Abstract

Twisted light carrying orbital angular momentum (OAM), which features helical phase front, has shown its potential applications in diverse areas, especially in optical communications. For OAM-based free-space optical (FSO) links, a significant challenge is the power fading induced by atmospheric turbulence. In this paper, we experimentally demonstrate the mitigation of atmospheric turbulence effects with an OAM-based transmitter mode diversity scheme. By designing multi-OAM phase patterns, we successfully generate multiple OAM modes (OAM-1,0,1, OAM+2,+3,+4, OAM+5,+6,+7) carrying the same data stream for transmitter diversity without adding system complexity. An intensity-modulated direct-detection (IM-DD) system with 39.06 Gbit/s discrete multi-tone (DMT) signal is employed to confirm the feasibility of the OAM-based transmitter mode diversity scheme under atmosphere turbulence. The obtained experimental results show that the received power fluctuation and average bit-error rate (BER) are decreased under moderate to strong turbulence compared to the traditional single OAM mode transmission. In addition, the required transmitted power at 10% interruption probability is relaxed by nearly 2 dB under moderate to strong turbulence.

© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Twisted light beams carrying orbital angular momentum (OAM) that exploit the spatial structure physical dimension of electromagnetic waves have been intensively investigated in wide applications such as optical manipulation, optical tweezers, sensor, imaging, metrology, astronomy, and quantum entanglement [17]. OAM-carrying twisted light is a helically phased beam comprising an azimuthal phase term exp(ilφ), carrying an OAM of $l\hbar$ per photon ($\hbar$: reduced Plank’s constant), where l is referred to topological charge and φ is the azimuthal angle [8]. Due to the intrinsic orthogonality and unbounded states of OAM modes, one can realize high-capacity and spectrally-efficient twisted optical communications through efficiently OAM multiplexing. Consequently, OAM-carrying twisted light has shown great potential in optical communications [911].

For OAM-based free-space optical (FSO) links, numerous experiments using high-volume OAM multiplexing have achieved ultra-high spectral efficiency and petabit-scale FSO links [1214]. However, most of the proof-of-concept experiments of OAM-based FSO communications are tested without considering the effects of atmospheric turbulence. In practical FSO communication scenarios, atmospheric turbulence can easily distort the wavefront of OAM beams and cause random power fluctuations [15]. Theoretical and experimental results have shown that turbulence-induced fading can severely impair the performance of FSO communication links, increasing interruption probability and the average bit error ratio (BER) [16,17]. Therefore, the mitigation of turbulence distortion is essential to enable realistic use of OAM-based FSO communications.

In order to mitigate turbulence induced power fluctuations, adaptive optics (AO) is widely investigated in the previous work. Generally, wavefront sensing devices (e.g., Shack-Hartmann wavefront sensor) and phase correction devices (e.g., spatial-light-modulators (SLM) or digital micromirror devices (DMD)) are necessary in AO-based method [18,19]. However, the optical system complexity, cost and the capability of real-time processing of AO-based system still remain challenges for practical FSO link. Another approach for increasing link reliability is to use spatial diversity transmission and reception. For an OAM-based FSO system with spatial diversity, the same OAM beams are transmitted and received by multiple spatial apertures, in which the spatial apertures are separated to bring diversity gain [20,21]. It has recently been shown that mode diversity also provides such diversity gain, and much fewer apertures are required. In mode diversity scheme, multiple orthogonal spatial modes carrying the same data stream are transmitted/received in a single aperture pair. As a subset of Laguerre-Gaussian (LG) modes, OAM modes can also be used for mode diversity as an alternative mode base set. Mode diversity can be realized at the receiver in the form of single-input multiple-output system. At the receiver, the power coupled from the fundamental Gaussian mode into other higher-order modes is collected by modes de-multiplexer [22]. Mode diversity can also be realized at the transmitter in the form of multiple-input single-output system. In this scheme, different spatial modes are generated at the transmitter, and only one of the transmitted modes is detected. Recently, a transmitter diversity scheme based on one Hermite-Gaussian (HG) mode and one LG mode has shown improvement in bit error rate under atmospheric turbulence [23]. Mode diversity can be realized at both the transmitter and the receiver in the form of a multiple-input multiple-output system [24]. Very recently, a mitigation approach utilizing OAM-based mode diversity at both the transmitter and the receiver combined with space diversity has showing enhancement of link robustness under atmospheric turbulence [25]. In these reported OAM-based mode diversity schemes, the transmitter diversity is always combined with receiver diversity to reduce the influence of the turbulence. Actually, by only using OAM-based transmitter mode diversity, one may also mitigate the influence of atmosphere turbulence, which has not been reported yet. Moreover, in the previous work, two OAM modes are combined with a beam splitter at the transmitter side for mode diversity, which will induce extra power loss and additional hardware complexity. Here we propose an OAM-based transmitter mode diversity scheme where the mode sets can be flexibly generated under different strengths of turbulence. By using a special designed phase pattern, one can successfully generate multiple collinear OAM modes with high efficiency.

In this paper, we investigated the performance of an OAM FSO system based on transmitter mode diversity under weak to strong atmospheric turbulence. In the proposed transmitter mode diversity scheme, a novel multi-input single-output (MISO) architecture which has a same system complexity with the single OAM transmission is designed for improving system reliability. To prove the feasibility of the proposed scheme, an intensity-modulated direct-detection (IM-DD) system transmitting three OAM modes with the same 39.06 Gbit/s discrete multi-tone (DMT) signal is experimentally demonstrated. Experimental results show that, compared with single OAM transmission, the required transmitter power at average BER of 3.8×10−3 is relaxed by 3 dB, 3 dB, 4.7 dB and 2 dB under different atmosphere turbulence strength $D/{r_0}$=0.7, $D/{r_0}$=1, $D/{r_0}$=2 and $D/{r_0}$=4 with mode sets OAM+5,+6,+7, OAM+2,+3,+4, OAM-1,0,1 and OAM-1,0,1, respectively. Compared with single OAM transmission, the required transmitted power at 10% interruption probability is relaxed by nearly 2 dB under moderate to strong turbulence. Moreover, we investigate the link performance using the same OAM sets with different power distribution and different numbers of OAM modes.

2. Concept and principle

The concept and principle of the proposed scheme is illustrated in Fig. 1. Figure 1(a) shows the traditional OAM mode transmission system, which is a single-input single-output (SISO) system. Here we consider an OAM-based transmitter mode diversity system with multiple transmitted OAM beams carrying the same data stream, as shown in Fig. 1(b). By designing the multi-OAM phase pattern, one can easily generate the intended OAM mode and its adjacent N-1 mode states with equal power collinearly. Compared to SISO OAM transmission case, our scheme can avoid increasing transmitter/receiver complexity. The only difference between them is the employed phase patterns for the generation of input modes. Note that the transmit power of each beam should be scaled by 1/N to conserve the overall transmit power. After propagation through turbulence, the power of the transmitted OAM modes will couple to their neighboring modes. At the receiver side, only the intended OAM mode in the middle of the transmitted mode set is received for signal detection. In the single OAM transmission system, the power of the transmitted OAM mode will leak to other neighboring OAM modes randomly due to the turbulence. Thus, the received power would have a severe fluctuation, which may lead to the interruption of communication. In the OAM-based transmitter mode diversity system, the power of the transmitted modes will couple to each other. It is possible to receive the power coupled from the neighboring modes to the desired OAM mode. Due to the turbulence-induced mode coupling among the transmitted modes, the received power might achieve a relative stable condition with smaller standard deviation than single OAM mode transmission. Thus, the proposed transmitter mode diversity scheme can be used to reduce the interruption probability and improve the reliability of the FSO link.

 figure: Fig. 1.

Fig. 1. Concept and principle of the proposed FSO communication link using OAM-based transmitter-diversity for increased tolerance to atmospheric turbulence. (a) Single-input single-output (SISO) transmission with only one OAM mode, (b) Multi-input single-output (MISO) system with multiple OAM modes.

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3. Experimental setup

The experimental setup of the proposed OAM based transmitter mode diversity scheme is shown in Fig. 3. An IM-DD system using the 16 quadrature amplitude modulation (16QAM) DMT signal is built to demonstrate the proposed scheme. At the transmitter, an arbitrary waveform generator (Tektronix AWG 70001) operating at a sample rate of 25 GSa/s is used to generate electrical DMT signal. The real-valued DMT signal is generated by using Hermitian symmetry for a 512-point inverse fast Fourier transformation (IFFT) input. Among the 512 sub-carriers, 200 subcarriers are used to transmit effective data, and the effective bandwidth of the generated DMT signal is 9.76 GHz. A 40-sample CP is added in front of each DMT signals. After amplification, the generated DMT signal is intensity modulated onto an optical signal at the wavelength of 1550 nm by an optical intensity modulator (IM). Then, the signal is attenuated by a variable optical attenuator to control the total transmitted optical power.

After being collimated and linearly polarized, the generated Gaussian beam is directly converted to a particular transmitted mode set carrying the same 9.76-Gbaud DMT signals through SLM1. Limited by the number of available SLMs, the phase pattern loaded on the SLM1 is the combination of a multi-OAM phase pattern and a pseudo-random phase mask which follows the Kolmogorov spectrum statistics (as shown in Fig. 2(a)). The construction detail of the multi-OAM phase pattern is discussed in our previous work [26]. In our experiment, the conversion efficiency of the SLM for the generation of the multi-OAM beam is above 90%, and the insertion loss for generating OAM+3 beam and OAM+2,+3,+4 beam by the phase-only SLM (HAMAMATSU LCOS-SLM X15223-08) are 1.84 dB and 2.13 dB, respectively. Moreover, we keep the same output optical power of SLM to eliminate the influence of the loss on the experiment results. The turbulence strengths can be characterized by the ratio $D/{r_0}$, where D is the beam diameter, and ${r_0}$ is the Fried parameter. In our experiment, the beam size D of a set of OAM beams is 3 mm. Here it should be noted that three different transmitted set (OAM-1,0,1, OAM+2,+3,+4, OAM+5,+6,+7) under different turbulence strength ($D/{r_0}$= 0.7, 1, 2) are considered as a proof of concept demonstration. For each turbulence strength and mode set, only the intended OAM mode in the middle of the transmitted set is detected. To effectively simulate the practical FSO transmission of 1.3 km with beam diameter D at 10 cm, we scale the practical distance down to 1.2 m for laboratory realization by Fresnel scaling theory. At the receiver, only the intended OAM mode is detected by SLM2 loaded with simple fork grating phase patterns (as shown in Fig. 2(b)). Due to the turbulence, the power of the neighboring OAM modes coupled into the intended OAM state can also be collected for signal detection. Then the signals on the received OAM is amplified and filtered by an optical band-pass filter before detected by a photo detector (PD). After optical-to-electrical conversion, the generated electrical signal is captured by a real-time oscilloscope (Tektronix DPO73304SX) with a sampling rate of 100 GSa/s and finally processed by off-line DSP for DMT demodulation. For each strength of turbulence, 50 random phase masks for turbulence emulation are generated for measuring the received optical power. Then, we use the same 50 random phase masks to calculate the average BER and interruption probability against transmitted power for transmitter mode diversity schemes using different OAM sets.

 figure: Fig. 2.

