–B312 (2011). [CrossRef]   [PubMed]  

9. H. Choi, Y. Takushima, H. Y. Choi, J. H. Chang, and Y. C. Chung, “Modulation-Format-Free Bias Control Technique for MZ Modulator Based on Differential Phasor Monitor,” in Proc. of OFC (2011), Paper. JWA033.

10. P. S. Cho and M. Nazarathy, “Bias control for optical OFDM transmitters,” IEEE Photon. Technol. Lett. 22(14), 1030–1032 (2010). [CrossRef]  

11. Q. Yang, Y. Ma, and W. Shieh, “107 Gb/s Coherent Optical OFDM Reception Using Orthogonal Band Multiplexing,” in Proc. of OFC (2008), Paper. PDP7.

References

  • View by:

  1. G. Li, “Recent advances in coherent optical communication,” Adv. Opt. Photon. 1(2), 279–307 (2009).
    [Crossref]
  2. I. B. Djordjevic and B. Vasic, “Orthogonal frequency division multiplexing for high-speed optical transmission,” Opt. Express 14(9), 3767–3775 (2006).
    [Crossref] [PubMed]
  3. W. Shieh and C. Athaudage, “Coherent optical orthogonal frequency division multiplexing,” Electron. Lett. 42(10), 587–589 (2006).
    [Crossref]
  4. W. Shieh, H. Bao, and Y. Tang, “Coherent optical OFDM: theory and design,” Opt. Express 16(2), 841–859 (2008).
    [Crossref] [PubMed]
  5. T. Sugihara, T. Yoshida, and K. Ishida, “Effect of Modulator Bias Control in the Presence of a Finite Extinction Ratio in DQPSK Pre-equalization Systems,” J. Lightwave Technol. 29(15), 2235–2248 (2011).
  6. 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 Proc. of OFC (2007), Paper. OTuH5.
  7. H. Kawakami, E. Yoshida, and Y. Miyamoto, “Asymmetric dithering technique for bias condition monitoring in optical QPSK modulator,” Electron. Lett. 46(6), 430–431 (2010).
    [Crossref]
  8. H. Kawakami, T. Kobayashi, E. Yoshida, and Y. Miyamoto, “Auto bias control technique for optical 16-QAM transmitter with asymmetric bias dithering,” Opt. Express 19(26), B308–B312 (2011).
    [Crossref] [PubMed]
  9. H. Choi, Y. Takushima, H. Y. Choi, J. H. Chang, and Y. C. Chung, “Modulation-Format-Free Bias Control Technique for MZ Modulator Based on Differential Phasor Monitor,” in Proc. of OFC (2011), Paper. JWA033.
  10. P. S. Cho and M. Nazarathy, “Bias control for optical OFDM transmitters,” IEEE Photon. Technol. Lett. 22(14), 1030–1032 (2010).
    [Crossref]
  11. Q. Yang, Y. Ma, and W. Shieh, “107 Gb/s Coherent Optical OFDM Reception Using Orthogonal Band Multiplexing,” in Proc. of OFC (2008), Paper. PDP7.

2011 (2)

2010 (2)

P. S. Cho and M. Nazarathy, “Bias control for optical OFDM transmitters,” IEEE Photon. Technol. Lett. 22(14), 1030–1032 (2010).
[Crossref]

H. Kawakami, E. Yoshida, and Y. Miyamoto, “Asymmetric dithering technique for bias condition monitoring in optical QPSK modulator,” Electron. Lett. 46(6), 430–431 (2010).
[Crossref]

2009 (1)

2008 (1)

2006 (2)

I. B. Djordjevic and B. Vasic, “Orthogonal frequency division multiplexing for high-speed optical transmission,” Opt. Express 14(9), 3767–3775 (2006).
[Crossref] [PubMed]

W. Shieh and C. Athaudage, “Coherent optical orthogonal frequency division multiplexing,” Electron. Lett. 42(10), 587–589 (2006).
[Crossref]

Athaudage, C.

W. Shieh and C. Athaudage, “Coherent optical orthogonal frequency division multiplexing,” Electron. Lett. 42(10), 587–589 (2006).
[Crossref]

Bao, H.

