1 Introduction
With the effective compensation of chromatic dispersion, the pulse broadening caused by polarization mode dispersion (PMD) and the bit error rate have become the limiting factors for the development of high-speed fiber-optic communication systems. Due to the random variation of PMD [1], PMD compensation must be a dynamic compensation system that tracks its changes in real time, which requires a feedback signal that accurately reflects the change in PMD. The PMD feedback signal mainly includes two kinds of polarization degrees (DOP) [2, 3] and electric power. PMD causes the pulse on the two polarization main states to move away, causing the optical signal DOP to drop, so the DOP information can be used to detect the change of PMD. However, DOP feedback is affected by various factors such as pulse shape signal pattern, ASE noise, modulation chirp and polarization dependent loss [4]. The trend of DOP and PMD changes for different types of lines is also different, making the compensation system The applicability has dropped significantly. With the development of high-frequency electronic devices, the electric power feedback method has attracted people's attention [5]. The PMD causes the optical pulse signal to broaden in the time domain. After receiving by photoelectric conversion, the optical spectrum width is narrowed in the frequency domain, resulting in a decrease in the electrical power of a specific frequency component 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, and does not affect the trend of the feedback signal with the first-order PMD [6]. This paper analyzes the influence of the first-order PMD on the received signal spectrum of the 40 Gbit/s fiber-optic communication system, and verifies the relationship between the signal power spectrum and the differential group delay (DGD) at the 12 GHz frequency.
2 Theoretical analysis of the factors affecting the received signal spectrum
The first-order PMD broadens the optical pulse during the transmission of the optical fiber. The photoelectric detecting device converts the input optical signal pulse into an electrical pulse, and its spectral distribution is related to the pattern of the pulse signal, the pulse shape, and various factors such as DGD [7, 8]. .
Let the signal transmitted in the optical fiber be a random sequence of arbitrary waveforms, the symbol period is T0, and the power spectrum is S(ω). After the fiber is affected by the first-order PMD, the narrow-band power spectral density of the electrical pulse output by the photodiode (PIN) can be characterized as [5]
Where: [f(ωe)] South pulse waveform f(t) determines that ωe is the selected monitoring frequency; R is the responsiveness of PIN; γ is the splitting ratio; Δτ is DGD. It can be seen that the total power spectral density of the received electrical signal is selected with the selected monitoring frequency.
The body amplitude is determined by f(t), and the trend of change is determined by γ and Δτ.
In the 40 Gbit/s high-speed transmission system, the return-to-zero (RZ) code Gaussian pulse is mostly used, and the Fourier transform of the waveform function is substituted into the equation (1), and the power spectral density of the RZ code Gaussian pulse is obtained.
For a 40 Gbit/s system, the symbol period T0=25 ps, the pulse half width T0=6 ps, the amplitude factor exp(-T20ω2e/2) with the receiving frequency f(f=ωe/2π) As shown in Fig. 1, as the receiving frequency increases, the overall amplitude monotonously decreases; the higher the selected receiving frequency, the smaller the amplitude of the obtained electric power spectral density.
When 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 trend of SE(ωe) is determined by γ, Δτ and ωe. The effects of each parameter on SE(ωe) are discussed separately below. Since the Δτ caused by the PMD effect exceeds 1 symbol period, the signal will deteriorate and it is difficult to recover. Therefore, when studying the actual PMD effect, it is only necessary to consider the SE(ωe) curve when Δτ changes within 1 symbol period. Just fine.
1) When ωe is constant (ωe=2πf, f=12 GHz can be selected), and let y take 0.0, 0.1, 0.0, 0.5, 0.7, 0.9 and 1.0, respectively, and SE(ωe) with Δτ 2 is shown. It can be seen that when γ=0.5, the slope of the curve is the largest; when γ≠0.5, the γ value tends to both ends (0 or 1), and the change of SE(ωe) curve is more gentle; 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 is transmitted along one of the polarization principal states of the fiber [9], and no PMD effect is generated. Moreover, when γ = 0.3 and = γ 0.7 and γ = 0.1 and γ = 0.9, the SE (ωe) curves coincide, indicating that the curve is symmetrical about γ = 0.5.
2) Let γ be certain (γ=0.5), change the receiving frequency to 10, 12, 20 and 40 GHz respectively. The curve of SE(ωe) with Δτ is shown in Fig. 3. The higher the f, the steeper the curve changes. The sensitivity of the change in electric power spectral density is higher, but when f = 40 GHz, the curve is no longer monotonously changed. At the same time, considering the two conditions of single value and sensitivity, the receiving frequency should not be chosen too high, nor should it be chosen too low. It is best to choose 20 GHz, but it can also be selected between 10 and 20 GHz according to the actual situation.
Experimental study on the effect of DGD on electric power spectral density
The pseudo-random code generator sends a 10 Gbit/s non-RZ (NRZ) pseudo-random sequence code, and the LiNbO3 external modulator remodulates the optical signal that has been sinusoidally modulated, thereby obtaining a 10 Gbit/s RZ pseudo-random sequence. The optical signal is then narrowed by a dispersion-compensating fiber (DCF) and then enters 10 (3bit/s & TImes; 4 multiplexer, respectively adjusting three polarization controllers (PC1, PC2, PC3) and adding a polarizer at the output, The OTDM 40 Gbit/s RZ pseudo-random sequence optical signal outputted as line polarization can be obtained. After PC4 and differential delay line (DDL), a 40 Gbit/s RZ code optical signal with first-order PMD effect is generated. A PIN with a bandwidth of 40 GHz generates a photocurrent, which is preamplified to generate a photovoltage on the resistor R, and then passes through a high frequency narrowband amplifier and a narrowband bandpass filter to obtain a narrowband signal having a center frequency of 12.03 GHz. The frequency is preferably selected at 20 GHz, but the frequency of 20 GHz is too high for the electrical device to be realized. Considering the existing experimental conditions, the selected detection frequency is 12.03 GHz. In the device, the bandwidth of the high-frequency narrowband amplifier is 300 MHz. , narrow band pass filter The bandwidth of 100 MHz, and the center frequency is 12.03 GHz.
After the 40 Gbit/s optical Rz code signal passes through the PIN, it is converted into an electrical signal of 40 Gbit/s Rz code, and then amplified and filtered, and then connected to the spectrometer to observe the spectral characteristics of the center frequency of 12 GHz.
When measuring the curve of electric power spectral density as a function of DGD, first adjust PC4 to make the split ratio into DDL 0.5, then change DDL to change from 0 to 1 symbol period of 25 ps in steps of 1 ps, and change DDL every time. The electric power spectral density of the 12 GHz frequency is measured by an electric spectrometer, and the change of the 40 Gbit/s Rz code signal with the first-order PMD effect is 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 electrical power spectral density and DGD is shown in the experimental data points in Figure 7. Comparing the theoretical curve of Fig. 4 with the experimental curve of Fig. 7, the experimental and theoretical calculations agree well. At Δτ=0, both theoretical and experimental values ​​are maximum; when Δτ is increased, both theoretical and experimental values ​​are decreased; At Δτ = 25 ps, both theoretical and experimental values ​​are minimal.
4 Conclusion
The effects of pulse waveform, splitting ratio, receiving frequency and DGD on the power spectrum of the received signal are analyzed theoretically, and the appropriate frequency receiving range is given. The relationship between the electrical power spectral density of the 40 Gbit/s Rz code pseudo-random signal at the receiving frequency of 12 GHz and the change of DGD is measured by 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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