Fig. 2. Experimental setup of OAM free space communication system based on transmitter mode diversity. Insets (a) a combination of a multi-OAM phase pattern and pseudo-random phase masks; (b) fork grating phase patterns of OAM-3. AWG: arbitrary waveform generator; IM: intensity modulator; PC: polarization controller; VOA: variable optical attenuator; Col.: collimator; Pol.: polarizer; L1: lens (f=100 mm); L2: aspheric lenses (f=18.4 mm); EDFA: erbium-doped fiber amplifier; OC: optical coupler; OTF: optical tunable filter; PD: photo detector.

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4. Experimental results

We first characterize the transmission performance of OAM modes in emulated atmospheric turbulence with different strengths. Figure 3 shows the measured intensity profiles of the single OAM transmission scheme and transmitter mode diversity scheme with and without turbulence. Three different OAM mode sets (OAM-1,0,1, OAM+2,+3,+4, OAM+5,+6,+7) are employed for mode transmitter diversity. For single OAM transmission case, only the central OAM mode (OAM0, OAM+3, OAM+6) in each transmitted set is selected as intended mode for comparison. From the measured intensity profiles, one can find that the OAM mode will get distorted with the increase of turbulence strength. Moreover, high-order OAM modes are more sensitive to the turbulence.

 figure: Fig. 3.

Fig. 3. Measured intensity profiles of the single OAM transmission scheme and transmitter mode diversity scheme with and without turbulence.

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Then we characterize the received power fluctuations for different transmitted OAM modes sets under weak to strong turbulence distortions with the total transmitting power at 0 dBm. Figures 46 show the received power and the corresponding cumulative probability of the received OAM beams for transmitter diversity scheme. In Fig. 4, we transmitted OAM-1, OAM0 and OAM+1 with equal power in transmitter diversity scheme under four different turbulence strengths. Here we compute the difference between the maximum value and the minimum value of the received power to describe the power fluctuation regime. When the turbulence strength is $D/{r_0} = 2$ and $D/{r_0} = 4$, the fluctuation of the receiving power of the single OAM0 mode transmission case is 27.8 dB and 28.9 dB, respectively. For the transmitter diversity scheme, its fluctuations are 19 dB, 25 dB, respectively. The results indicate that the OAM based transmitter diversity scheme suffers a smaller fluctuation of the received power than the single OAM mode transmission case, when the turbulence strength is $D/{r_0} = 2$ and $D/{r_0} = 4$. However, under turbulence strength $D/{r_0} = 0.7$ and $D/{r_0} = 1$, the fluctuation of the received power of transmitter diversity scheme is almost same with the single OAM transmission, which is mainly because that the turbulence is not strong enough to couple the neighboring modes to the desired OAM mode.

 figure: Fig. 4.

Fig. 4. Experimental received power and cumulative probability of received power with transmitting power at 0 dBm under turbulence strength D/r0 = 0.7, 1, 2 and 4. For single OAM transmission, an OAM0 beam is transmitted; for transmitter mode diversity, an OAM-1,0,1 beam is transmitted.

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 figure: Fig. 5.

Fig. 5. Experimental receiving power and cumulative probability of receiving power with transmitting power at 0 dBm under turbulence strength D/r0 = 0.7, 1, 2. For single OAM transmission, an OAM+3 beam is transmitted; for transmitter mode diversity, an OAM+2,+3,+4 beam is transmitted.

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 figure: Fig. 6.

Fig. 6. Experimental receiving power and cumulative probability of receiving power with transmitting power at 0 dBm under turbulence strength D/r0 = 0.7, 1, 2. For single OAM transmission, an OAM+6 beam is transmitted; for transmitter mode diversity, an OAM+5,+6,+7 beam is transmitted.

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In Fig. 5 and Fig. 6, the topological order of the intended OAM mode is increased to +3 and +6, respectively. When the turbulence strengths are $D/{r_0} = 1$ for OAM+2,+3,+4 and $D/{r_0} = 0.7$ for OAM+5,+6,+7, the fluctuations of the received power with the transmitter diversity scheme are reduced by about 8 dB compared to single OAM mode transmission case, as shown in Fig. 5(b) and Fig. 6(a). It has been theoretically revealed higher order OAM modes are more affected by turbulence-induced distortions [15]. This phenomenon is also verified in the experiment. From Figs. 46, we can find that the higher order OAM based transmitter diversity system will have higher received power fluctuation under the same turbulence. When turbulence is too strong, as shown in Fig. 5(c) and Figs. 6(b) and (c), the received power fluctuations of OAM-based transmitter diversity and single OAM transmission get closer, which is mainly because the power of the transmitted modes may spread to further OAM mode from the intended one due to strong mode coupling. It should be note that both too weak and too strong mode coupling will cause the performance degradation of the proposed scheme.

The average bit error rate (BER) performance of a 16QAM-DMT signal and the interruption probability as the transmitted power changed with different transmitter architecture are also investigated. The interruption probability is corresponded to the ratio where the BER exceeds the forward error correction (FEC) threshold, and the threshold BER is set to $3.8 \times {10^{ - 3}}$. Figure 7 shows the performance of OAM FSO system based on transmitter mode diversity using OAM-1,0,1. For turbulence strength $D/{r_0} = 2$ and $D/{r_0} = 4$, both the average BER and the interruption probability of the transmitter diversity scheme achieves better performance than single OAM0 transmission case, as shown in Fig. 7(c) and Fig. 7(d). The required transmitter power at BER of 3.8×10−3 is relaxed by about 4.7 dB and 2 dB when the turbulence strength is $D/{r_0} = 2$ and $D/{r_0} = 4$. For interruption probability of 10%, the transmitter diversity scheme could relax the required transmitter power by about 1.7 dB and 3 dB under turbulence strength of $D/{r_0} = 2$ and $D/{r_0} = 4$. Under turbulence strength $D/{r_0} = 0.7$ and $D/{r_0} = 1$, the transmitter diversity scheme suffers a higher power penalty compared to single OAM0 transmission, which implies the low receiving power of the intended OAM mode for relatively weak mode coupling between neighboring modes and the intended mode, and is consist with Fig. 4.

 figure: Fig. 7.

Fig. 7. Experimental results for the average BER and the interruption probability against transmitted power for transmitter mode diversity using OAM-1,0,1.

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 Figures 8 and 9 present the measured average BER and the interruption probability against transmitted power for transmitter mode diversity schemes using OAM+2,+3,+4 and OAM+5,+6,+7. When the turbulence strengths are $D/{r_0} = 1$ for OAM+2,+3,+4 and $D/{r_0} = 0.7$ for OAM+5,+6,+7, it can be seen from the results in Fig. 8(b) and Fig. 9(a) that: 1) Compared with single OAM transmission case, the required transmitter power at BER of 3.8×10−3 is relaxed by 3 dB for OAM+2,+3,+4 and OAM+5,+6,+7, respectively. 2) By utilizing the transmitter diversity scheme, the required transmitter power for interruption probability of 10% of the transmitter diversity scheme could relax by about 1.8 dB, 2 dB. In Fig. 8(a, c) and Fig. 9(b, c), the average BER and the interruption probability of the transmitter diversity scheme are approximately same as the single OAM transmission cases, which can be ascribed to the weak or the strong mode coupling among transmitted modes. Here different transmitted OAM modes sets based transmitter diversity schemes under different turbulence strength are considered. It can be deduced from the results that the OAM modes sets used for transmitter diversity should be modified under different turbulence strength to achieve better performance.

 figure: Fig. 8.

Fig. 8. Experimental results for the average BER and the interruption probability against transmitted power for transmitter mode diversity schemes using OAM+2,+3,+4.

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 figure: Fig. 9.

Fig. 9. Experimental results for the average BER and the interruption probability against transmitted power for transmitter mode diversity schemes using OAM+5,+6,+7.

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We then investigate the system performance using the same OAM sets with different power distribution. Figure 10 shows the measured system performance for transmitter mode diversity using OAM+2,+3,+4 with power distribution 1:2:1 under turbulence $D/{r_0} = 1$. Comparing to single OAM+3 mode transmission, the required transmitter power for interruption probability of 10% of the transmitter diversity scheme could relax by about 1 dB, which is a little worse than the OAM mode diversity with the same transmitted power. The experimental results show that the power distribution of the employed OAM modes for transmitter diversity has a great influence on the transmission performance, which is related to the turbulence strength. To achieve better performance, one may need to optimized the power distribution under different turbulence strengths.

 figure: Fig. 10.

Fig. 10. Experimental results for transmitter mode diversity schemes with different power distribution. (a) Received power. (b) Cumulative probability of received power. (c) Average BER against transmitted power. (d) Interruption probability against transmitted power.

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In addition, we also study the system performance using different numbers of the employed OAM modes. Figure 11 shows the measured system performance for the mode diversity scheme using OAM+1,+2,+3,+4,+5 with equal power under turbulence $D/{r_0} = 1$. Comparing to single OAM+3 mode transmission, the required transmitter power for interruption probability of 10% of the transmitter diversity scheme could only relax by about 0.3 dB, which is worse than the OAM mode diversity with OAM+2,+3,+4. Actually, the number of the employed OAM modes for transmitter mode diversity will have great impact on the transmission performance. However, when the number of modes increases, the power of each OAM mode will decrease, which may cause the reduction of average received power and degrade the transmission performance.

 figure: Fig. 11.

Fig. 11. Experimental results for transmitter mode diversity schemes with different numbers of the employed modes at the transmitter. (a) Received power. (b) Cumulative probability of received power, (c) Average BER against transmitted power. (d) Interruption probability against transmitted power.

