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Abstract
Optical-fiber-based polarization scramblers can reduce the impact of polarization sensitive performance of various optical fiber systems. Here, we propose a simple and efficient polarization scrambler based on an all-optical Mach-Zehnder structure by combining a polarization beam splitter and an amplified fiber ring. To totally decoherence one polarization split beam, a fiber ring together with an amplifier is incorporated. The ratio of two orthogonal beams can be controlled by varying the amplification factor, and we observe different evolution trajectories of the output state of polarizations on the Poincaré sphere. When the amplification factor exceeds a certain threshold, the scrambler system exhibits nearly ideal polarization scrambling behavior. A commercial single wavelength laser with a linewidth of 3 MHz is utilized to characterize the scrambling performance. We found that when the sampling rate is 1.6 MSa/s, a scrambling speed up to 2000krad/s can be obtained for the average degree of polarization being less than 0.1. We also exploit these random polarization fluctuations to generate random binary numbers, indicating that the proposed technique is a good candidate for a random bit generator.
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Optical fibers fail to maintain the state of polarization (SOP) of light propagating through them, due to the random birefringence induced by core defects, external stress, bending, temperature, et al [1]. This behavior leads to polarization instability in most fiber systems, which is, in general, a source of additional noise [2]. Polarization scramblers transform the polarized light into non-polarized one to obtain a highly random polarization state, and mitigate the polarization mode dispersion or polarization-dependent loss [3]. The use of polarization scramblers has been reported in many applications such as optical fiber sensors [4,5], fiber-optic gyroscopes [6,7], high precision spectrophotometer [8], fiber amplifiers [9,10], secure key [11], et al. Additionally, they can be used to measure the polarization dependence of fiber-optic components and systems. For that purpose, the scrambling speed induced by the scrambler device should be high enough to match the scale of fast polarization changes encountered in high-speed fiber optic systems [12].
To scramble the polarization, many schemes have been proposed, which have been traditionally enabled by using waveguide electro-optic phase modulation techniques or fiber squeezers [13–17]. But the operating speeds of the polarization scramblers based on the fiber squeezer are limited by the mechanical devices, resulting in a scrambling speed of less than 100 KHz. The scrambling speed of polarization scramblers utilizing electro-optic modulation is contingent upon the modulation frequency. Furthermore, their scrambling uniformity is constrained by the non-randomness of external drivers. In the last few years, polarization scramblers based on all-optical interactions have become an alternative and complementary approach to break the speed limitations. For example, an all-optical polarization scrambler structure based on incoherent fiber ring was proposed [18], where input light undergone a series of recirculation inside fiber ring, and they recombined incoherently at the output. Other similar scheme was also demonstrated by cascading the fiber rings [19]. Meanwhile, polarization scramblers based on nonlinear interaction, have drawn wide attentions. Specifically, the intensity fluctuations of an incoherent pump beam are converted into polarization fluctuations of the input signal through the Kerr effect, achieving polarization scrambling of the signal [20]. A new structure based on nonlinear interaction between an incident signal and its intense backward replica generated at the fiber-end through an amplified reflective delayed loop was reported [21]. By adjusting the amplification factor g, a fully scrambled SOP output and a maximum scrambling speed of 600 krad/s were obtained [22].
Other kinds of polarization scramblers are proposed based on the input signal is split into two, one part is delayed with respect to the other and both are subsequently recombined. These types of scramblers can be classified into Lyot-type and Mach-Zehnder structure-based [23–26]. The drawback of Lyot-based polarization scramblers is that they accumulate only a small differential delay as the signal propagates along the two fiber axes. To fully scramble a laser with a 3 MHz linewidth, approximately 1200 km of fiber would be required. In contrast, a Mach-Zehnder structure using a polarization beam splitter (PBS) requires only about 66 meters of fiber. Recently, we demonstrated a novel structure based on a polarization beam splitting fiber loop, which increased the effective time delay through multiple circulations by fiber loop, enabling the further polarization scrambling of narrow-linewidth or high-coherence signals [27].
