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Abstract
Vortex beams carrying orbital angular momentum (OAM), which feature helical wavefronts, have been regarded as an alternative degree of freedom for free-space optical (FSO) communication systems. However, in practical applications, atmospheric turbulence and limited-size receiving aperture effects will cause OAM modal degradation and seriously reduce the received power. In this paper, by controlling the radial phase distribution of conventional OAM beams, quasi-ring Airy vortex beams (QRAVBs) are successfully generated in the experiments to increase the received power under the limited-size receiving aperture conditions. By employing 72-Gbit/s 16-ary quadrature amplitude modulation (16-QAM) discrete multi-tone (DMT) signals, we successfully demonstrate free-space data transmission with QRAVBs in the experiments. Moreover, the transmission performance of QRAVBs under atmospheric turbulence is also evaluated. Comparing with conventional OAM beam and Bessel beam, the obtained results show that QRAVBs can achieve higher received power and better BER performance under limited-size receiving aperture and atmospheric turbulence conditions.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Free-space optical (FSO) communication has gained much research enthusiasm owing to its abilities for providing higher data capacity and improving security, as compared to traditional radio-frequency techniques [1–4]. Recently, there has been a great number of works on FSO communications with spatially orthogonal beams as the spatial modes provide a new degree of freedom to encode information, thereby greatly increasing the system capacity and spectral efficiency within a finite spatial bandwidth of an optical channel [5–7]. Among those families of spatial modes that have been investigated, the orbital angular momentum (OAM) modes of light have been used widely and successfully to increase the information capacity of a FSO link. An OAM-carrying vortex beam has a helical phase-front described by exp(ilφ), where l is the topological charge and φ is the azimuthal angle [8,9]. Benefiting from the multiplexing of vortex beams, ultra-high spectrally-efficient and petabit-scale free-space data transmission in the laboratory have been successfully demonstrated [10–13].
However, due to the unique phase and amplitude structure of OAM beams, there are still two main challenges that may degrade the transmission performance of such OAM-multiplexed FSO communication links, especially for long-distance data transmission. One is the divergence and the other is atmospheric turbulence. The divergence of OAM beams may cause power loss and channel crosstalk when the receiver aperture size is limited [14]. Generally, an OAM beam has a ring-shaped intensity profile that has low power near the beam center. Moreover, OAM beams with higher mode states diverge faster than lower-order OAM beams, thus making it difficult to fully capture the higher-order OAM beams [15,16]. To suppress the divergence of OAM beams, one efficient way is to use the focusing lens, which will directly reduce the beam diameter at the receiver side [17,18]. However, when the transmission distance changes, the parameter of the employed focusing lens should be reset accordingly. Another main challenge is the atmospheric turbulence, which will scramble the wavefronts of the OAM modes and induce modal crosstalk among the multiplexed OAM modes, thereby deteriorating the bit error rates (BER) performance [19–21]. Previous reports have shown various approaches for mitigation turbulence effect, including adaptive optics (AO), multiple-input multiple-output (MIMO) equalization, and deep learning-based wavefront correction [22–26]. Recently, some structured light beams carrying OAM have been reported for their anti-turbulence ability in free-space transmission [27,28]. Bessel beams are one of the OAM-carrying structured light beams, which have non-diffracting and self-healing properties in FSO links. It has been demonstrated that Bessel beams will outperform conventional OAM beams in terms of channel efficiency and BER, particularly through high levels of turbulence [29,30].
Ring Airy vortex beam (RAVB), as another type of OAM-carrying light beam, has been investigated due to its abruptly autofocusing property. Recently, it has been verified in simulation that the autofocusing RAVB can mitigate the modal degradation induced by atmospheric turbulence [31–34]. It has been shown that the abruptly autofocusing property of the RAVB could help to weaken the beam spreading and channel crosstalk induced by atmospheric turbulence. Moreover, by employing a tailored Airy vortex beam array, the intermodal crosstalk and vortex splitting can be effectively reduced under atmospheric turbulence, which could improve the FSO system communication performance. However, the performance of FSO communication with RAVBs has not been investigated in experiments yet. In addition, the autofocusing property of the RAVBs may also reduce the optical power loss under a limited-size receiving aperture. In theory, the divergence of a light beam can be controlled by adjusting its radial phase distribution. Thus, by carefully designing the radial phase of conventional OAM beams, it might be possible to generate quasi-ring Airy vortex beams (QRAVBs) with proper transmission characteristics and improve the data transmission performance of OAM-carrying light beams under limited-size receiving aperture and atmospheric turbulence conditions.