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5. Conclusion and discussion

In summary, we experimentally explore a transmitter mode diversity ($3 \times 1$ MISO) architecture in the OAM FSO link to further increase system tolerance to turbulence. To verify the feasibility of our proposed transmitter diversity scheme, an IM-DD system transmitting three OAM mode sets (OAM-1,0,1, OAM+2,+3,+4, OAM+5,+6,+7) with 39.06 Gbit/s 16QAM-DMT signal over 1.2 m free space link are experimentally demonstrated. Moreover, a simple multi-OAM phase pattern has been designed to efficiently generate three OAM modes simultaneously without adding system complexity. By utilizing OAM based transmitter mode diversity scheme, the fluctuations of the receiver power are reduced. The required transmitter power at average BER of 3.8×10−3 is relaxed by 3 dB, 3 dB, 4.7 dB and 2 dB under different atmosphere turbulence strength $D/{r_0}$=0.7, $D/{r_0}$=1, $D/{r_0}$=2 and $D/{r_0}$=4 using transmitter mode diversity scheme with mode sets OAM+5,+6,+7, OAM+2,+3,+4, OAM-1,0,1 and OAM-1,0,1, respectively. Compared with single OAM transmission, the required transmitted power at 10% interruption probability is relaxed by nearly 2 dB under moderate to strong turbulence. It should be note that OAM-based transmitter mode diversity scheme with particular mode states will have a specific effective turbulence strength range, which is mainly because the transmission characteristic of different OAM states under the same turbulence strength is significantly different. In addition, the proposed OAM-based transmitter mode diversity scheme can be easily combined with receiver mode diversity to further improve the transmission performance under atmosphere turbulence. Moreover, it is possible to choose OAM mode groups with sufficiently interval for mode-group multiplexing under atmosphere turbulence, in which each group is consist of several adjacent OAM modes for mode diversity, such as OAM+5,+6,+7 and OAM-5,-6,-7. Here all beams in each mode group carry the same data stream, while different mode groups carry different data stream. Considering the low-level crosstalk between different OAM mode groups in turbulence, it is possible to recover each mode group separately and mode diversity can be employed to suppress intra-mode-group crosstalk caused by turbulence. A further application in the mode-division multiplexed link of the proposed scheme will be explored in the future.

Funding

Science and Technology Research Program of Chongqing Municipal Education Commission (KJQN201900637, KJQN202000622); Doctoral Initial Funding of Chongqing University of Posts and Telecommunications (A2019-20, A2019-21); National Natural Science Foundation of China (61805031, 62001072); Science and Technology Commission of Shanghai Municipality (SKLSFO2018-06).

Disclosures

The authors declare no conflicts of interest.

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24. B. B. Yousif and E. E. Elsayed, “Performance enhancement of an orbital-angular-momentum-multiplexed free-space optical link under atmospheric turbulence effects using spatial-mode multiplexing and hybrid diversity based on adaptive MIMO equalization,” IEEE Access 7, 84401–84412 (2019). [CrossRef]  

25. L. Li, H. Song, R. Zhang, Z. Zhao, C. Liu, K. Pang, H. Song, J. Du, A. N. Willner, A. Almaiman, B. Lynn, R. Bock, M. Tur, and A. E. Willner, “Increasing system tolerance to turbulence in a 100-Gbit/s QPSK free-space optical link using both mode and space diversity,” Opt. Commun. 480, 126488 (2021). [CrossRef]  

26. L. Zhu and J. Wang, “Simultaneous generation of multiple orbital angular momentum (OAM) modes using a single phase-only element,” Opt. Express 23(20), 26221–26233 (2015). [CrossRef]  

References

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  1. A. M. Yao and M. J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photonics 3(2), 161–204 (2011).
    [Crossref]
  2. S. Franke-Arnold, L. Allen, and M. Padgett, “Advances in optical angular momentum,” Laser Photonics Rev. 2(4), 299–313 (2008).
    [Crossref]
  3. K. Dholakia and T. Čižmár, “Shaping the future of manipulation,” Nat. Photonics 5(6), 335–342 (2011).
    [Crossref]
  4. M. Padgett and R. Bowman, “Tweezers with a twist,” Nat. Photonics 5(6), 343–348 (2011).
    [Crossref]
  5. S. Furhapter, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “Spiral phase contrast imaging in microscopy,” Opt. Express 13(3), 689–694 (2005).
    [Crossref]
  6. M. P. J. Lavery, F. C. Speirits, S. M. Barnett, and M. J. Padgett, “Detection of a spinning object using light’s orbital angular momentum,” Science 341(6145), 537–540 (2013).
    [Crossref]
  7. A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
    [Crossref]
  8. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
    [Crossref]
  9. J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
    [Crossref]
  10. F. Feng, X. Jin, D. O’Brien, F. P. Payne, and T. D. Wilkinson, “Mode-Group Multiplexed Transmission using OAM modes over 1 km Ring-Core Fiber without MIMO Processing,” in Optical Fiber Communication Conference (Optical Society of America, 2017), paper Th2A.43.
  11. R. Zhang, H. Tan, J. Zhang, L. Shen, J. Liu, Y. Liu, L. Zhang, and S. Yu, “A novel ring-core fiber supporting MIMO-free 50 km transmission over high-order OAM modes,” in Optical Fiber Communication Conference (Optical Society of America, 2019), paper M1E.4.
  12. J. Wang, S. Li, C. Li, L. Zhu, C. Gui, D. Xie, Y. Qiu, Q. Yang, and S. Yu, “Ultra-high 230-bit/s/Hz Spectral Efficiency Using OFDM/OQAM 64-QAM Signals Over Pol-Muxed 22 Orbital Angular Momentum (OAM) Modes,” in Optical Fiber Communication Conference (Optical Society of America, 2014), paper W1H.4.
  13. J. Wang, S. Li, M. Luo, J. Liu, L. Zhu, C. Li, D. Xie, Q. Yang, S. Yu, J. Sun, X. Zhang, W. Shieh, and A. E. Willner, “N-dimentional Multiplexing Link With 1.036-Pbit/s Transmission Capacity and 112.6-bit/s/Hz Spectral Efficiency Using OFDM-8QAM Signals Over 368 WDM Pol-muxed 26 OAM Modes,” in European Conference on Optical Communication (ECOC, 2014), paper Mo.4.5.1.
  14. J. Wang, J. Liu, X. Lv, L. Zhu, D. Wang, S. Li, A. Wang, Y. Zhao, Y. Long, J. Du, X. Hu, N. Zhou, S. Chen, L. Fang, and F. Zhang, “Ultra-high 435-bit/s/Hz spectral efficiency using N-dimentional multiplexing and modulation link with pol-muxed 52 orbital angular momentum (OAM) modes carrying Nyquist 32-QAM signals,” in European Conference on Optical Communication (ECOC, 2015), paper Th.2.5.4.
  15. J. A. Anguita, M. A. Neifeld, and B. V. Vasic, “Modeling channel interference in an orbital angular momentum-multiplexed laser link,” Proc. SPIE (SPIE, 2009), paper 74640U.
  16. G. Funes, M. Vial, and J. A. Anguita, “Orbital-angular-momentum crosstalk and temporal fading in a terrestrial laser link using single-mode fiber coupling,” Opt. Express 23(18), 23133–233142 (2015).
    [Crossref]
  17. M.P. Lavery, C. Peuntinger, K. Guenthner, T. Bauer, P. Banze, D. Elser, R.W. Boyd, M. Padgett, C. Marquardt, and G. Leuchs, “Long distance free-space propagation of light carrying orbital angular momentum,” in Lasers Congress (Optical Society of America, 2016), paper LTh3B.1.
  18. Y. Ren, G. Xie, H. Huang, C. Bao, Y. Yan, N. Ahmed, M. P. J. Lavery, B. I. Erkmen, S. Dolinar, M. Tur, M. A. Neifeld, M. J. Padgett, R. W. Boyd, J. H. Shapiro, and A. E. Willner, “Adaptive optics compensation of multiple orbital angular momentum beams propagating through emulated atmospheric turbulence,” Opt. Lett. 39(10), 2845–2848 (2014).
    [Crossref]
  19. M. N. Horensteina, S. Pappasa, A. Fishov, and T. G. Bifano, “Electrostatic micromirrors for subaperturing in an adaptive optics system,” J. Electrost. 54(3-4), 321–332 (2002).
    [Crossref]
  20. Y. Ren, Z. Wang, G. Xie, L. Li, A. J. Willner, Y. Cao, Z. Zhao, Y. Yan, N. Ahmed, N. Ashrafi, S. Ashrafi, R. Bock, M. Tur, and A. E. Willner, “Atmospheric turbulence mitigation in an OAM-based MIMO free-space optical link using spatial diversity combined with MIMO equalization,” Opt. Lett. 41(11), 2406–2409 (2016).
    [Crossref]
  21. L. Zou, L. Wang, and S. Zhao, “Turbulence mitigation scheme based on spatial diversity in orbital-angular-momentum multiplexed system,” Opt. Commun. 400, 123–127 (2017).
    [Crossref]
  22. H. Song, L. Li, K. Pang, R. Zhang, K. Zou, Z. Zhao, J. Du, H. Song, C. Liu, Y. Cao, A. N. Willner, R. Bock, B. Lynn, M. Tur, and A. E. Willner, “Demonstration of enhanced tolerance to turbulence and misalignment of a 10-Gbit/s QPSK free-space optical link by utilizing two aperture pairs combined with detecting multiple modes,” in Optical Fiber Communication Conference (Optical Society of America, 2019), paper Th2A.41.
  23. M. A. Cox, L. Cheng, C. Rosales-Guzmán, and A. Forbes, “Modal diversity for robust free-space optical communications,” Phys. Rev. Appl. 10(2), 024020 (2018).
    [Crossref]
  24. B. B. Yousif and E. E. Elsayed, “Performance enhancement of an orbital-angular-momentum-multiplexed free-space optical link under atmospheric turbulence effects using spatial-mode multiplexing and hybrid diversity based on adaptive MIMO equalization,” IEEE Access 7, 84401–84412 (2019).
    [Crossref]
  25. L. Li, H. Song, R. Zhang, Z. Zhao, C. Liu, K. Pang, H. Song, J. Du, A. N. Willner, A. Almaiman, B. Lynn, R. Bock, M. Tur, and A. E. Willner, “Increasing system tolerance to turbulence in a 100-Gbit/s QPSK free-space optical link using both mode and space diversity,” Opt. Commun. 480, 126488 (2021).
    [Crossref]
  26. L. Zhu and J. Wang, “Simultaneous generation of multiple orbital angular momentum (OAM) modes using a single phase-only element,” Opt. Express 23(20), 26221–26233 (2015).
    [Crossref]

2021 (1)

L. Li, H. Song, R. Zhang, Z. Zhao, C. Liu, K. Pang, H. Song, J. Du, A. N. Willner, A. Almaiman, B. Lynn, R. Bock, M. Tur, and A. E. Willner, “Increasing system tolerance to turbulence in a 100-Gbit/s QPSK free-space optical link using both mode and space diversity,” Opt. Commun. 480, 126488 (2021).
[Crossref]

2019 (1)

