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Abstract
An innovative approach has been proposed for adaptive bias control in optical IQ modulators. In contrast to traditional approaches that utilize sine dither, this method employs a linear frequency modulated (LFM) signal as the dither, associated with the fractional Fourier Transform (FrFT) to extract the bias point drift. The LFM signal, after undergoing FrFT, transforms into a compressed signal (CS) with energy concentration in the fractional domain. Utilizing this signal for bias point monitoring, the proposed method demonstrates robust bias control even in the presence of substantial interferences, as substantiated by comprehensive simulations and experimental investigations. Remarkably, in a 20-Gbaud 16QAM signal transmission, the proposed approach achieves stable control of the bias point for over 4 hours, even in the presence of voltage fluctuations, while effectively reducing the dither amplitude by half. Furthermore, it maintains a low bit error rate (BER) below 10−5 even under intentional external interference.
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1. Introduction
The exponential increase in internet traffic has created a pressing need for expanding capacity. In this context, coherent optical communication has emerged as an indispensable approach to meet this demand, owing to its exceptional spectral efficiency and advantages in coherent reception [1]. Within coherent optical communication systems, the optical IQ modulator is necessary in the electro-optic conversion of advanced modulation formats [2]. The bias point of the optical IQ modulator holds utmost significance in ensuring the performance of the optical transmitter [3]. However, in practical implementations, the bias point inevitably drifts due to the environmental factors such as temperature fluctuations and mechanical stresses [4], which significantly compromise the performance of the optical transmitter.
In recent years, there has been extensive research focusing on bias control in optical IQ modulators [5]. The earlier approaches directly monitor the output power of the modulators [6,7]. However, its accuracy dramatically diminishes in the presence of the laser power fluctuation or the modulation of communication signals. Thus, the bias control utilizing a sine dither at the bias input port of optical IQ modulators is proposed. Associated with the Fast Fourier Transform (FFT) analysis [8–10] or correlation operations [11–13], it can extract the bias state from the harmonic components of the collected dither. However, this method encounters challenges when noises obscure the second harmonic generated by the lower sine dither. Furthermore, under this approach, the bias control characteristics sometimes exhibit variations in response to changes in communication signal power. Additionally, the bias drift in the phase (P) channel has an unignorable impact on the bias control of in-phase (I) and quadrature (Q) channels. These issues greatly restrict the precise control in fast-changing environmental conditions. Notable advancements include dither vector mapping [14] and bias control techniques based on neural networks [15]. Although these methods made progress in algorithm complexity and control accuracy, considering the needs of actual communication systems, they still cannot replace the traditional sine dither scheme.
At present, the bias control method using sine dither has become the majority choice for its appropriate control precision and system complexity. This method can basically meet the bias control requirements of many experiments. As communication scenarios become increasingly diverse and communication environments become more complex, it has been found that there are still many problems in the inspection of various communication systems with different requirements. Firstly, the second harmonic of the sine dither is too weak, which is easily affected by the power fluctuation of the communication signal, leading to a decrease in bias control accuracy or failure; while higher dither power can have an impact on the communication signal. Secondly, the bias control of the I and Q channels is related to the state of the P channel bias point, which means it must be ensured that no drift is in the P channel to precisely control the I and Q channel bias points . However, when environmental conditions change, it is difficult to quickly determine and correct the drift of the bias point. These issues make this method using sine dither unsuitable for communication scenarios with arbitrary communication signal power, large signal power fluctuations, and rapid changes in environmental conditions. To further improve the robustness of bias control, on one hand, it is necessary to enhance the anti-interference ability of the dither with weak power. On the other hand, it is urgent to develop independent control of each channel, for wide range application in optical communication systems especially with various communication signal power.
In this paper, we propose a bias control method for optical IQ modulators using linear frequency modulated (LFM) signal as the dither. LFM can be obtained by performing fractional Fourier transform (FrFT) on direct-current (DC), while applying FrFT of a specified order on LFM can transform it into a compressed signal (CS) [16]. FrFT is a generalization of the traditional Fourier transform, it can transform a signal into a domain where both time and frequency information are mixed in a fractional manner [17]. Therefore, the FrFT provides an effective tool for the intuitive analysis and process of LFM signals. The peak of the CS generated by applying FrFT to the LFM signal serves as the monitoring parameter for the bias point drift in I and Q channels, as well as for monitoring P channel using the peak power of the CS generated by performing FrFT on LFM signal harmonics [18]. This approach not only enables precise bias control but also significantly reduces the requirements on dither power. Additionally, the bias control on each channel of I, Q, and P is hardly influenced by the bias drift from other two channels. Even under a strong interference from voltage fluctuations, the proposed method exhibits a high-performance bias control, demonstrating its remarkable robustness and superior applicability for various application scenarios. To evaluate the effectiveness of this method, we constructed a 20-GBaud 16QAM back-to-back experiment. By employing our approach, long-term stable transmission is achieved even under a voltage swing up to ±3 V, while the average amplitude of the employed dither signal is only 0.16 V, which is lower to a half compared to previous studies.