In this paper, by controlling the radial phase distribution of conventional OAM beams, QRAVBs are successfully generated to reduce the power loss induced by the limited-size receiving aperture effect. We successfully demonstrate free-space data transmission using QRAVBs with different mode states (l=+1, +3, +6) in the experiments with 72-Gbit/s 16-ary quadrature amplitude modulation (16-QAM) discrete multi-tone (DMT) signal. Moreover, the data transmission performance of QRAVBs under atmospheric turbulence is also evaluated. Comparing with conventional OAM beams and Bessel beams, the observed experimental results show that QRAVBs achieve higher received optical power and better BER performance under limited-size receiving aperture and atmospheric turbulence.
2. Concept and principle of QRAVB FSO communications
]The concept and principle of QRAVB FSO communications are illustrated in Fig. 1. In a conventional OAM mode transmission system in Fig. 1(a), (a) spiral phase plate is usually employed for the generation of OAM mode. After long distance free-space transmission under atmospheric turbulence, the OAM beam will suffer from mode distortion and beam divergence. When the receiver aperture size is limited, the OAM beam at the receiver side cannot be fully captured. Thus, it will seriously reduce the received power and lead to the interruption of communication. By carefully designing the radial phase of the OAM beam, one can control the divergence of the OAM beam and improve the received optical power, as shown in Fig. 1(b). Here, we propose a simple and efficient method to generate the QRAVB with a single phase-only element. By adding radial phase distribution onto the spiral phase of OAM beams, we can get the required phase profile for generating QRAVB, which can be expressed as below:
where l is the topological charge of the OAM beam, k is the wave number, $\varphi$is the azimuth angle, r is the radius, a is the design parameter of the radial phase. When a Gaussian beam is passed through the phase pattern, a QRAVB is generated subsequently. By adjusting parameter a, one can easily control the divergence of the generated light beam for different transmission distances.
Fig. 1. The concept and principle of QRAVB FSO communications under limited-size receiving aperture and atmospheric turbulence. (a) Conventional OAM beam transmission; (b) QRAVB transmission.
To theoretically demonstrate the transmission of the QRAVB in free space, the average intensity distribution over a finite aperture can be determined through the Fresnel diffraction integral. Moreover, we also simulate the transmission of conventional OAM beam and Bessel beam for comparison. The simulation results of the three OAM-carrying light beams (l=+3) are illustrated in Fig. 2. The input Gaussian beam has a beam diameter of 6.4 cm and a wavelength of 1550 nm. The parameter a of the QRAVB is set to 8 × 10−4 to maximize the optical power of the inner OAM ring at the receiving plane, as marked with a white dash line at 120 m. Figure 2(d) shows the intensity profiles of the three different OAM-carrying light beams at z=120 m. The simulation results show that the OAM beam spreading is obviously suppressed by adding radial phase distribution. Figure 3 shows the relative intensity distribution at the received plane of the three different OAM-carrying light beams. Comparing with conventional OAM beam and Bessel beam, QRAVB has more power in the inner ring, which will improve the received power under a limited-size receiving aperture.
Fig. 2. The simulated transmission intensity distribution of three different OAM-carrying beams transmitting in a 200 m free-space link. (a) conventional OAM, (b) Bessel beam, (c) QRAVB, (d) Intensity profiles of three OAM-carrying light beams at z=120 m.
Fig. 3. The simulated relative intensity distribution at the received plane (z=120 m) of the three different OAM-carrying light beams.
3. Experimental configuration
The experimental configuration of the free-space QRAVB data transmission is shown in Fig. 4. At the transmitter, a 72 Gbit/s 16-QAM-DMT signal is generated by an optical intensity modulator (IM). Then, the signal is attenuated by a variable optical attenuator to control the transmitted optical power. Hereafter, the data-carrying light is sent to the collimator to generate a free-space Gaussian beam. A polarizer (Pol.) is used for light polarization alignment with the polarization-sensitive spatial light modulator (SLM). Then the light is expanded by a beam expander with two lenses (f1=30mm, f2=100mm). The beam diameter D of the expanded Gaussian beam is 6.4 mm. The data-carrying QRAVB is generated immediately after SLM1, which is loaded with the desired phase pattern described in the previous section with parameter a=0.026. The phase profiles loaded on the SLM1 contains two parts. One is the phase patterns for generating required QRAVBs, the other is the pseudo-random phase masks for emulating the atmospheric. By adding pseudo-random phase masks to the desired phase pattern for generating QRAVBs, as shown in Fig. 4(a), we can simulate the light beam transmission under atmospheric turbulence conditions in the experiments. The pseudo-random phase masks are generated following the Kolmogorov spectrum statistics. In this paper, turbulence strength is characterized by the ratio $ D/{r_0}$, where D is the beam diameter, and ${r_0}$ is the Fried parameter. In order to remove the undesired diffraction order, a two-lens 4f imaging system with a pinhole is employed. The loss by the mode conversion process to generate QRAVBs is about 1.4 dB by using SLM1, which is nearly the same as the generation of conventional OAM beams and Bessel beams. Then, the light beam is reflected by a mirror. After 1.2 m free-space propagation, the QRAVB is converted back to a Gaussian-like beam for detection by another SLM (SLM2), which can emulate 120 m free-space transmission with a beam diameter of 6.4 cm. An InGaAs camera is used to capture the intensity profile of the transmitted light beam. To test the limited-size receiving aperture effect of the OAM-carrying light beams, we can control the phase patterns loaded on SLM2, as shown in Fig. 4(b). By adjusting the diameter of the transparent circular mask, one can control the size of the receiving aperture and test the corresponding transmission performance. At last, the back converted Gaussian-like beam is coupled into single-mode fiber (SMF) for signal detection.
