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 [1–7]. 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 [9–11].

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 [12–14]. 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.

 

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.

 

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.

 

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 4–6 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.

 

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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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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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. 4–6, 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.

 

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.

 

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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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.

 

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.

 

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.