B. B. Yousif and E. E. Elsayed, “Performance enhancement of an orbital-angular-momentum-multiplexed free-space optical link under atmospheric turbulence effects using spatial-mode multiplexing and hybrid diversity based on adaptive MIMO equalization,” IEEE Access 7, 84401–84412 (2019).
[Crossref]

2018 (1)

M. A. Cox, L. Cheng, C. Rosales-Guzmán, and A. Forbes, “Modal diversity for robust free-space optical communications,” Phys. Rev. Appl. 10(2), 024020 (2018).
[Crossref]

2017 (1)

L. Zou, L. Wang, and S. Zhao, “Turbulence mitigation scheme based on spatial diversity in orbital-angular-momentum multiplexed system,” Opt. Commun. 400, 123–127 (2017).
[Crossref]

2016 (1)

2015 (2)

2014 (1)

2013 (1)

M. P. J. Lavery, F. C. Speirits, S. M. Barnett, and M. J. Padgett, “Detection of a spinning object using light’s orbital angular momentum,” Science 341(6145), 537–540 (2013).
[Crossref]

2012 (1)

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

2011 (3)

A. M. Yao and M. J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photonics 3(2), 161–204 (2011).
[Crossref]

K. Dholakia and T. Čižmár, “Shaping the future of manipulation,” Nat. Photonics 5(6), 335–342 (2011).
[Crossref]

M. Padgett and R. Bowman, “Tweezers with a twist,” Nat. Photonics 5(6), 343–348 (2011).
[Crossref]

2008 (1)

S. Franke-Arnold, L. Allen, and M. Padgett, “Advances in optical angular momentum,” Laser Photonics Rev. 2(4), 299–313 (2008).
[Crossref]

2005 (1)

2002 (1)

M. N. Horensteina, S. Pappasa, A. Fishov, and T. G. Bifano, “Electrostatic micromirrors for subaperturing in an adaptive optics system,” J. Electrost. 54(3-4), 321–332 (2002).
[Crossref]

2001 (1)

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
[Crossref]

1992 (1)

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref]

Ahmed, N.

Allen, L.

S. Franke-Arnold, L. Allen, and M. Padgett, “Advances in optical angular momentum,” Laser Photonics Rev. 2(4), 299–313 (2008).
[Crossref]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref]

Almaiman, A.

L. Li, H. Song, R. Zhang, Z. Zhao, C. Liu, K. Pang, H. Song, J. Du, A. N. Willner, A. Almaiman, B. Lynn, R. Bock, M. Tur, and A. E. Willner, “Increasing system tolerance to turbulence in a 100-Gbit/s QPSK free-space optical link using both mode and space diversity,” Opt. Commun. 480, 126488 (2021).
[Crossref]

Anguita, J. A.

G. Funes, M. Vial, and J. A. Anguita, “Orbital-angular-momentum crosstalk and temporal fading in a terrestrial laser link using single-mode fiber coupling,” Opt. Express 23(18), 23133–233142 (2015).
[Crossref]

J. A. Anguita, M. A. Neifeld, and B. V. Vasic, “Modeling channel interference in an orbital angular momentum-multiplexed laser link,” Proc. SPIE (SPIE, 2009), paper 74640U.

Ashrafi, N.

Ashrafi, S.

Banze, P.

M.P. Lavery, C. Peuntinger, K. Guenthner, T. Bauer, P. Banze, D. Elser, R.W. Boyd, M. Padgett, C. Marquardt, and G. Leuchs, “Long distance free-space propagation of light carrying orbital angular momentum,” in Lasers Congress (Optical Society of America, 2016), paper LTh3B.1.

Bao, C.

Barnett, S. M.

M. P. J. Lavery, F. C. Speirits, S. M. Barnett, and M. J. Padgett, “Detection of a spinning object using light’s orbital angular momentum,” Science 341(6145), 537–540 (2013).
[Crossref]

Bauer, T.

M.P. Lavery, C. Peuntinger, K. Guenthner, T. Bauer, P. Banze, D. Elser, R.W. Boyd, M. Padgett, C. Marquardt, and G. Leuchs, “Long distance free-space propagation of light carrying orbital angular momentum,” in Lasers Congress (Optical Society of America, 2016), paper LTh3B.1.

Beijersbergen, M. W.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref]

Bernet, S.

Bifano, T. G.

M. N. Horensteina, S. Pappasa, A. Fishov, and T. G. Bifano, “Electrostatic micromirrors for subaperturing in an adaptive optics system,” J. Electrost. 54(3-4), 321–332 (2002).
[Crossref]

Bock, R.

L. Li, H. Song, R. Zhang, Z. Zhao, C. Liu, K. Pang, H. Song, J. Du, A. N. Willner, A. Almaiman, B. Lynn, R. Bock, M. Tur, and A. E. Willner, “Increasing system tolerance to turbulence in a 100-Gbit/s QPSK free-space optical link using both mode and space diversity,” Opt. Commun. 480, 126488 (2021).
[Crossref]

Y. Ren, Z. Wang, G. Xie, L. Li, A. J. Willner, Y. Cao, Z. Zhao, Y. Yan, N. Ahmed, N. Ashrafi, S. Ashrafi, R. Bock, M. Tur, and A. E. Willner, “Atmospheric turbulence mitigation in an OAM-based MIMO free-space optical link using spatial diversity combined with MIMO equalization,” Opt. Lett. 41(11), 2406–2409 (2016).
[Crossref]

H. Song, L. Li, K. Pang, R. Zhang, K. Zou, Z. Zhao, J. Du, H. Song, C. Liu, Y. Cao, A. N. Willner, R. Bock, B. Lynn, M. Tur, and A. E. Willner, “Demonstration of enhanced tolerance to turbulence and misalignment of a 10-Gbit/s QPSK free-space optical link by utilizing two aperture pairs combined with detecting multiple modes,” in Optical Fiber Communication Conference (Optical Society of America, 2019), paper Th2A.41.

Bowman, R.

M. Padgett and R. Bowman, “Tweezers with a twist,” Nat. Photonics 5(6), 343–348 (2011).
[Crossref]

Boyd, R. W.

Boyd, R.W.

M.P. Lavery, C. Peuntinger, K. Guenthner, T. Bauer, P. Banze, D. Elser, R.W. Boyd, M. Padgett, C. Marquardt, and G. Leuchs, “Long distance free-space propagation of light carrying orbital angular momentum,” in Lasers Congress (Optical Society of America, 2016), paper LTh3B.1.

Cao, Y.

Y. Ren, Z. Wang, G. Xie, L. Li, A. J. Willner, Y. Cao, Z. Zhao, Y. Yan, N. Ahmed, N. Ashrafi, S. Ashrafi, R. Bock, M. Tur, and A. E. Willner, “Atmospheric turbulence mitigation in an OAM-based MIMO free-space optical link using spatial diversity combined with MIMO equalization,” Opt. Lett. 41(11), 2406–2409 (2016).
[Crossref]

H. Song, L. Li, K. Pang, R. Zhang, K. Zou, Z. Zhao, J. Du, H. Song, C. Liu, Y. Cao, A. N. Willner, R. Bock, B. Lynn, M. Tur, and A. E. Willner, “Demonstration of enhanced tolerance to turbulence and misalignment of a 10-Gbit/s QPSK free-space optical link by utilizing two aperture pairs combined with detecting multiple modes,” in Optical Fiber Communication Conference (Optical Society of America, 2019), paper Th2A.41.

Chen, S.

J. Wang, J. Liu, X. Lv, L. Zhu, D. Wang, S. Li, A. Wang, Y. Zhao, Y. Long, J. Du, X. Hu, N. Zhou, S. Chen, L. Fang, and F. Zhang, “Ultra-high 435-bit/s/Hz spectral efficiency using N-dimentional multiplexing and modulation link with pol-muxed 52 orbital angular momentum (OAM) modes carrying Nyquist 32-QAM signals,” in European Conference on Optical Communication (ECOC, 2015), paper Th.2.5.4.

Cheng, L.

M. A. Cox, L. Cheng, C. Rosales-Guzmán, and A. Forbes, “Modal diversity for robust free-space optical communications,” Phys. Rev. Appl. 10(2), 024020 (2018).
[Crossref]

Cižmár, T.

K. Dholakia and T. Čižmár, “Shaping the future of manipulation,” Nat. Photonics 5(6), 335–342 (2011).
[Crossref]

Cox, M. A.

M. A. Cox, L. Cheng, C. Rosales-Guzmán, and A. Forbes, “Modal diversity for robust free-space optical communications,” Phys. Rev. Appl. 10(2), 024020 (2018).
[Crossref]

Dholakia, K.

K. Dholakia and T. Čižmár, “Shaping the future of manipulation,” Nat. Photonics 5(6), 335–342 (2011).
[Crossref]

Dolinar, S.

Y. Ren, G. Xie, H. Huang, C. Bao, Y. Yan, N. Ahmed, M. P. J. Lavery, B. I. Erkmen, S. Dolinar, M. Tur, M. A. Neifeld, M. J. Padgett, R. W. Boyd, J. H. Shapiro, and A. E. Willner, “Adaptive optics compensation of multiple orbital angular momentum beams propagating through emulated atmospheric turbulence,” Opt. Lett. 39(10), 2845–2848 (2014).
[Crossref]

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Du, J.

L. Li, H. Song, R. Zhang, Z. Zhao, C. Liu, K. Pang, H. Song, J. Du, A. N. Willner, A. Almaiman, B. Lynn, R. Bock, M. Tur, and A. E. Willner, “Increasing system tolerance to turbulence in a 100-Gbit/s QPSK free-space optical link using both mode and space diversity,” Opt. Commun. 480, 126488 (2021).
[Crossref]

H. Song, L. Li, K. Pang, R. Zhang, K. Zou, Z. Zhao, J. Du, H. Song, C. Liu, Y. Cao, A. N. Willner, R. Bock, B. Lynn, M. Tur, and A. E. Willner, “Demonstration of enhanced tolerance to turbulence and misalignment of a 10-Gbit/s QPSK free-space optical link by utilizing two aperture pairs combined with detecting multiple modes,” in Optical Fiber Communication Conference (Optical Society of America, 2019), paper Th2A.41.

J. Wang, J. Liu, X. Lv, L. Zhu, D. Wang, S. Li, A. Wang, Y. Zhao, Y. Long, J. Du, X. Hu, N. Zhou, S. Chen, L. Fang, and F. Zhang, “Ultra-high 435-bit/s/Hz spectral efficiency using N-dimentional multiplexing and modulation link with pol-muxed 52 orbital angular momentum (OAM) modes carrying Nyquist 32-QAM signals,” in European Conference on Optical Communication (ECOC, 2015), paper Th.2.5.4.

Elsayed, E. E.