Cho, P. S.

P. S. Cho and M. Nazarathy, “Bias control for optical OFDM transmitters,” IEEE Photon. Technol. Lett. 22(14), 1030–1032 (2010).
[Crossref]

Djordjevic, I. B.

Ishida, K.

Kawakami, H.

H. Kawakami, T. Kobayashi, E. Yoshida, and Y. Miyamoto, “Auto bias control technique for optical 16-QAM transmitter with asymmetric bias dithering,” Opt. Express 19(26), B308–B312 (2011).
[Crossref] [PubMed]

H. Kawakami, E. Yoshida, and Y. Miyamoto, “Asymmetric dithering technique for bias condition monitoring in optical QPSK modulator,” Electron. Lett. 46(6), 430–431 (2010).
[Crossref]

Kobayashi, T.

Li, G.

Miyamoto, Y.

H. Kawakami, T. Kobayashi, E. Yoshida, and Y. Miyamoto, “Auto bias control technique for optical 16-QAM transmitter with asymmetric bias dithering,” Opt. Express 19(26), B308–B312 (2011).
[Crossref] [PubMed]

H. Kawakami, E. Yoshida, and Y. Miyamoto, “Asymmetric dithering technique for bias condition monitoring in optical QPSK modulator,” Electron. Lett. 46(6), 430–431 (2010).
[Crossref]

Nazarathy, M.

P. S. Cho and M. Nazarathy, “Bias control for optical OFDM transmitters,” IEEE Photon. Technol. Lett. 22(14), 1030–1032 (2010).
[Crossref]

Shieh, W.

W. Shieh, H. Bao, and Y. Tang, “Coherent optical OFDM: theory and design,” Opt. Express 16(2), 841–859 (2008).
[Crossref] [PubMed]

W. Shieh and C. Athaudage, “Coherent optical orthogonal frequency division multiplexing,” Electron. Lett. 42(10), 587–589 (2006).
[Crossref]

Sugihara, T.

Tang, Y.

Vasic, B.

Yoshida, E.

H. Kawakami, T. Kobayashi, E. Yoshida, and Y. Miyamoto, “Auto bias control technique for optical 16-QAM transmitter with asymmetric bias dithering,” Opt. Express 19(26), B308–B312 (2011).
[Crossref] [PubMed]

H. Kawakami, E. Yoshida, and Y. Miyamoto, “Asymmetric dithering technique for bias condition monitoring in optical QPSK modulator,” Electron. Lett. 46(6), 430–431 (2010).
[Crossref]

Yoshida, T.

Adv. Opt. Photon. (1)

Electron. Lett. (2)

W. Shieh and C. Athaudage, “Coherent optical orthogonal frequency division multiplexing,” Electron. Lett. 42(10), 587–589 (2006).
[Crossref]

H. Kawakami, E. Yoshida, and Y. Miyamoto, “Asymmetric dithering technique for bias condition monitoring in optical QPSK modulator,” Electron. Lett. 46(6), 430–431 (2010).
[Crossref]

IEEE Photon. Technol. Lett. (1)

P. S. Cho and M. Nazarathy, “Bias control for optical OFDM transmitters,” IEEE Photon. Technol. Lett. 22(14), 1030–1032 (2010).
[Crossref]

J. Lightwave Technol. (1)

Opt. Express (3)

Other (3)

H. Choi, Y. Takushima, H. Y. Choi, J. H. Chang, and Y. C. Chung, “Modulation-Format-Free Bias Control Technique for MZ Modulator Based on Differential Phasor Monitor,” in Proc. of OFC (2011), Paper. JWA033.

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 Proc. of OFC (2007), Paper. OTuH5.

Q. Yang, Y. Ma, and W. Shieh, “107 Gb/s Coherent Optical OFDM Reception Using Orthogonal Band Multiplexing,” in Proc. of OFC (2008), Paper. PDP7.