2. Principle and simulation
Figure 1 illustrates the procedure for generating, and processing LFM dithers in the proposed method, where ${V_{BI}}$, ${V_{BQ}}$, and ${V_{BP}}$ represent the DC bias voltages of I, Q, and P channels, respectively, while ${V_{SI}}$ and ${V_{SQ}}$ are the communication signal voltages of I and Q channels, respectively. The LFM dither is generated through the application of P-order FrFT on a DC signal. The real part of the LFM dither is applied to I channel of the optical IQ modulator, along with the DC bias voltage. Similarly, the imaginary part of the LFM dither, together with DC bias voltage, are applied to Q channel of the optical IQ modulator. The received signal at the output end of the optical IQ modulator is processed using FrFT with the optimal order of 1-P [19] to generate a CS. The peak of the CS is monitored for bias point drift tracking.
The LFM dithers in the above figure can be written as
where A is the amplitude of the LFM dithers, ${\varphi _0}$ is initial phases of the two LFM dithers, k denotes the frequency tuning rate. The relationship between the order P of FrFT transformation and k can be expressed asWhen communication signals are not considered, the transmission function of an optical IQ modulator can be expressed as
The derived formula above indicates that the bias drift in each channel of I, Q, and P has an impact on the output power of CS signal. Bias control methods for each channel will be explored by following simulations.
Firstly, we investigate the relationship between the peak power of the CS and the bias point drift of I and Q channels. In this simulation, it is assumed that the bias point of P channel remains in an optimal state with a phase of ${\pi / 2}$. When studying on I (Q) channel, we assume that the other channel remains in the optimal bias point. The LFM dither, depicted in Fig. 1, is loaded to the bias input port with an average voltage approximately equal to 3% of the half-wave voltage of the modulator. The FrFT order P of the generated LFM dither is set to 0.5. The target bias point for both I and Q channels is the null point. Figure 2 illustrates the CS response under specific bias drift conditions in I and Q channels. Considering that the half-wave voltage of IQ modulator in the simulation is around 8 V, the presented drift range in Fig. 2 is set to fall within the range of ±2 V. It is evident that there is a positive correlation between the peak power of the CS and the absolute value of the bias point drift.
Subsequently, we investigate the fundamental relationship between the drift of I and Q bias points and the peak power of the CS, where no bias point drift is introduced in P channel. Figure 3 presents the variation of the CS peak with respect to both I and Q channel drifts. Notably, an increase in either I or Q channel drift leads to a increase in the peak power. Thus, by locking the CS peak power to the minimum point, the bias of I and Q channels can be controlled at the null points for modulations.
Equation (6) demonstrates the generation of LFM dither with higher tuning rates through the transmission of LFM dither via optical IQ modulator. However, as LFM dither with higher tuning rates is relatively weak, our focus lies on second harmonic of the tuning rate dither (2nd dither) with its corresponding CS peak (2nd peak). We next investigate the relationship between the 2nd peak and the drift in the bias point of P channel.
According to Eq. (3), when the FrFT order of input LFM dither is set to 0.5, the optimal transformation order for FrFT with a 2nd dither is determined to be 0.705. The simulation results illustrate the CS signal after FrFT with a 2nd dither under varying degrees of bias point drift in P channel, as depicted in Fig. 4. The figure clearly reveals prominent peaks in the CS of the 2nd dither, further affirming the presence of 2nd dither, which aligns with the derived formula.
Figure 5(a) shows the variation of the 2nd peak with the drift bias point of P channel. Comparing with Fig. 5(b) to Fig. 5(e), it has been demonstrated that ideal 2nd peak curve can only be achieved when the LFM dither order P is set to 0.5, and the real and imaginary values of the LFM dither are respectively applied to I and Q channels. This results in a symmetric curve centered around the zero-drift point of P channel, with the minimum value obtained at the optimal bias point. These settings are carefully chosen to enhance the characteristics of the P bias points for feedback control.