B. B. Yousif and E. E. Elsayed, “Performance enhancement of an orbital-angular-momentum-multiplexed free-space optical link under atmospheric turbulence effects using spatial-mode multiplexing and hybrid diversity based on adaptive MIMO equalization,” IEEE Access 7, 84401–84412 (2019).
[Crossref]

Elser, D.

M.P. Lavery, C. Peuntinger, K. Guenthner, T. Bauer, P. Banze, D. Elser, R.W. Boyd, M. Padgett, C. Marquardt, and G. Leuchs, “Long distance free-space propagation of light carrying orbital angular momentum,” in Lasers Congress (Optical Society of America, 2016), paper LTh3B.1.

Erkmen, B. I.

Fang, L.

J. Wang, J. Liu, X. Lv, L. Zhu, D. Wang, S. Li, A. Wang, Y. Zhao, Y. Long, J. Du, X. Hu, N. Zhou, S. Chen, L. Fang, and F. Zhang, “Ultra-high 435-bit/s/Hz spectral efficiency using N-dimentional multiplexing and modulation link with pol-muxed 52 orbital angular momentum (OAM) modes carrying Nyquist 32-QAM signals,” in European Conference on Optical Communication (ECOC, 2015), paper Th.2.5.4.

Fazal, I. M.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Feng, F.

F. Feng, X. Jin, D. O’Brien, F. P. Payne, and T. D. Wilkinson, “Mode-Group Multiplexed Transmission using OAM modes over 1 km Ring-Core Fiber without MIMO Processing,” in Optical Fiber Communication Conference (Optical Society of America, 2017), paper Th2A.43.

Fishov, A.

M. N. Horensteina, S. Pappasa, A. Fishov, and T. G. Bifano, “Electrostatic micromirrors for subaperturing in an adaptive optics system,” J. Electrost. 54(3-4), 321–332 (2002).
[Crossref]

Forbes, A.

M. A. Cox, L. Cheng, C. Rosales-Guzmán, and A. Forbes, “Modal diversity for robust free-space optical communications,” Phys. Rev. Appl. 10(2), 024020 (2018).
[Crossref]

Franke-Arnold, S.

S. Franke-Arnold, L. Allen, and M. Padgett, “Advances in optical angular momentum,” Laser Photonics Rev. 2(4), 299–313 (2008).
[Crossref]

Funes, G.

Furhapter, S.

Guenthner, K.

M.P. Lavery, C. Peuntinger, K. Guenthner, T. Bauer, P. Banze, D. Elser, R.W. Boyd, M. Padgett, C. Marquardt, and G. Leuchs, “Long distance free-space propagation of light carrying orbital angular momentum,” in Lasers Congress (Optical Society of America, 2016), paper LTh3B.1.

Gui, C.

J. Wang, S. Li, C. Li, L. Zhu, C. Gui, D. Xie, Y. Qiu, Q. Yang, and S. Yu, “Ultra-high 230-bit/s/Hz Spectral Efficiency Using OFDM/OQAM 64-QAM Signals Over Pol-Muxed 22 Orbital Angular Momentum (OAM) Modes,” in Optical Fiber Communication Conference (Optical Society of America, 2014), paper W1H.4.

Horensteina, M. N.

M. N. Horensteina, S. Pappasa, A. Fishov, and T. G. Bifano, “Electrostatic micromirrors for subaperturing in an adaptive optics system,” J. Electrost. 54(3-4), 321–332 (2002).
[Crossref]

Hu, X.

J. Wang, J. Liu, X. Lv, L. Zhu, D. Wang, S. Li, A. Wang, Y. Zhao, Y. Long, J. Du, X. Hu, N. Zhou, S. Chen, L. Fang, and F. Zhang, “Ultra-high 435-bit/s/Hz spectral efficiency using N-dimentional multiplexing and modulation link with pol-muxed 52 orbital angular momentum (OAM) modes carrying Nyquist 32-QAM signals,” in European Conference on Optical Communication (ECOC, 2015), paper Th.2.5.4.

Huang, H.

Y. Ren, G. Xie, H. Huang, C. Bao, Y. Yan, N. Ahmed, M. P. J. Lavery, B. I. Erkmen, S. Dolinar, M. Tur, M. A. Neifeld, M. J. Padgett, R. W. Boyd, J. H. Shapiro, and A. E. Willner, “Adaptive optics compensation of multiple orbital angular momentum beams propagating through emulated atmospheric turbulence,” Opt. Lett. 39(10), 2845–2848 (2014).
[Crossref]

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Jesacher, A.

Jin, X.

F. Feng, X. Jin, D. O’Brien, F. P. Payne, and T. D. Wilkinson, “Mode-Group Multiplexed Transmission using OAM modes over 1 km Ring-Core Fiber without MIMO Processing,” in Optical Fiber Communication Conference (Optical Society of America, 2017), paper Th2A.43.

Lavery, M. P. J.

Lavery, M.P.

M.P. Lavery, C. Peuntinger, K. Guenthner, T. Bauer, P. Banze, D. Elser, R.W. Boyd, M. Padgett, C. Marquardt, and G. Leuchs, “Long distance free-space propagation of light carrying orbital angular momentum,” in Lasers Congress (Optical Society of America, 2016), paper LTh3B.1.

Leuchs, G.

M.P. Lavery, C. Peuntinger, K. Guenthner, T. Bauer, P. Banze, D. Elser, R.W. Boyd, M. Padgett, C. Marquardt, and G. Leuchs, “Long distance free-space propagation of light carrying orbital angular momentum,” in Lasers Congress (Optical Society of America, 2016), paper LTh3B.1.

Li, C.

J. Wang, S. Li, C. Li, L. Zhu, C. Gui, D. Xie, Y. Qiu, Q. Yang, and S. Yu, “Ultra-high 230-bit/s/Hz Spectral Efficiency Using OFDM/OQAM 64-QAM Signals Over Pol-Muxed 22 Orbital Angular Momentum (OAM) Modes,” in Optical Fiber Communication Conference (Optical Society of America, 2014), paper W1H.4.

J. Wang, S. Li, M. Luo, J. Liu, L. Zhu, C. Li, D. Xie, Q. Yang, S. Yu, J. Sun, X. Zhang, W. Shieh, and A. E. Willner, “N-dimentional Multiplexing Link With 1.036-Pbit/s Transmission Capacity and 112.6-bit/s/Hz Spectral Efficiency Using OFDM-8QAM Signals Over 368 WDM Pol-muxed 26 OAM Modes,” in European Conference on Optical Communication (ECOC, 2014), paper Mo.4.5.1.

Li, L.

L. Li, H. Song, R. Zhang, Z. Zhao, C. Liu, K. Pang, H. Song, J. Du, A. N. Willner, A. Almaiman, B. Lynn, R. Bock, M. Tur, and A. E. Willner, “Increasing system tolerance to turbulence in a 100-Gbit/s QPSK free-space optical link using both mode and space diversity,” Opt. Commun. 480, 126488 (2021).
[Crossref]

Y. Ren, Z. Wang, G. Xie, L. Li, A. J. Willner, Y. Cao, Z. Zhao, Y. Yan, N. Ahmed, N. Ashrafi, S. Ashrafi, R. Bock, M. Tur, and A. E. Willner, “Atmospheric turbulence mitigation in an OAM-based MIMO free-space optical link using spatial diversity combined with MIMO equalization,” Opt. Lett. 41(11), 2406–2409 (2016).
[Crossref]

H. Song, L. Li, K. Pang, R. Zhang, K. Zou, Z. Zhao, J. Du, H. Song, C. Liu, Y. Cao, A. N. Willner, R. Bock, B. Lynn, M. Tur, and A. E. Willner, “Demonstration of enhanced tolerance to turbulence and misalignment of a 10-Gbit/s QPSK free-space optical link by utilizing two aperture pairs combined with detecting multiple modes,” in Optical Fiber Communication Conference (Optical Society of America, 2019), paper Th2A.41.

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J. Wang, J. Liu, X. Lv, L. Zhu, D. Wang, S. Li, A. Wang, Y. Zhao, Y. Long, J. Du, X. Hu, N. Zhou, S. Chen, L. Fang, and F. Zhang, “Ultra-high 435-bit/s/Hz spectral efficiency using N-dimentional multiplexing and modulation link with pol-muxed 52 orbital angular momentum (OAM) modes carrying Nyquist 32-QAM signals,” in European Conference on Optical Communication (ECOC, 2015), paper Th.2.5.4.

J. Wang, S. Li, C. Li, L. Zhu, C. Gui, D. Xie, Y. Qiu, Q. Yang, and S. Yu, “Ultra-high 230-bit/s/Hz Spectral Efficiency Using OFDM/OQAM 64-QAM Signals Over Pol-Muxed 22 Orbital Angular Momentum (OAM) Modes,” in Optical Fiber Communication Conference (Optical Society of America, 2014), paper W1H.4.

J. Wang, S. Li, M. Luo, J. Liu, L. Zhu, C. Li, D. Xie, Q. Yang, S. Yu, J. Sun, X. Zhang, W. Shieh, and A. E. Willner, “N-dimentional Multiplexing Link With 1.036-Pbit/s Transmission Capacity and 112.6-bit/s/Hz Spectral Efficiency Using OFDM-8QAM Signals Over 368 WDM Pol-muxed 26 OAM Modes,” in European Conference on Optical Communication (ECOC, 2014), paper Mo.4.5.1.

Liu, C.

L. Li, H. Song, R. Zhang, Z. Zhao, C. Liu, K. Pang, H. Song, J. Du, A. N. Willner, A. Almaiman, B. Lynn, R. Bock, M. Tur, and A. E. Willner, “Increasing system tolerance to turbulence in a 100-Gbit/s QPSK free-space optical link using both mode and space diversity,” Opt. Commun. 480, 126488 (2021).
[Crossref]

H. Song, L. Li, K. Pang, R. Zhang, K. Zou, Z. Zhao, J. Du, H. Song, C. Liu, Y. Cao, A. N. Willner, R. Bock, B. Lynn, M. Tur, and A. E. Willner, “Demonstration of enhanced tolerance to turbulence and misalignment of a 10-Gbit/s QPSK free-space optical link by utilizing two aperture pairs combined with detecting multiple modes,” in Optical Fiber Communication Conference (Optical Society of America, 2019), paper Th2A.41.

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J. Wang, S. Li, M. Luo, J. Liu, L. Zhu, C. Li, D. Xie, Q. Yang, S. Yu, J. Sun, X. Zhang, W. Shieh, and A. E. Willner, “N-dimentional Multiplexing Link With 1.036-Pbit/s Transmission Capacity and 112.6-bit/s/Hz Spectral Efficiency Using OFDM-8QAM Signals Over 368 WDM Pol-muxed 26 OAM Modes,” in European Conference on Optical Communication (ECOC, 2014), paper Mo.4.5.1.