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Figures (9)

Fig. 1
Fig. 1 The auto bias control configuration.
Fig. 2
Fig. 2 The relative power as a function of (a)φbias,I and φbias,Q, (b)φbias,I with differentφbias,Q andφIQ.
Fig. 3
Fig. 3 The power of the 2nd harmonic vs.φIQ with differentφbias,I andφbias,Q;
Fig. 4
Fig. 4 The power of (a) the 1st harmonic versusφbias,I andφbias,Q, (b) the 1st harmonic component versusφbias,I.
Fig. 5
Fig. 5 Experimental setup for evaluation the proposed auto bias control technique.
Fig. 6
Fig. 6 The current power as a function of △φbias,I.
Fig. 7
Fig. 7 The 2nd harmonic component power as a function of △φIQ
Fig. 8
Fig. 8 The 1st harmonic power as a function of φbias,I
Fig. 9
Fig. 9 The BER performance of a 10.6 Gb/s OFDM signals with and without dither signal

Equations (9)

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E o = E i 2 [cos( π 2 V I + V bias,I V π )+cos( π 2 V Q + V bias,Q V π ) e j ϕ IQ ]
P o = P i 8 [ 2+cos( ϕ I + ϕ bias,I )+cos( ϕ Q + ϕ bias,Q )+4cos ( ϕ I + ϕ bias,I ) 2 cos ( ϕ Q + ϕ bias,Q ) 2 cos ϕ IQ ]
V bias,I = V π + V drift,I + V dith cos( ω dith t) V bias,Q = V π + V drift,Q + V dith sin( ω dith t)
V I (t)= 2 N sc Re{ c k }cos( 2π f s (k1)t ) V Q (t)= 2 N sc Im{ c k }sin( 2π f s (k1)t )
F 1 =2+cos( ϕ I + ϕ bias,I )+cos( ϕ Q + ϕ bias,Q ) F 2 =4cos( ϕ I + ϕ bias,I 2 )cos( ϕ Q + ϕ bias,Q 2 )cos ϕ IQ
F 1 (t)21+ ( ϕ I + ϕ bias,I +π ) 2 2 1+ ( ϕ Q + ϕ bias,Q +π ) 2 2 = π 2 V π 2 ( V I (t)+ V drift,I + V dith cos(2π f dith t) ) 2 2 + π 2 V π 2 ( V Q (t)+ V drift,Q + V dith sin(2π f dith t) ) 2 2 = π 2 2 V π 2 ( 2 V dith [ V drift,I cos(2π f dith t)+ V drift,Q sin(2π f dith t) ]+ V dith 2 + V drift,I 2 + V drift,Q 2 ) + π 2 2 V π 2 ( V I 2 (t)+ V Q 2 (t)+2 V I (t)( V drift,I + V dith cos(2π f dith t) )+2 V Q (t)( V drift,Q + V dith sin(2π f dith t)) )
F 2 (t)=4sin( ϕ I + ϕ bias,I +π 2 )sin( ϕ Q + ϕ bias,Q +π 2 )cos ϕ IQ 4( ϕ I + ϕ bias,I +π 2 )( ϕ Q + ϕ bias,Q +π 2 )cos ϕ IQ = π 2 ( V I (t)+ V drift,I + V dith cos(2π f dith t) V π V Q (t)+ V drift,Q + V dith sin(2π f dith t) V π )cos ϕ IQ = π 2 V π 2 { V drift,I V drift,Q + V dith [ V drift,Q cos( ω dith t)+ V drift,I sin( ω dith t)]+0.5 V dith 2 cos(2 ω dith t)}cos ϕ IQ + π 2 V π 2 { V I (t) V Q (t)+ V I (t) V dith cos(2π f dith t)+ V I (t) V drift,I + V Q (t) V drift,Q + V Q (t) V dith sin(2π f dith t)}cos ϕ IQ
F 1 (t) π 2 2 V π 2 { V drift,I 2 + V drift,Q 2 + V dith 2 DC harmonic component + 2 V dith [ V drift,I cos(2π f dith t)+ V drift,Q sin(2π f dith t) ] 1 st harmonic component }
F 2 (t) π 2 V π 2 { V dith [ V drift,Q cos(2π f dith t)+ V drift,I sin(2π f dith t) ] 1 st harmonic component + 0.5 V dith 2 cos(4π f dith t) 2 nd harmonic component }cos ϕ IQ

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