Fig. 5. Curve of 2nd peak power changing with P channel bias point drift at different LFM dither. (a) Order P = 0.5, real part of LFM to I channel and imag part to Q channel, (b) Order P = 0.2, real part of LFM to I channel and imag part to Q channel, (c) Order P = 0.8, real part of LFM to I channel and imag part to Q channel, (d) Order P = 0.5, real part of LFM to both I channel and Q channel, (e) Order P = 0.5, imag part of LFM to both I channel Q channel.
The aforementioned simulation illustrates the principle of the bias control for I, Q and P channel respectively, where the investigation is conducted assuming the other channels at their ideal states. However, in practical scenarios, multiple channels generally experience bias point drift simultaneously. The following simulation aims to demonstrate the mutual influence between the bias control of I, Q and P channels. Due to the highly similar characteristics between I and Q channels, simulation results are only represented by I channel. Figure 6(a) illustrates the CS peak power in response to I channel drift under different bias point drifts of P channel, while Fig. 6(b) shows the 2nd peak power as a function of P channel drift under different bias point drifts of I channel.
Fig. 6. (a) Interference of P channel on monitoring I channel bias point drift ;(b) Interference of I channel on monitoring P channel bias point drift.
Figure 6 demonstrates that in our bias control approach, monitoring the CS peak power to regulate the bias point position of I or Q channel is trivially affected by the drift of P channel bias point. Additionally, under different drift of I channel, the 2nd peak power consistently reaches its minimum when there is no drift in P channel. Hence, it can be concluded that the proposed approach exhibits ignorable interference among the bias controls of each channel, allowing for flexible adjustment of the sequence of channel bias control and adaptivity in response to environmental changes.
Figure 7 display the specifical bias control process based on the above simulation results. Firstly, a rough estimation of the bias point positions in I and Q channels is carried out through direct detection of feedback power, without applying any dither. The bias point of P channel is temporarily set to an empirical value of approximately 2.5 V. Subsequently, the precise determination of the bias point positions in I, Q, and P channels is performed by applying LFM dither. The bias points in I and Q channels are initially determined by monitoring the CS peak, followed by the determination of P channel bias point by monitoring the 2nd peak. Finally, real-time monitoring of the drift in the bias points of all three channels is conducted, and timely corrections are made, as is illustrated in Fig. 7.
3. Experimental setup and results
Figure 8 shows the structure of the automatic bias control (ABC) module in this scheme. The feedback optical signal is first converted into a voltage signal by the photodetector (PD) and transimpedance amplifier (TIA), and then sampled into a digital signal through an analog-to-digital converter (ADC). The core processing unit of the ABC module is a digital signal processing chip (TMS320C6748), which consists of three steps: FrFT computation, bias point determination, and generation of bias voltage together with dither. Finally, the processed voltages are outputted to the optical IQ modulator in the form of analog signals through a digital-to-analog converter (DAC).
Figure 9 presents a self-coherent communication experimental system employed to test our bias control scheme. For the sake of simplifying the experimental devices and intuitively observing the effect of ABC, only the system of single-polarization is considered in the following experiments. A laser operating at a central wavelength of 1550 nm emits 20 mW of light, which is divided into the signal channel and the local oscillator channel using a 50:50 coupler. An arbitrary waveform generator (AWG) generates a 20 GBaud 16QAM signal, which is modulated onto the optical carrier using an optical IQ modulator with a half-wave voltage of approximately 5 V. The ABC module generates a DC bias voltage applied to the DC ports of I, Q and P channels and a low-frequency LFM dither with a maximum frequency below 800 Hz applied to I and Q channels. A coupler directs 5% of the output light from the optical IQ modulator back to the ABC module for bias point monitoring and updating of the DC bias voltage. The remaining 95% of the output light is detected by an optical power meter at the receiving end, while the signal is acquired using an 80 Gbps integrated coherent receiver (ICR) for subsequent offline digital signal processing (DSP) analysis of the transmission quality.
Figure 10 shows the results of the experimental test on the relationship between CS peak power and bias drift. The results validate the simulation conclusions depicted in Fig. 2 and Fig. 4. It can be observed that in the experiment, the variations of the CS peak with respect to the drift of I and Q channel bias points, as well as the variations of the 2nd peak with respect to the drift of P channel bias point, are in consist with those observed in the simulations. This further validates the bias control principle employed in this method. The slight difference between Fig. 10 and Fig. 2, Fig. 4, is due to the fact that the single LFM dither sequence in the experiment is half shorter than the simulation sequence to reduce the computational complexity of the DSP chip. Nevertheless, sufficient accuracy of the bias control can still be maintained.