Compared to previous work, we have proposed a structure for an all-optical polarization scrambler based on the combination of a polarization beam splitter and a fiber ring (FR), which can be used for the generation of random bits. In the component of decoherence, we use an Er-doped fiber amplifier (EDFA) and a fiber ring to replace long single-mode fiber (SMF). The degree of polarization scrambling can be controlled by changing the amplification to adjust the ratio of the two orthogonal light beams. When the amplification factor exceeds a certain threshold, the system exhibits an ideal polarization scrambling regime, reducing the delay fiber length requirements by six orders of magnitude compared to Lyot structures, and by one order of magnitude compared to the standard Mach-Zehnder structures. We characterize the scrambling performance for 3 MHz linewidth laser. When the sampling rate is 1.6 MSa/s, we obtain a scrambling speed up to 2000krad/s with an average degree of polarization (DOP) less than 0.1. Moreover, we observe different polarization dynamic evolutions when adjusting amplification factor g, indicating that the trajectory for system entering into ideal polarization scrambling regime is determined by the amplitude difference between the decoherenced component and the non-decoherenced one. Then two lasers with different linewidths as input are tested to compare the effect of polarization scrambling. Finally, the random SOP dynamics induced by the scrambler is exploited to generate random binary sequences.
2. Main principle
As depicted in Fig. 1(a), the input light E(t) is split into two orthogonal polarization directions by PBS as
Fig. 1. (a) Amplitude difference between Ex and Ey for input lasers with three different polarization states, whose polarizations are split by a PBS. (b) Amplitude difference between Ex and Ey induced by propagation loss, even the two amplitudes are equally split by a PBS in the input E (input). (c) Amplitudes of two components are compensated to be equal. The original inequality is induced either by propagation loss or polarization splitting.
3. Experimental setup
Figure 2 denotes the main experimental setup. We used a commercial continuous wave (CW) distributed feedback laser as input source. In our polarization scrambler, the polarization controller1 (PC1) is used to modify the SOP of the input beam; therefore, the scrambling regime of the system is not determined by input SOP. Then, the input signal is split into two orthogonal components by PBS1, namely, p- and s-wave, which are denoted by double-headed arrows and dots, respectively. Here, one component for s-wave is delayed with respect to the other, and then they are subsequently recombined by PBS4. Blue lines denote laser beams propagating in SMF, and red lines indicate those propagating within polarization maintaining fibers. Black lines are electrical signals. The non-polarization-maintaining delayed fiber branch consists of an EDFA followed by a single FR structure as well as a PC2. PBS2, PBS3 are used to connect polarization-maintaining component and SMF. The gain of the EFDA is carefully controlled to adjust the amplification factor g. The FR is made of a 2 × 2 SMF directional coupler whose coupling ratio is 50:50, and the two pigtails are spliced together to form a loop. PC2 is used to fine-tune the SOP to optimize the output power of this component. The recombination beam is measured by a high-speed polarimeter (Novoptel PM1000) with a maximum sampling rate up to 100 MSa/s. Furthermore, for random bit generation experiments, the output signal SOP is projected on a polarizer (Pol) in order to convert the polarization randomness into intensity fluctuations. Opto-electrical conversion is fulfilled by photodetectors (PD) with analog bandwidth of 8 GHz, and resulting random signals are acquired by high-speed oscilloscope (Tektronix, DSA72004B) with bandwidth of 20 GHz and a sampling rate of 50 GSa s-1. The degree of randomness of the obtained data is analyzed quantitatively by the autocorrelation and cross-correlation method.
Fig. 2. Experimental setup of the polarization scrambler. PBS: polarization beam splitter, FR: fiber ring, PC: polarization controller, CW: continuous wave, OC: optical coupler.
