1 Introduction
With the effective compensation of chromatic dispersion, the pulse broadening caused by polarization mode dispersion (PMD) and the drop in bit error rate have become the limiting factors for the development of high-speed optical fiber communication systems. Due to the characteristics of PMD random changes [1], PMD compensation must be a dynamic compensation system that tracks its changes in real time, which requires a feedback signal that accurately reflects PMD changes. The PMD feedback signal mainly includes two degrees of polarization (DOP) [2, 3] and electrical power. PMD causes the pulses on the two polarization main states to move away, causing the DOP of the optical signal to drop. Therefore, DOP information can be used to detect changes in PMD. However, DOP feedback is affected by many factors such as pulse shape signal pattern, ASE noise, modulation chirp, and polarization-related loss [4]. The trend of DOP and PMD changes for different types of lines is also different, making the compensation system The applicability of the software has dropped significantly. With the development of high-frequency electronic devices, the electric power feedback method has attracted people's attention [5]. PMD causes the optical pulse signal to widen in the time domain. After receiving through photoelectric conversion, the width of the electrical spectrum in the frequency domain becomes narrower, resulting in the weakening of the electrical power of specific frequency components in the received signal spectrum. The advantage of electric power feedback is that the pulse shape and signal pattern can only affect the overall amplitude of the feedback signal, but not the change trend of the feedback signal with the first-order PMD [6]. This paper analyzes the effect of first-order PMD on the received signal spectrum of 40 Gbit / s optical fiber communication system, and verifies the relationship between the signal power spectrum and the differential group delay (DGD) at 12 GHz.
2 Theoretical analysis of factors affecting the received signal spectrum
The first-order PMD broadens the optical pulse during fiber transmission. The photodetection device converts the input optical signal pulse into an electrical pulse. Its spectral distribution is related to the pulse signal pattern, pulse shape, and DGD [7, 8] and other factors .
Assume that the signal transmitted in the optical fiber is a random sequence of arbitrary waveforms, the symbol period is T0, and its power spectrum is S (ω). After the optical fiber affected by the first-order PMD is transmitted, the narrow-band power spectral density of the electrical pulse output by the photodiode (PIN) can be characterized as [5]
Among them: [f (ωe)] The south pulse waveform f (t) is determined, ωe is the selected monitoring frequency; R is the responsivity of PIN; γ is the spectral ratio; △ τ is DGD. It can be seen that when the monitoring frequency is selected, the total power spectral density of the received electrical signal
The body amplitude is determined by f (t), and the change trend is determined by γ and Δτ.
In the 40 Gbit / s high-speed transmission system, most of them use the return-to-zero (RZ) code Gaussian pulse, and the Fourier transform of the waveform function is substituted into the equation (1). The power spectral density of the RZ code Gaussian pulse is
For a 40 Gbit / s system, the symbol period T0 = 25 ps, set the pulse half width T0 = 6 ps, the relationship between the amplitude factor exp (-T20ω2e / 2) and the received frequency f (f = ωe / 2π) is shown in the figure As shown in 1, as the receiving frequency increases, the overall amplitude decreases monotonously; the higher the selected receiving frequency, the smaller the amplitude of the obtained electrical power spectral density.
After the monitoring frequency is selected, the amplitude can be normalized, and the power spectral density can be expressed as
It can be seen from equation (3) that the changing trend of SE (ωe) is determined by γ, Δτ and ωe. The effects of various parameters on SE (ωe) are discussed below. When the Δτ caused by the PMD effect exceeds 1 symbol period, the signal will deteriorate so hard to recover, so when studying the actual PMD effect, you only need to consider the SE (ωe) curve when Δτ changes within the range of 1 symbol period That's it.
1) When ωe is fixed (ωe = 2πf, f = 12 GHz can be selected), and let y be 0.0, 0.1, 0.0, 0.5, 0.7, 0.9 and 1.0, respectively, the variation curve of SE (ωe) with Δτ is shown in the figure 2 shows. It can be seen that when), γ = 0.5, the slope of the curve is the largest; when) γ ≠0.5, the more γ value tends to both ends (0 or 1), the smoother the change of SE (ωe) curve; when γ = 0.0 and 1.0 , The slope of the SE (ωe) curve is zero and becomes a straight line, indicating that the optical pulse propagates along one of the polarization main states of the fiber [9], and no PMD effect occurs. Moreover, when γ = 0.3 and = γ0.7 and γ = 0.1 and γ = 0.9, the SE (ωe) curves coincide, indicating that the curve is symmetrical with γ = 0.5 as the center.