R. Zhang, H. Tan, J. Zhang, L. Shen, J. Liu, Y. Liu, L. Zhang, and S. Yu, “A novel ring-core fiber supporting MIMO-free 50 km transmission over high-order OAM modes,” in Optical Fiber Communication Conference (Optical Society of America, 2019), paper M1E.4.

J. Wang, J. Liu, X. Lv, L. Zhu, D. Wang, S. Li, A. Wang, Y. Zhao, Y. Long, J. Du, X. Hu, N. Zhou, S. Chen, L. Fang, and F. Zhang, “Ultra-high 435-bit/s/Hz spectral efficiency using N-dimentional multiplexing and modulation link with pol-muxed 52 orbital angular momentum (OAM) modes carrying Nyquist 32-QAM signals,” in European Conference on Optical Communication (ECOC, 2015), paper Th.2.5.4.

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R. Zhang, H. Tan, J. Zhang, L. Shen, J. Liu, Y. Liu, L. Zhang, and S. Yu, “A novel ring-core fiber supporting MIMO-free 50 km transmission over high-order OAM modes,” in Optical Fiber Communication Conference (Optical Society of America, 2019), paper M1E.4.

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J. Wang, J. Liu, X. Lv, L. Zhu, D. Wang, S. Li, A. Wang, Y. Zhao, Y. Long, J. Du, X. Hu, N. Zhou, S. Chen, L. Fang, and F. Zhang, “Ultra-high 435-bit/s/Hz spectral efficiency using N-dimentional multiplexing and modulation link with pol-muxed 52 orbital angular momentum (OAM) modes carrying Nyquist 32-QAM signals,” in European Conference on Optical Communication (ECOC, 2015), paper Th.2.5.4.

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J. Wang, S. Li, M. Luo, J. Liu, L. Zhu, C. Li, D. Xie, Q. Yang, S. Yu, J. Sun, X. Zhang, W. Shieh, and A. E. Willner, “N-dimentional Multiplexing Link With 1.036-Pbit/s Transmission Capacity and 112.6-bit/s/Hz Spectral Efficiency Using OFDM-8QAM Signals Over 368 WDM Pol-muxed 26 OAM Modes,” in European Conference on Optical Communication (ECOC, 2014), paper Mo.4.5.1.

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J. Wang, J. Liu, X. Lv, L. Zhu, D. Wang, S. Li, A. Wang, Y. Zhao, Y. Long, J. Du, X. Hu, N. Zhou, S. Chen, L. Fang, and F. Zhang, “Ultra-high 435-bit/s/Hz spectral efficiency using N-dimentional multiplexing and modulation link with pol-muxed 52 orbital angular momentum (OAM) modes carrying Nyquist 32-QAM signals,” in European Conference on Optical Communication (ECOC, 2015), paper Th.2.5.4.

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L. Li, H. Song, R. Zhang, Z. Zhao, C. Liu, K. Pang, H. Song, J. Du, A. N. Willner, A. Almaiman, B. Lynn, R. Bock, M. Tur, and A. E. Willner, “Increasing system tolerance to turbulence in a 100-Gbit/s QPSK free-space optical link using both mode and space diversity,” Opt. Commun. 480, 126488 (2021).
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H. Song, L. Li, K. Pang, R. Zhang, K. Zou, Z. Zhao, J. Du, H. Song, C. Liu, Y. Cao, A. N. Willner, R. Bock, B. Lynn, M. Tur, and A. E. Willner, “Demonstration of enhanced tolerance to turbulence and misalignment of a 10-Gbit/s QPSK free-space optical link by utilizing two aperture pairs combined with detecting multiple modes,” in Optical Fiber Communication Conference (Optical Society of America, 2019), paper Th2A.41.

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F. Feng, X. Jin, D. O’Brien, F. P. Payne, and T. D. Wilkinson, “Mode-Group Multiplexed Transmission using OAM modes over 1 km Ring-Core Fiber without MIMO Processing,” in Optical Fiber Communication Conference (Optical Society of America, 2017), paper Th2A.43.

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Y. Ren, G. Xie, H. Huang, C. Bao, Y. Yan, N. Ahmed, M. P. J. Lavery, B. I. Erkmen, S. Dolinar, M. Tur, M. A. Neifeld, M. J. Padgett, R. W. Boyd, J. H. Shapiro, and A. E. Willner, “Adaptive optics compensation of multiple orbital angular momentum beams propagating through emulated atmospheric turbulence,” Opt. Lett. 39(10), 2845–2848 (2014).
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L. Li, H. Song, R. Zhang, Z. Zhao, C. Liu, K. Pang, H. Song, J. Du, A. N. Willner, A. Almaiman, B. Lynn, R. Bock, M. Tur, and A. E. Willner, “Increasing system tolerance to turbulence in a 100-Gbit/s QPSK free-space optical link using both mode and space diversity,” Opt. Commun. 480, 126488 (2021).
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H. Song, L. Li, K. Pang, R. Zhang, K. Zou, Z. Zhao, J. Du, H. Song, C. Liu, Y. Cao, A. N. Willner, R. Bock, B. Lynn, M. Tur, and A. E. Willner, “Demonstration of enhanced tolerance to turbulence and misalignment of a 10-Gbit/s QPSK free-space optical link by utilizing two aperture pairs combined with detecting multiple modes,” in Optical Fiber Communication Conference (Optical Society of America, 2019), paper Th2A.41.

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F. Feng, X. Jin, D. O’Brien, F. P. Payne, and T. D. Wilkinson, “Mode-Group Multiplexed Transmission using OAM modes over 1 km Ring-Core Fiber without MIMO Processing,” in Optical Fiber Communication Conference (Optical Society of America, 2017), paper Th2A.43.

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M.P. Lavery, C. Peuntinger, K. Guenthner, T. Bauer, P. Banze, D. Elser, R.W. Boyd, M. Padgett, C. Marquardt, and G. Leuchs, “Long distance free-space propagation of light carrying orbital angular momentum,” in Lasers Congress (Optical Society of America, 2016), paper LTh3B.1.

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J. Wang, S. Li, C. Li, L. Zhu, C. Gui, D. Xie, Y. Qiu, Q. Yang, and S. Yu, “Ultra-high 230-bit/s/Hz Spectral Efficiency Using OFDM/OQAM 64-QAM Signals Over Pol-Muxed 22 Orbital Angular Momentum (OAM) Modes,” in Optical Fiber Communication Conference (Optical Society of America, 2014), paper W1H.4.

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R. Zhang, H. Tan, J. Zhang, L. Shen, J. Liu, Y. Liu, L. Zhang, and S. Yu, “A novel ring-core fiber supporting MIMO-free 50 km transmission over high-order OAM modes,” in Optical Fiber Communication Conference (Optical Society of America, 2019), paper M1E.4.

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J. Wang, S. Li, M. Luo, J. Liu, L. Zhu, C. Li, D. Xie, Q. Yang, S. Yu, J. Sun, X. Zhang, W. Shieh, and A. E. Willner, “N-dimentional Multiplexing Link With 1.036-Pbit/s Transmission Capacity and 112.6-bit/s/Hz Spectral Efficiency Using OFDM-8QAM Signals Over 368 WDM Pol-muxed 26 OAM Modes,” in European Conference on Optical Communication (ECOC, 2014), paper Mo.4.5.1.

Song, H.

L. Li, H. Song, R. Zhang, Z. Zhao, C. Liu, K. Pang, H. Song, J. Du, A. N. Willner, A. Almaiman, B. Lynn, R. Bock, M. Tur, and A. E. Willner, “Increasing system tolerance to turbulence in a 100-Gbit/s QPSK free-space optical link using both mode and space diversity,” Opt. Commun. 480, 126488 (2021).
[Crossref]

L. Li, H. Song, R. Zhang, Z. Zhao, C. Liu, K. Pang, H. Song, J. Du, A. N. Willner, A. Almaiman, B. Lynn, R. Bock, M. Tur, and A. E. Willner, “Increasing system tolerance to turbulence in a 100-Gbit/s QPSK free-space optical link using both mode and space diversity,” Opt. Commun. 480, 126488 (2021).
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H. Song, L. Li, K. Pang, R. Zhang, K. Zou, Z. Zhao, J. Du, H. Song, C. Liu, Y. Cao, A. N. Willner, R. Bock, B. Lynn, M. Tur, and A. E. Willner, “Demonstration of enhanced tolerance to turbulence and misalignment of a 10-Gbit/s QPSK free-space optical link by utilizing two aperture pairs combined with detecting multiple modes,” in Optical Fiber Communication Conference (Optical Society of America, 2019), paper Th2A.41.

H. Song, L. Li, K. Pang, R. Zhang, K. Zou, Z. Zhao, J. Du, H. Song, C. Liu, Y. Cao, A. N. Willner, R. Bock, B. Lynn, M. Tur, and A. E. Willner, “Demonstration of enhanced tolerance to turbulence and misalignment of a 10-Gbit/s QPSK free-space optical link by utilizing two aperture pairs combined with detecting multiple modes,” in Optical Fiber Communication Conference (Optical Society of America, 2019), paper Th2A.41.

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M. P. J. Lavery, F. C. Speirits, S. M. Barnett, and M. J. Padgett, “Detection of a spinning object using light’s orbital angular momentum,” Science 341(6145), 537–540 (2013).
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L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
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R. Zhang, H. Tan, J. Zhang, L. Shen, J. Liu, Y. Liu, L. Zhang, and S. Yu, “A novel ring-core fiber supporting MIMO-free 50 km transmission over high-order OAM modes,” in Optical Fiber Communication Conference (Optical Society of America, 2019), paper M1E.4.