For a polarization scrambler based on a Mach–Zehnder fiber delay-line structure, to reduce the mutual coherence of the orthogonal polarization modes and realize polarization scrambling effectively [24], the length of the fiber delay line must be longer than the coherence length of the light source. The 2 × 2 fused single-mode coupler with 1 m of fiber pigtail at each port yields a delay line ∼2 m in length. Amplify the light in order to maximize the amount of light that circulates through the fiber ring. Once the time delay induced by propagation of recirculating length is larger than the coherence time of the laser source, the mutual coherence of the orthogonal polarization components can be totally suppressed. Then, as each recirculating beam passing through the FR is incoherent with others, all beams recombine incoherently at the output of FR [18], followed by recombination with another orthogonal beam through another PBS. Due to the random phase of the two beams of light, the DOP of the output light is reduced drastically. Compared to traditional electro-optic phase modulation techniques or fiber squeezers, this method relies on random phase synthesis between light beams and is not constrained by the electronic driving modulators or mechanical devices, resulting in faster scrambling speeds.
4. Results and discussion
4.1 Polarization scrambling comparisons for different polarization states
To be more representative and without losing generality, we set the amplification factor g to be 1, namely the amplification would not influence the polarization scrambling performance. The SOPs of input laser are adjusted to be three states, as indicted schematically in Fig. 1(a). The corresponding outputs on the Poincaré sphere for the three input states are depicted in Fig. 3(a). For state 1, the energy of the input lasers after polarization splitting via PBS1 mainly contributes to the p-wave, and the corresponding output SOP is concentrated in a small area. Here, the decoherence in the s-wave branch do not contribute significantly to the combined output after superposition via PBS4. It is obvious that when the SOP of the input lasers are adjusted from state 1 to state 2, through properly setting PC1, the amplitudes for the two polarized components are gradually to be comparable, and the output SOPs exhibit more randomly on the Poincaré sphere. The reason is clear: the larger the intensity of s-wave branch, the more contribution the decoherence to the combined lasers. An optimal polarization scrambling performance occurs for the state 3, where the amplitudes of the two polarized components are almost equal.
Fig. 3. (a) Three typical outputs for different input states selected by adjusting PC1. All Poincaré spheres are with the same coordinate frame and only first one is shown for a better display. (b)-(d) Probability distribution histograms of the three normalized Stokes parameters S1, S2 and S3.
The polarization scrambling performance can be quantitatively revealed by the probability distributions. We characterize the experimental probability histograms of three normalized Stokes parameters S1, S2 and S3 for each state. The points on the Poincaré sphere in state 1 are concentrated around a fixed point, and the corresponding probability histogram is located at a certain bin of the Stokes parameters (Fig. 3(b)). As the points scatter to a small area in state 2, the probability density function (PDF) is unevenly distributed between −1 and 1 (Fig. 3(c)). In state 3, the PDF of all normalized Stokes parameters appears almost uniform (Fig. 3(d)), which provides further evidence of the polarization randomization. Note that a perfectly uniform density function of the Stokes components would correspond to the ideal polarization scrambling regime.
4.2 Influence of the amplification factor on the polarization scrambling performance
To fully scramble the SOP, the amplitude difference between p- and s-wave caused by polarization splitting or propagation loss shall be compensated properly. In our configuration, field intensities of the two superimposed components in PBS4 can be manipulated to be equal by properly setting amplification factor g. Here, we investigate the polarization scrambling performance for different amplification factors. The input state 1 is taken for example, and similar evolution dynamics can be found for other states. Figure 4 depicts the evolution trajectories of the output SOPs on Poincaré sphere for state 1 when increasing the amplification factor g. The obtained output SOPs are projected into the S1-S3 plane. Three different regions for various g parameter can be observed, ranging from an ordered pattern to a disorder pattern and then to a partial disorder pattern. By finely tuning PC1, when p-wave energy predominates, the output pattern is a single point on the Poincaré sphere, corresponding to the ordered state, with the amplification factor g being 1. In this case, due to fixed PC1 after adjustment, the scrambling process is relative weak. When the amplification factor g increases slowly, the system becomes unstable and begins to oscillate. Further improving the power of EDFA, polarization points spread gradually. For g ranging from 250 to 350, where the intensities of the two components are approximately equal, the trajectory of output SOP almost uniformly covers the complete surface of the sphere, achieving nondeterministic and totally random polarization scrambling of the output signal. In addition, the amplitude of the output signal with complete polarization scrambling remains stable. The corresponding DOP is about 0.08. By continuingly increasing g, the power of s-wave predominates of the recombined laser, and the polarization distribution of output lasers evolve from one semisphere to the opposite semisphere. The corresponding DOP increases to 0.54, and output SOP becoming partially scrambling.