Fig. 4. The experimental configuration of the proposed free-space QRAVB data transmission. (a) the phase profile for generating QRAVB with atmospheric turbulence; (b) the phase profile for emulating limited-size receiving aperture.
4. Experimental results
Figure 5 shows the recorded intensity profiles of the received light beams after 1.2 m transmission with and without turbulence. Conventional OAM beams and Bessel beams are also generated by changing the phase patterns loaded on SLM1 in the experiments for comparison with topological charges l= +1, +3 and +6. As seen from the recorded intensity images, the beam diameter gets larger with the increasing of topological charge for all the OAM-carrying light beams. In addition, the conventional OAM beams have the largest beam diameter at the receiver side. The QRAVBs have more power near the center of the light beam comparing with Bessel beams, which consists with the simulation results. Under weak strength atmospheric turbulence D/r0 = 1, all the OAM-carrying light beams get distortion. As seen from the recorded intensity profiles, the Bessel beam and QRAVB seem less affected by the turbulence.
Fig. 5. The recorded intensity profiles of the received light beams after 1.2 m transmission with and without turbulence
By changing the phase patterns loaded on the SLM2, we plot the received power of the generated light beams under different receiving aperture diameters (d=10, 4, 3, 2 mm) without turbulence, as shown in Fig. 6. The transmitted power of the light beams is set to 0 dBm. When the receiving aperture diameter is 10 mm, three light beams nearly have the same received power due to the relatively large receiving aperture size. When the receiving aperture diameter gets smaller, the received power of the conventional OAM beam is greatly reduced especially for high order modes, which will seriously influence communication performance and increase the BER. By transmitting Bessel beams and QRAVBs, the received power will highly increase under small receiving apertures as shown in the curves. The received power of QRAVBs is nearly 10 dB higher than conventional OAM beams and 2 dB higher than Bessel beams under limited-size receiving aperture d=3 mm. The experimental results of the received optical power are consistent with the recorded intensity profiles in Fig. 5. The observed experimental results show that QRAVBs can highly improve the received optical power under limited-size receiving apertures.
Fig. 6. The received power of the three kinds of light beams under different receiving aperture diameters (d=10, 4, 3, 2 mm) without turbulence. (a) l=+1; (b) l=+3; (c) l=+6.
Then, we characterize the received power fluctuations of the three kinds of light beams under atmospheric turbulence strength D/r0 = 1 with transmitted power at 0 dBm. For each condition, 50 independent random phase masks are generated in the experiments to emulate the atmospheric turbulence. Figure 7 shows the received power and the corresponding cumulative probability of the three transmitted OAM-carrying light beams (l=+3) with receiving aperture diameters of 10 mm and 3 mm. As shown in Figs. 7(a) and (b), we observe that the Bessel beam and QRAVB have smaller power fluctuation than the conventional OAM beam, which shows better anti-turbulence transmission performance. In addition, the average received power of QRAVB is about 2 dB higher than the Bessel beam. When the receiving aperture diameter is reduced to 3 mm, as shown in Figs. 7(c) and (d), large received power loss is observed by using conventional OAM beams. Moreover, QRAVB has the highest received power under different receiving aperture diameters in the experiments, which shows favorable transmission performance.
Fig. 7. The received power and the corresponding cumulative probability of the three transmitted OAM-carrying light beams (l=+3). (a) and (b) receiving aperture diameter of 10 mm; (c) and (d) receiving aperture diameter of 3 mm.
In addition, we also test the received optical power fluctuation of QRAVB with different topological charges (l=+1, +3, +6) under turbulence strength D/r0 = 1 and 4 with a limited-size receiving aperture diameter of 3 mm, as shown in Fig. 8. We find that higher order modes are more affected by turbulence. Seen from Figs. 8(a) and (b), the received power of different mode states is all above −20 dBm under turbulence strength D/r0 = 1. Under strong turbulence D/r0 = 4, the received power is greatly reduced to −35 dBm with wide fluctuations, which may cause communication interruption.