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L. Li, H. Song, R. Zhang, Z. Zhao, C. Liu, K. Pang, H. Song, J. Du, A. N. Willner, A. Almaiman, B. Lynn, R. Bock, M. Tur, and A. E. Willner, “Increasing system tolerance to turbulence in a 100-Gbit/s QPSK free-space optical link using both mode and space diversity,” Opt. Commun. 480, 126488 (2021).
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Y. Ren, Z. Wang, G. Xie, L. Li, A. J. Willner, Y. Cao, Z. Zhao, Y. Yan, N. Ahmed, N. Ashrafi, S. Ashrafi, R. Bock, M. Tur, and A. E. Willner, “Atmospheric turbulence mitigation in an OAM-based MIMO free-space optical link using spatial diversity combined with MIMO equalization,” Opt. Lett. 41(11), 2406–2409 (2016).
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Y. Ren, G. Xie, H. Huang, C. Bao, Y. Yan, N. Ahmed, M. P. J. Lavery, B. I. Erkmen, S. Dolinar, M. Tur, M. A. Neifeld, M. J. Padgett, R. W. Boyd, J. H. Shapiro, and A. E. Willner, “Adaptive optics compensation of multiple orbital angular momentum beams propagating through emulated atmospheric turbulence,” Opt. Lett. 39(10), 2845–2848 (2014).
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J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
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J. Wang, J. Liu, X. Lv, L. Zhu, D. Wang, S. Li, A. Wang, Y. Zhao, Y. Long, J. Du, X. Hu, N. Zhou, S. Chen, L. Fang, and F. Zhang, “Ultra-high 435-bit/s/Hz spectral efficiency using N-dimentional multiplexing and modulation link with pol-muxed 52 orbital angular momentum (OAM) modes carrying Nyquist 32-QAM signals,” in European Conference on Optical Communication (ECOC, 2015), paper Th.2.5.4.

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J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

J. Wang, S. Li, C. Li, L. Zhu, C. Gui, D. Xie, Y. Qiu, Q. Yang, and S. Yu, “Ultra-high 230-bit/s/Hz Spectral Efficiency Using OFDM/OQAM 64-QAM Signals Over Pol-Muxed 22 Orbital Angular Momentum (OAM) Modes,” in Optical Fiber Communication Conference (Optical Society of America, 2014), paper W1H.4.

J. Wang, S. Li, M. Luo, J. Liu, L. Zhu, C. Li, D. Xie, Q. Yang, S. Yu, J. Sun, X. Zhang, W. Shieh, and A. E. Willner, “N-dimentional Multiplexing Link With 1.036-Pbit/s Transmission Capacity and 112.6-bit/s/Hz Spectral Efficiency Using OFDM-8QAM Signals Over 368 WDM Pol-muxed 26 OAM Modes,” in European Conference on Optical Communication (ECOC, 2014), paper Mo.4.5.1.

J. Wang, J. Liu, X. Lv, L. Zhu, D. Wang, S. Li, A. Wang, Y. Zhao, Y. Long, J. Du, X. Hu, N. Zhou, S. Chen, L. Fang, and F. Zhang, “Ultra-high 435-bit/s/Hz spectral efficiency using N-dimentional multiplexing and modulation link with pol-muxed 52 orbital angular momentum (OAM) modes carrying Nyquist 32-QAM signals,” in European Conference on Optical Communication (ECOC, 2015), paper Th.2.5.4.

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A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
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F. Feng, X. Jin, D. O’Brien, F. P. Payne, and T. D. Wilkinson, “Mode-Group Multiplexed Transmission using OAM modes over 1 km Ring-Core Fiber without MIMO Processing,” in Optical Fiber Communication Conference (Optical Society of America, 2017), paper Th2A.43.

Willner, A. E.

L. Li, H. Song, R. Zhang, Z. Zhao, C. Liu, K. Pang, H. Song, J. Du, A. N. Willner, A. Almaiman, B. Lynn, R. Bock, M. Tur, and A. E. Willner, “Increasing system tolerance to turbulence in a 100-Gbit/s QPSK free-space optical link using both mode and space diversity,” Opt. Commun. 480, 126488 (2021).
[Crossref]

Y. Ren, Z. Wang, G. Xie, L. Li, A. J. Willner, Y. Cao, Z. Zhao, Y. Yan, N. Ahmed, N. Ashrafi, S. Ashrafi, R. Bock, M. Tur, and A. E. Willner, “Atmospheric turbulence mitigation in an OAM-based MIMO free-space optical link using spatial diversity combined with MIMO equalization,” Opt. Lett. 41(11), 2406–2409 (2016).
[Crossref]

Y. Ren, G. Xie, H. Huang, C. Bao, Y. Yan, N. Ahmed, M. P. J. Lavery, B. I. Erkmen, S. Dolinar, M. Tur, M. A. Neifeld, M. J. Padgett, R. W. Boyd, J. H. Shapiro, and A. E. Willner, “Adaptive optics compensation of multiple orbital angular momentum beams propagating through emulated atmospheric turbulence,” Opt. Lett. 39(10), 2845–2848 (2014).
[Crossref]

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

J. Wang, S. Li, M. Luo, J. Liu, L. Zhu, C. Li, D. Xie, Q. Yang, S. Yu, J. Sun, X. Zhang, W. Shieh, and A. E. Willner, “N-dimentional Multiplexing Link With 1.036-Pbit/s Transmission Capacity and 112.6-bit/s/Hz Spectral Efficiency Using OFDM-8QAM Signals Over 368 WDM Pol-muxed 26 OAM Modes,” in European Conference on Optical Communication (ECOC, 2014), paper Mo.4.5.1.

H. Song, L. Li, K. Pang, R. Zhang, K. Zou, Z. Zhao, J. Du, H. Song, C. Liu, Y. Cao, A. N. Willner, R. Bock, B. Lynn, M. Tur, and A. E. Willner, “Demonstration of enhanced tolerance to turbulence and misalignment of a 10-Gbit/s QPSK free-space optical link by utilizing two aperture pairs combined with detecting multiple modes,” in Optical Fiber Communication Conference (Optical Society of America, 2019), paper Th2A.41.

Willner, A. J.

Willner, A. N.

L. Li, H. Song, R. Zhang, Z. Zhao, C. Liu, K. Pang, H. Song, J. Du, A. N. Willner, A. Almaiman, B. Lynn, R. Bock, M. Tur, and A. E. Willner, “Increasing system tolerance to turbulence in a 100-Gbit/s QPSK free-space optical link using both mode and space diversity,” Opt. Commun. 480, 126488 (2021).
[Crossref]

H. Song, L. Li, K. Pang, R. Zhang, K. Zou, Z. Zhao, J. Du, H. Song, C. Liu, Y. Cao, A. N. Willner, R. Bock, B. Lynn, M. Tur, and A. E. Willner, “Demonstration of enhanced tolerance to turbulence and misalignment of a 10-Gbit/s QPSK free-space optical link by utilizing two aperture pairs combined with detecting multiple modes,” in Optical Fiber Communication Conference (Optical Society of America, 2019), paper Th2A.41.

Woerdman, J. P.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref]

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J. Wang, S. Li, M. Luo, J. Liu, L. Zhu, C. Li, D. Xie, Q. Yang, S. Yu, J. Sun, X. Zhang, W. Shieh, and A. E. Willner, “N-dimentional Multiplexing Link With 1.036-Pbit/s Transmission Capacity and 112.6-bit/s/Hz Spectral Efficiency Using OFDM-8QAM Signals Over 368 WDM Pol-muxed 26 OAM Modes,” in European Conference on Optical Communication (ECOC, 2014), paper Mo.4.5.1.

J. Wang, S. Li, C. Li, L. Zhu, C. Gui, D. Xie, Y. Qiu, Q. Yang, and S. Yu, “Ultra-high 230-bit/s/Hz Spectral Efficiency Using OFDM/OQAM 64-QAM Signals Over Pol-Muxed 22 Orbital Angular Momentum (OAM) Modes,” in Optical Fiber Communication Conference (Optical Society of America, 2014), paper W1H.4.

Xie, G.

Yan, Y.

Yang, J.-Y.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
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J. Wang, S. Li, C. Li, L. Zhu, C. Gui, D. Xie, Y. Qiu, Q. Yang, and S. Yu, “Ultra-high 230-bit/s/Hz Spectral Efficiency Using OFDM/OQAM 64-QAM Signals Over Pol-Muxed 22 Orbital Angular Momentum (OAM) Modes,” in Optical Fiber Communication Conference (Optical Society of America, 2014), paper W1H.4.

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A. M. Yao and M. J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photonics 3(2), 161–204 (2011).
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B. B. Yousif and E. E. Elsayed, “Performance enhancement of an orbital-angular-momentum-multiplexed free-space optical link under atmospheric turbulence effects using spatial-mode multiplexing and hybrid diversity based on adaptive MIMO equalization,” IEEE Access 7, 84401–84412 (2019).
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Yu, S.

J. Wang, S. Li, C. Li, L. Zhu, C. Gui, D. Xie, Y. Qiu, Q. Yang, and S. Yu, “Ultra-high 230-bit/s/Hz Spectral Efficiency Using OFDM/OQAM 64-QAM Signals Over Pol-Muxed 22 Orbital Angular Momentum (OAM) Modes,” in Optical Fiber Communication Conference (Optical Society of America, 2014), paper W1H.4.

J. Wang, S. Li, M. Luo, J. Liu, L. Zhu, C. Li, D. Xie, Q. Yang, S. Yu, J. Sun, X. Zhang, W. Shieh, and A. E. Willner, “N-dimentional Multiplexing Link With 1.036-Pbit/s Transmission Capacity and 112.6-bit/s/Hz Spectral Efficiency Using OFDM-8QAM Signals Over 368 WDM Pol-muxed 26 OAM Modes,” in European Conference on Optical Communication (ECOC, 2014), paper Mo.4.5.1.

R. Zhang, H. Tan, J. Zhang, L. Shen, J. Liu, Y. Liu, L. Zhang, and S. Yu, “A novel ring-core fiber supporting MIMO-free 50 km transmission over high-order OAM modes,” in Optical Fiber Communication Conference (Optical Society of America, 2019), paper M1E.4.

Yue, Y.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
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A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
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J. Wang, J. Liu, X. Lv, L. Zhu, D. Wang, S. Li, A. Wang, Y. Zhao, Y. Long, J. Du, X. Hu, N. Zhou, S. Chen, L. Fang, and F. Zhang, “Ultra-high 435-bit/s/Hz spectral efficiency using N-dimentional multiplexing and modulation link with pol-muxed 52 orbital angular momentum (OAM) modes carrying Nyquist 32-QAM signals,” in European Conference on Optical Communication (ECOC, 2015), paper Th.2.5.4.

Zhang, J.

R. Zhang, H. Tan, J. Zhang, L. Shen, J. Liu, Y. Liu, L. Zhang, and S. Yu, “A novel ring-core fiber supporting MIMO-free 50 km transmission over high-order OAM modes,” in Optical Fiber Communication Conference (Optical Society of America, 2019), paper M1E.4.

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R. Zhang, H. Tan, J. Zhang, L. Shen, J. Liu, Y. Liu, L. Zhang, and S. Yu, “A novel ring-core fiber supporting MIMO-free 50 km transmission over high-order OAM modes,” in Optical Fiber Communication Conference (Optical Society of America, 2019), paper M1E.4.

Zhang, R.