The scrambling performances can be evaluated quantitatively by scrambling speed V and the averaged DOP, which are defined as follows [22]:
Fig. 5. Polarization scrambling performance for state 1 (a), state 2 (b), and state 3 (c). The black square represents V, and the red dot represents DOP.
For both the three input states, an optimized amplification factor can be found for a fully random SOP output, which can be inferred by the DOP less than 0.1. While, the required amplification factors for the three states are totally different. For state 1, owing to the dominance of p-wave energy, a much larger amplification factor g, is needed so that the amplified s-wave is comparable to the p-wave. As depicted in Figs. 5(a)-(c), as the amplification factor g increases steadily, the scrambling speed also increases continuously, whereas the DOP drops from 1 to almost 0. When the polarization scrambler is fully scrambled, V reaches its maximum value and DOP becomes less than 0.1. With further increasing g, the amplified s-wave is much larger than the p-wave, and the corresponding V and DOP change in the opposite direction. The obtained two lines are consistent with the SOP evolution on Poincaré sphere illustrated in Fig. 4. Similar trends are obtained for the state 2 and state 3. However, we found that the maximum scrambling speed (state 1 and state 2) is around 2000krad/s, whereas it is about 1000 krad/s in state 3. The inconsistency of scrambling speed can be attributed to spontaneous emission noise of amplifier. When the amplification factor is low, the weak spontaneous emission has little impact on polarization. However, as the amplification increases, the interaction between amplified spontaneous emission noise and the original light signal promotes polarization scrambling [20].
In addition, our observations indicate that the trajectory of system entering into totally random polarization scrambling regime is different when adjusting the amplification factor g. Specifically, in Figs. 5(a)–(c), we have identified three distinct regions, I, II, and III, each displaying unique dynamics. Here, we also take the state 1 as an example, and the SOP trajectories for different amplification factors within 10 s are depicted in Fig. 6. For region I (Fig. 6(a)), where the power of p-wave is dominant, the SOP is initially distributed on the left, and it gradually spreads to the right over time until it covers the entire sphere. Within region II (Fig. 6(b)), the field intensities of two superimposed components are equal, and the SOP forms a loop in the middle of the sphere before rapidly extending to both sides. As g is increased further, the system transitions to region III, where the power of s-wave is greater than that of p-wave. The evolution track of SOP transits from right to left over time until it covers almost homogeneously on the surface of the Poincaré sphere (Fig. 6(c)). This trajectory is opposite to the behavior in region I. More details about the polarization trajectories are visualized by the Visualization 1 in supplementary file.
Fig. 6. (a)-(c) The trajectories of SOP entering into totally random polarization scrambling regime in region I, II, III, for state 1, respectively (see Visualization 1).