Fig. 8. The received power and the corresponding cumulative probability of QRAVB with different topological charge (l=+1, +3, +6) under turbulence. (a) and (b) D/r0 = 1; (c) and (d) D/r0 = 4.
To evaluate the crosstalk of QRAVBs under atmospheric turbulence, we also measure the power spectrum of QRAVBs with different topological charges (l=+1, +3, +6) under atmospheric turbulence D/r0 = 1 and 4, as shown in Fig. 9. Under turbulence D/r0 = 1, as shown in Figs. 9(a-c), the mode crosstalk between the neighboring modes is less than −12 dB for all the transmitted mode states. Moreover, under a limited-size receiving aperture diameter of 3 mm, the mode crosstalk is nearly the same as the one receiving all the fields. When the turbulence strength increases to D/r0 = 4, shown in Figs. 9(d-f), the crosstalk significantly increases, especially for the higher order modes. The experiments results indicate that one may use QRAVBs with large mode spacing (e.g. l=+1 and l=+4) for mode division multiplexing under strong turbulence.
Fig. 9. The measured power spectrum of QRAVBs with different topological charges (l=+1, +3, +6). (a-c) Measured power spectrum under atmospheric turbulence D/r0 = 1; (d-f) Measured power spectrum under atmospheric turbulence D/r0 = 4.
At last, we measure the BER performance of free-space QRAVBs transmission under limited-size receiving aperture and atmospheric turbulence, as shown in Fig. 10. Here, we also compare the performance with the conventional OAM beam and Bessel beam. Figure 10(a) shows the measured average BER against transmitted power for the OAM-carrying light beams (l=+3) with receiving aperture of 10 mm under turbulence strength of D/r0 = 1. Comparing with the conventional OAM transmission case, the required transmitter power at BER of 3.8×10−3 (7% HD-FEC threshold) is relaxed by 4 dB for QRAVB and 2 dB for Bessel beam. When the receiving aperture diameter decreases to 3 mm, the required transmitter power can be relaxed by about 10 dB for QRAVB and 8 dB for Bessel beam, as plotted in Fig. 10(b). The measured BER performance is consistent with the received power shown in Fig. 7. In addition, we also measure the BER curves of QRAVBs with different topological charges (l=+1, +3, +6) under turbulence strength D/r0 = 1 and 4 with a limited-size receiving aperture of 3 mm, as shown in Fig. 10(c) and (d). Under turbulence strength D/r0 = 1, the required transmitted power is about −14 dBm, −10 dBm and −6 dBm for l=+1, +3, +6, respectively. When the turbulence strength increases to D/r0 = 4, the required transmitted power is about 2 dBm, 10 dBm, and 12 dBm for l=+1, +3, +6, respectively. The observed BER curves indicate that higher order QRAVB are more affected by the strong atmospheric turbulence, which might require other methods to mitigate the effect.
Fig. 10. Measured average BER against transmitted power of three kinds of OAM-carrying light beams (l =+3) under turbulence strength of D/r0 = 1 with receiving aperture of (a) 10 mm and (b) 3 mm; Measured average BER against transmitted power of QRAVBs with different topological charge (l =+1, +3, +6) under turbulence (c) D/r0 = 1 and (d) D/r0 = 4.
5. Conclusion and discussion
In summary, we have presented a simple and efficient approach to generate autofocusing QRAVBs with a single phase-only element for free-space vortex beam communication. By adding proper radial phase distribution onto the spiral phase of OAM beams, QRAVBs are successfully generated in the experiments to increase the received power under limited-size receiving apertures. By employing 72-Gbit/s 16-QAM discrete multi-tone DMT signal, we successfully demonstrate free-space data transmission using QRAVBs with different mode states (l=+1, +3, +6) in the experiments. Under a limited-size receiving aperture of 3 mm, the required transmitter power at BER of 3.8×10−3 is relaxed by 10 dB comparing with the conventional OAM beam under atmospheric turbulence D/r0 = 1. Moreover, the anti-turbulence ability of the QRAVB is evaluated, and it is found that the anti-turbulence ability of the beam is similar to that of the Bessel beam. Comparing with conventional OAM beam and Bessel beam, the experimental results show that QRAVB achieves higher received power and better BER performance under limited-size receiving aperture and atmospheric turbulence.
Funding
National Natural Science Foundation of China (12104078, 61805031, 62001072); Science and Technology Research Program of Chongqing Municipal Education Commission (KJQN201900637, KJQN202000622); Science and Technology Commission of Shanghai Municipality (SKLSFO2018-06).
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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