2) Let γ be fixed (γ = 0.5), and change the receiving frequency to 10, 12, 20 and 40 GHz respectively. The curve of SE (ωe) with Δτ is shown in Figure 3. The higher the f, the steeper the curve change , The sensitivity of the change of the electric power spectral density is higher, but when f = 40 GHz, the curve no longer changes monotonously. At the same time, considering the two conditions of single value and sensitivity, the receiving frequency should be neither too high nor too low. It is ideal to choose 20 GHz, but it can also be chosen between 10 and 20 GHz according to the actual situation.
3 Experimental study of the effect of DGD on electrical power spectral density
The pseudo-random code generator sends out a 10 Gbit / s non-RZ (NRZ) pseudo-random sequence code, and through the LiNbO3 external modulator, the secondary modulation of the optical signal after sine wave modulation has been performed, thereby obtaining a 10 Gbit / s RZ pseudo-random sequence After the optical signal is narrowed by dispersion compensation fiber (DCF), it enters 10 (3bit / s & TImes; 4 multiplexer, adjusts three polarization controllers (PC1, PC2, PC3) and adds a polarizer at the output end, You can get a linearly polarized OTDM 40 Gbit / s RZ pseudo-random sequence optical signal. After passing through PC4 and differential delay line (DDL), a 40 Gbit / s RZ code optical signal with first-order PMD effect is generated and entered A PIN with a bandwidth of 40 GHz generates a photocurrent, and after pre-amplification, a photovoltage is generated on the resistor R. After passing through a high-frequency narrowband amplifier and a narrowband bandpass filter, a narrowband electrical signal with a center frequency of 12.03 GHz is obtained. Selected receiver It is best to choose the frequency at 20 GHz, but the frequency of 20 GHz has too high requirements on electrical components, which is not easy to achieve. Considering the existing experimental conditions, the detection frequency point is selected to be 12.03 GHz. In the device, the high-frequency narrow-band amplifier bandwidth is 300 MHz , Narrowband bandpass filter The bandwidth of 100 MHz, and the center frequency is 12.03 GHz.
After passing through PIN, the 40 Gbit / s optical Rz code signal is converted into an electrical signal of 40 Gbit / s Rz code, and then amplified and filtered, and then connected to an electrical spectrometer to observe the spectral characteristic with a center frequency of 12 GHz.
When measuring the curve of electric power spectral density with DGD, first adjust PC4 to make the split ratio into DDL 0.5, then change DDL from 0 to 1 symbol period 25 ps in 1 ps steps, every time DDL changes, Use an electrical spectrometer to measure the electrical power spectral density at the frequency of 12 GHz. At the same time, the change of the 40 Gbit / s Rz code signal with the first-order PMD effect can be observed from the oscilloscope, and the Δτ is recorded as 2.5, 5.0, 7.5, 10.0 and Signal eye diagram at 12.5 ps.
The relationship between the electrical power spectral density and DGD is shown in the experimental data points in Figure 7. Comparing the theoretical curve of Figure 4 with the experimental curve of Figure 7, the experimental and theoretical calculations are in good agreement. At Δτ = 0, the theoretical and experimental values ​​are maximum; when Δτ increases, both the theoretical and experimental values ​​decrease; At Δτ = 25 ps, the theoretical and experimental values ​​are the smallest.
4 Conclusion
The theory analyzes the influence of pulse waveform, split ratio, receiving frequency and DGD on the received signal power spectrum, and gives a suitable frequency receiving range. The relationship between the electric power spectral density of a 40 Gbit / s Rz code pseudo-random signal at a receiving frequency of 12 GHz and DGD at a splitting ratio of 0.5 was measured through experiments. The experimental results show the correctness of the theoretical analysis. The signal power spectrum component provides an important basis for the first-order PMD compensation of the feedback signal.
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