L. Li, H. Song, R. Zhang, Z. Zhao, C. Liu, K. Pang, H. Song, J. Du, A. N. Willner, A. Almaiman, B. Lynn, R. Bock, M. Tur, and A. E. Willner, “Increasing system tolerance to turbulence in a 100-Gbit/s QPSK free-space optical link using both mode and space diversity,” Opt. Commun. 480, 126488 (2021).
[Crossref]

R. Zhang, H. Tan, J. Zhang, L. Shen, J. Liu, Y. Liu, L. Zhang, and S. Yu, “A novel ring-core fiber supporting MIMO-free 50 km transmission over high-order OAM modes,” in Optical Fiber Communication Conference (Optical Society of America, 2019), paper M1E.4.

H. Song, L. Li, K. Pang, R. Zhang, K. Zou, Z. Zhao, J. Du, H. Song, C. Liu, Y. Cao, A. N. Willner, R. Bock, B. Lynn, M. Tur, and A. E. Willner, “Demonstration of enhanced tolerance to turbulence and misalignment of a 10-Gbit/s QPSK free-space optical link by utilizing two aperture pairs combined with detecting multiple modes,” in Optical Fiber Communication Conference (Optical Society of America, 2019), paper Th2A.41.

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J. Wang, S. Li, M. Luo, J. Liu, L. Zhu, C. Li, D. Xie, Q. Yang, S. Yu, J. Sun, X. Zhang, W. Shieh, and A. E. Willner, “N-dimentional Multiplexing Link With 1.036-Pbit/s Transmission Capacity and 112.6-bit/s/Hz Spectral Efficiency Using OFDM-8QAM Signals Over 368 WDM Pol-muxed 26 OAM Modes,” in European Conference on Optical Communication (ECOC, 2014), paper Mo.4.5.1.

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J. Wang, J. Liu, X. Lv, L. Zhu, D. Wang, S. Li, A. Wang, Y. Zhao, Y. Long, J. Du, X. Hu, N. Zhou, S. Chen, L. Fang, and F. Zhang, “Ultra-high 435-bit/s/Hz spectral efficiency using N-dimentional multiplexing and modulation link with pol-muxed 52 orbital angular momentum (OAM) modes carrying Nyquist 32-QAM signals,” in European Conference on Optical Communication (ECOC, 2015), paper Th.2.5.4.

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L. Li, H. Song, R. Zhang, Z. Zhao, C. Liu, K. Pang, H. Song, J. Du, A. N. Willner, A. Almaiman, B. Lynn, R. Bock, M. Tur, and A. E. Willner, “Increasing system tolerance to turbulence in a 100-Gbit/s QPSK free-space optical link using both mode and space diversity,” Opt. Commun. 480, 126488 (2021).
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J. Wang, J. Liu, X. Lv, L. Zhu, D. Wang, S. Li, A. Wang, Y. Zhao, Y. Long, J. Du, X. Hu, N. Zhou, S. Chen, L. Fang, and F. Zhang, “Ultra-high 435-bit/s/Hz spectral efficiency using N-dimentional multiplexing and modulation link with pol-muxed 52 orbital angular momentum (OAM) modes carrying Nyquist 32-QAM signals,” in European Conference on Optical Communication (ECOC, 2015), paper Th.2.5.4.

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J. Wang, S. Li, M. Luo, J. Liu, L. Zhu, C. Li, D. Xie, Q. Yang, S. Yu, J. Sun, X. Zhang, W. Shieh, and A. E. Willner, “N-dimentional Multiplexing Link With 1.036-Pbit/s Transmission Capacity and 112.6-bit/s/Hz Spectral Efficiency Using OFDM-8QAM Signals Over 368 WDM Pol-muxed 26 OAM Modes,” in European Conference on Optical Communication (ECOC, 2014), paper Mo.4.5.1.

J. Wang, S. Li, C. Li, L. Zhu, C. Gui, D. Xie, Y. Qiu, Q. Yang, and S. Yu, “Ultra-high 230-bit/s/Hz Spectral Efficiency Using OFDM/OQAM 64-QAM Signals Over Pol-Muxed 22 Orbital Angular Momentum (OAM) Modes,” in Optical Fiber Communication Conference (Optical Society of America, 2014), paper W1H.4.

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H. Song, L. Li, K. Pang, R. Zhang, K. Zou, Z. Zhao, J. Du, H. Song, C. Liu, Y. Cao, A. N. Willner, R. Bock, B. Lynn, M. Tur, and A. E. Willner, “Demonstration of enhanced tolerance to turbulence and misalignment of a 10-Gbit/s QPSK free-space optical link by utilizing two aperture pairs combined with detecting multiple modes,” in Optical Fiber Communication Conference (Optical Society of America, 2019), paper Th2A.41.

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B. B. Yousif and E. E. Elsayed, “Performance enhancement of an orbital-angular-momentum-multiplexed free-space optical link under atmospheric turbulence effects using spatial-mode multiplexing and hybrid diversity based on adaptive MIMO equalization,” IEEE Access 7, 84401–84412 (2019).
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L. Zou, L. Wang, and S. Zhao, “Turbulence mitigation scheme based on spatial diversity in orbital-angular-momentum multiplexed system,” Opt. Commun. 400, 123–127 (2017).
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L. Li, H. Song, R. Zhang, Z. Zhao, C. Liu, K. Pang, H. Song, J. Du, A. N. Willner, A. Almaiman, B. Lynn, R. Bock, M. Tur, and A. E. Willner, “Increasing system tolerance to turbulence in a 100-Gbit/s QPSK free-space optical link using both mode and space diversity,” Opt. Commun. 480, 126488 (2021).
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R. Zhang, H. Tan, J. Zhang, L. Shen, J. Liu, Y. Liu, L. Zhang, and S. Yu, “A novel ring-core fiber supporting MIMO-free 50 km transmission over high-order OAM modes,” in Optical Fiber Communication Conference (Optical Society of America, 2019), paper M1E.4.

J. Wang, S. Li, C. Li, L. Zhu, C. Gui, D. Xie, Y. Qiu, Q. Yang, and S. Yu, “Ultra-high 230-bit/s/Hz Spectral Efficiency Using OFDM/OQAM 64-QAM Signals Over Pol-Muxed 22 Orbital Angular Momentum (OAM) Modes,” in Optical Fiber Communication Conference (Optical Society of America, 2014), paper W1H.4.

J. Wang, S. Li, M. Luo, J. Liu, L. Zhu, C. Li, D. Xie, Q. Yang, S. Yu, J. Sun, X. Zhang, W. Shieh, and A. E. Willner, “N-dimentional Multiplexing Link With 1.036-Pbit/s Transmission Capacity and 112.6-bit/s/Hz Spectral Efficiency Using OFDM-8QAM Signals Over 368 WDM Pol-muxed 26 OAM Modes,” in European Conference on Optical Communication (ECOC, 2014), paper Mo.4.5.1.

J. Wang, J. Liu, X. Lv, L. Zhu, D. Wang, S. Li, A. Wang, Y. Zhao, Y. Long, J. Du, X. Hu, N. Zhou, S. Chen, L. Fang, and F. Zhang, “Ultra-high 435-bit/s/Hz spectral efficiency using N-dimentional multiplexing and modulation link with pol-muxed 52 orbital angular momentum (OAM) modes carrying Nyquist 32-QAM signals,” in European Conference on Optical Communication (ECOC, 2015), paper Th.2.5.4.

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H. Song, L. Li, K. Pang, R. Zhang, K. Zou, Z. Zhao, J. Du, H. Song, C. Liu, Y. Cao, A. N. Willner, R. Bock, B. Lynn, M. Tur, and A. E. Willner, “Demonstration of enhanced tolerance to turbulence and misalignment of a 10-Gbit/s QPSK free-space optical link by utilizing two aperture pairs combined with detecting multiple modes,” in Optical Fiber Communication Conference (Optical Society of America, 2019), paper Th2A.41.

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Figures (11)

Fig. 1.
Fig. 1. Concept and principle of the proposed FSO communication link using OAM-based transmitter-diversity for increased tolerance to atmospheric turbulence. (a) Single-input single-output (SISO) transmission with only one OAM mode, (b) Multi-input single-output (MISO) system with multiple OAM modes.
Fig. 2.
Fig. 2. Experimental setup of OAM free space communication system based on transmitter mode diversity. Insets (a) a combination of a multi-OAM phase pattern and pseudo-random phase masks; (b) fork grating phase patterns of OAM-3. AWG: arbitrary waveform generator; IM: intensity modulator; PC: polarization controller; VOA: variable optical attenuator; Col.: collimator; Pol.: polarizer; L1: lens (f=100 mm); L2: aspheric lenses (f=18.4 mm); EDFA: erbium-doped fiber amplifier; OC: optical coupler; OTF: optical tunable filter; PD: photo detector.
Fig. 3.
Fig. 3. Measured intensity profiles of the single OAM transmission scheme and transmitter mode diversity scheme with and without turbulence.
Fig. 4.
Fig. 4. Experimental received power and cumulative probability of received power with transmitting power at 0 dBm under turbulence strength D/r0 = 0.7, 1, 2 and 4. For single OAM transmission, an OAM0 beam is transmitted; for transmitter mode diversity, an OAM-1,0,1 beam is transmitted.
Fig. 5.
Fig. 5. Experimental receiving power and cumulative probability of receiving power with transmitting power at 0 dBm under turbulence strength D/r0 = 0.7, 1, 2. For single OAM transmission, an OAM+3 beam is transmitted; for transmitter mode diversity, an OAM+2,+3,+4 beam is transmitted.
Fig. 6.
Fig. 6. Experimental receiving power and cumulative probability of receiving power with transmitting power at 0 dBm under turbulence strength D/r0 = 0.7, 1, 2. For single OAM transmission, an OAM+6 beam is transmitted; for transmitter mode diversity, an OAM+5,+6,+7 beam is transmitted.
Fig. 7.
Fig. 7. Experimental results for the average BER and the interruption probability against transmitted power for transmitter mode diversity using OAM-1,0,1.
Fig. 8.
Fig. 8. Experimental results for the average BER and the interruption probability against transmitted power for transmitter mode diversity schemes using OAM+2,+3,+4.
Fig. 9.
Fig. 9. Experimental results for the average BER and the interruption probability against transmitted power for transmitter mode diversity schemes using OAM+5,+6,+7.
Fig. 10.
Fig. 10. Experimental results for transmitter mode diversity schemes with different power distribution. (a) Received power. (b) Cumulative probability of received power. (c) Average BER against transmitted power. (d) Interruption probability against transmitted power.
Fig. 11.
Fig. 11. Experimental results for transmitter mode diversity schemes with different numbers of the employed modes at the transmitter. (a) Received power. (b) Cumulative probability of received power, (c) Average BER against transmitted power. (d) Interruption probability against transmitted power.

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