4.3 Polarization scrambling performance for lasers with different linewidths
The proposed polarization scrambler structure can be utilized for lasers with any linewidths as long as the delay fiber in the FR is properly chosen. Here, given the specific parameters in our proposed structure, we compare the polarization scrambling performance for two input lasers with totally different linewidths, one with 3 MHz, while the other is 200 kHz. As shown in Figs. 7(a) and (d), if the SOP entering into PBS1 was mainly aligned on p-wave in the initial state, the output SOP is concentrated in a small area. In order to fully scramble the SOP, it is necessary to increase the power of s-wave, through which the polarization scatters more intensely on the Poincaré sphere (Figs. 7(b) and (e)). Finally, an optimized amplification factor can always be found, so that the amplitude of the two orthogonal components are equal, and the optimized polarization distributions can be found in Figs. 7(c) and (f), where both SOPs fluctuate with largest areas on the Poincaré sphere. Yet, performance difference is obvious as the two lasers have different linewidths. For laser with linewidth of 200 kHz, as the s-wave branch cannot be decohered completely by the FR, the evolution of the track only covers along a ring with certain thickness, while the lower left and upper right corners still cannot be filled (Fig. 7(c)). However, for the laser with linewidth of 3 MHz, decoherence can be achieved completely, and the SOPs spread from a fixed area, to a semi-circle, and finally to be random on the full Poincaré sphere (Figs. 7(d)-(f)).
Fig. 7. (a)-(c) Polarization scrambling states of a 200 kHz laser under different amplification factors. (d)-(f) Polarization scrambling states of a 3 MHz laser under different amplification factors.
5. Application
Polarization randomness in optical fiber can be an efficient source of randomness for the generation of random numbers [22,29,30]. Here, we demonstrate the practical application of our polarization scrambler as source for random binary sequences. The fluctuations of the output light intensity are exploited to experimentally generate random sequences. The principle of operation of random bit generation from polarization randomness is to convert the output field intensities of the scrambler into either a 0 or 1 according to some specific threshold, here calculated from the median value of the waveform. According to the setup in Fig. 2, after the projection on a polarizer, polarization randomness of the scramblered signal is transformed into the temporal fluctuations. Figure 8(a) displays a part of one experimental raw data (blue line) as well as clock signal (red line). Our clock has been chosen to 250 kHz whose frequency is selected below the typical correlation length of the test signal so as to ensure a reliable randomization [22]. The experimental raw data is sampled at each rising edge of the clock. After setting the threshold to the median value of 0.1618, the binary random sequence represented in Fig. 8(b) has been obtained.
Fig. 8. (a) Evolution of the light intensity over time (blue line). Square signal taken in correspondence of a clock (red line). (b) Random sequence generated after thresholding samples chosen in (a). (c) Autocorrelation of random sequence in (a). (d) Cross-correlation function of different random sequences generated in experiments.
The degree of randomness of the obtained temporally random sequence are tested through calculation of correlation function. Since the relative average value of temporal intensity is 0.5, we normalize it before the correlation calculations. The autocorrelation function for the zero-mean normalized binary sequence in Fig. 8(a) is depicted in Fig. 8(c), and the cross-correlation function between two different sequences is shown in Fig. 8(d). Both results show that sequences are autocorrelated only when there is a delay of 0, and and there is no significant correlation between two different sequences. All sequences generated through polarization randomness are random, which would be an effective method for generating random bit.
6. Conclusion
In summary, we have proposed an all-optical polarization scrambler structure by combination of polarization beam splitter and fiber ring. To compensate the amplitude difference induced by propagation loss or polarization splitting, optical amplification provided by EDFA is utilised in the decoherence component, for fully scrambling SOP of continuous wave lasers. By controlling the amplitude difference of the two orthogonal beams through changing the amplification factor g, we observed different polarization evolution trajectories for the system entering into totally random polarization scrambling regime. For such a scrambler, we obtained a scrambling speed up to 2000krad/s for a 3 MHz linewidth laser, where the DOP is less than 0.1. We also described how the SOP fluctuations induced by the polarization scrambler can be exploited to generate ensembles of random bit, by converting the polarization randomness of the output signal into temporal intensity fluctuation, which can generate random binary sequences by a digitalization process. The proposed polarization scrambler can reduce the impact of polarization sensitivity for various optical sensing systems, and is also reliable as random signal source for communications, optical signal process, et al.
Funding
National Natural Science Foundation of China (62075021).
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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