Fig. 10. Experimental measurement of CS peak variation with (a) I-channel and (b) Q-channel bias points, and (c) 2nd CS variation with P-channel bias point.
Figure 11 demonstrates the bias point searching capability of the proposed scheme under different levels of voltage fluctuation. In this experiment, communication signals of different amplitudes are applied to the signal port of the optical IQ modulator to generate power fluctuations. For comparison, the bias control performance using the power direct detection method under the same conditions is also shown. From the figure, it can be observed that our proposed scheme significantly suppresses the optical power in the signal channel to below −35 dBm. This close-to-extinction result indicates its correct control effect. In the absence of voltage fluctuation, the optical power of our proposed scheme is nearly 15 dB lower than that of the power direct detection method. Although there is a slight increase in optical power with the application of communication signal, our scheme still shows ideal bias control performance under ±4 V of signal amplitude, demonstrating its excellent fluctuation resistance.
The subsequent experiments are conducted to validate impact of average amplitude of applied dither on the effectiveness of bias control. In this context, the extinction ratio is defined as the ratio between the received power and input power (approximately 10 dBm) of the modulator at the signal channel. To comprehensively assess the resilience to fluctuation, Fig. 12 presents the calculated extinction ratio for different LFM dither voltages and fluctuation levels, as well as the ideal result of 53.5 dB obtained by manual method with the bias accuracy of 0.01 V. It is observed that even with extremely low power of LFM dither and high intensity of fluctuation interference, the bias point positions can still be accurately identified. For instance, under an average dither voltage of 3.2%Vπ and ±3 V of communication signal amplitude, an extinction ratio of 36.71 dB can be achieved, with a bias point error of only around 0.25 V for both I and Q channels. Therefore, we selected 3.2%Vπ as the average voltage dither adopted in the subsequent experiments.
Next an experimental validation is conducted to verify the stability of the bias control scheme over an extended period. Figure 13(a) shows a comparison of the BER performance between communication systems with and without implementation of the ABC module over a 4-hour duration. Concurrently, we track I, Q, and P channel bias voltages throughout the entire duration when the ABC module is employed in Fig. 13(b). With the adoption of the ABC module, the BER remains consistently below 1.5 × 10−5 over the entire 4-hour period. Conversely, in the absence of the ABC module, noticeable bias drift occurs, resulting in a continuous increase in the BER.
Finally, the performance of the ABC module under external interference is tested. The optimal bias point is determined at the 5th minute. Subsequently a hairdryer is then used to increase the environmental temperature of the optical IQ modulator. At the 30th minute, the hairdryer is turned off, allowing the temperature to naturally return to room level. Figure 14 illustrates the variation of the BER over a 50-minute duration, with and without the ABC module. Additionally, selected constellation diagrams at specific moments are included. To better observe the bias point status of P channel, the orthogonalization step of I and Q channels in the DSP stage is disabled. From Fig. 14, it can be observed that when the environmental conditions abruptly change at the 5th and 30th minutes, there is a certain increase in the BER. However, under the control of the ABC module, the BER quickly reverts to a low-error state, while the constellation diagrams maintain a standard configuration. In contrast, without the ABC module, the BER remains high, and the constellation diagrams exhibit noticeable divergence and distortion. This result further demonstrates the robustness of the proposed bias control scheme against external interference.
4. Conclusion
This paper presents a novel scheme for bias control in optical IQ modulators. The proposed approach applies independent LFM dithers to I and Q channels and utilizes FrFT to process the dithers. The bias points of I and Q channels are controlled by monitoring the peak power of the CS, while the bias point of P channel is controlled by the peak power of the 2nd peak. Theoretical analysis demonstrates the advantages of energy aggregation in the fractional domain of compressed signals for bias control, both monitored parameters are highly sensitive to bias point drift and remain unaffected by mutual interference or voltage fluctuation influence. Experimental results not only validate the simulation findings but also verify the robustness of the proposed method under low-dither and high-fluctuation conditions. It demonstrates the ability to withstand external interference over extended periods while ensuring optimal communication quality. Hence, the proposed scheme is well-suited for high-speed coherent optical communication systems in complex environments and diverse requirements, effectively addressing the challenges associated with bias control.
Funding
National Natural Science Foundation of China (61931010, 62225110).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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