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Abstract
Underwater wireless optical communication (UWOC) is a critical technology for underwater communication, providing high speed, low latency, and security advantages. However, the strong attenuation in the water channel still limits the UWOC systems and their performances require further improvement. In this study, an orbital angular momentum (OAM) multiplexing UWOC system that uses photon-counting detection is experimentally demonstrated. By employing a single-photon counting module to receive photon signals, we analyze the bit error rate (BER) and photon-counting statistics by building a theoretical model that fits the real system, and demodulate the OAM states in single photon level and implement signal processing using field programmable gate array (FPGA) programming. Based on these modules, a 2-OAM multiplexed UWOC link is established over a water channel of 9 m. By using on-off keying modulation and 2-pulse position modulation, we achieve a BER of 1.26×10−3 with data rate of 20Mbps and 3.17×10−4 with data rate of 10Mbps respectively, which below the forward error correction (FEC) threshold of 3.8×10−3. The total transmission loss is 37 dB under an emission power of 0.5 mW, which is equivalent to the attenuation of 283 m Jerlov I type seawater from the perspective of energy loss. Our verified communication scheme will benefit the development of long-range and high-capacity UWOC.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
The demand for high-speed, secure, and low-latency underwater communication technology has rapidly increased due to the continuous advancement of marine exploration and development activities [1,2]. Underwater acoustic communication (UAC) is currently the primary mode of underwater transmission and has made significant progress, with a transmission distance of up to 100 kilometers [2]. However, UAC’s limited bandwidth results in low transmission capacity and long delays, highlighting the advantages of UWOC. UWOC has been developed to provide high-speed, low-latency, and high-security data transmission, with smaller space requirements and energy consumption [1–5]. In certain underwater scenarios, UWOC may replace UAC for improved data transmission performance. Extensive research and new technologies have enabled UWOC to achieve data rates of Mbps [6] and Gbps [7–9], with link distances exceeding hundreds of meters [6,10]. UWOC and UAC can complement each other and serve underwater communication jointly.
In UWOC, the seawater channel causes significant attenuation of signal light despite the transmission window for blue-green light. Conventional photodiode-based receivers have a high detection threshold, which limits the maximum communication distance [6]. Single photon detectors (SPDs), commonly used in quantum field, can serve as receivers in UWOC systems to establish robust data links in large-loss underwater channels [11–14], thereby extending the communication range to meet the demands for long-distance UWOC. The feasibility of photon-counting receivers has been experimentally verified [15–19]. In 2016, Rao et al. achieved an underwater photon-counting link with a data rate of 10.416 Mbps in a 30-foot water channel [15]. By using 256-pulse position modulation (256PPM), Hu et al. achieved data transmission with a symbol error rate of 6.31$\times 10^{-4}$ over a 120m Jerlov II underwater channel, with a photonic efficiency of up to 3.32 bits/photon [16]. Yan et al. proposed an underwater photon-inter-correlation communication scheme [18] to establish data links in a 105m underwater channel with approximately $10^{-5}$ surviving photons per pulse at the receiver. In 2022, Gai et al. achieved photon-counting UWOC with polarization multiplexing over a 92 m water channel [19].
The demand for high-capacity underwater communication systems has prompted researchers to explore new methods for increasing capacity beyond the limitations of traditional multiplexing techniques that rely on time, wavelength, and polarization. Recent advances in mode-division multiplexing have introduced OAM as a promising approach for communications [20]. OAM beams [21,22], which have an infinite number of orthogonal modes, can be utilized as independent channels to significantly increase capacity [20,23–25]. By transmitting multiple OAM beams coaxially, each acting as an independent channel based on the orthogonal modes, underwater OAM multiplexing links can be established. Experimental demonstrations have shown that underwater links with total capacities of 4 Gbps and 40 Gbps at a distance of 1.2 m can be achieved using 4-OAM multiplexing [26]. The degradation effects of OAM beams in scattering, water flow, and turbulence environments have also been investigated. In 2021, Zhang et al. designed and demonstrated a compact and energy-efficient OAM multiplexing UWOC prototype system that supported the multiplexing of two 625 Mbps OAM channels in a 6 m underwater environment [27].
To enhance capacity and loss resistance in UWOC, this paper demonstrates an OAM multiplexing UWOC system based on photon-counting detection. The BER and photon-counting statistics are analyzed by constructing a theoretical model of UWOC with multiple OAM beams multiplexing and photon-counting detection. Using Q-plates to demodulate the OAM states of single photons and FPGA programming for signal processing, we establish a 2-OAM multiplexed UWOC system over a water channel of 9 m. As a result, the data rate is increased by a factor of 2. Here we mainly consider the attenuation of water channel and ignore the effect of salinity, bubbles, turbulences, etc. in the channel. The photon-counting detection with higher sensitivity can significantly reduce the detection threshold and thus improve the loss resistance of the system. This advancement has the potential to significantly contribute to the development of long-range and high-capacity UWOC systems.
2. Theoretical analysis
According to the principles of quantum optics, the photon statistics of each pulse reaching a SPD follows Poisson distribution [28]. Even after the loss of photoelectric conversion, an ideal SPD with a quantum efficiency of $\eta$ should still exhibit photon-counting statistics that follow the Poisson distribution. Photomultiplier tubes (PMTs) and single photon avalanche photodiodes (SPADs) are commonly used SPDs. However, SPADs exhibit a dead time effect due to the quenching process that occurs after a photon is detected. This effect results in periods of time, known as dead time, during which no response can occur for detected photons. Consequently, the actual photon counts within a detection period are limited, and an upper bound is imposed on the actual counts. Therefore, the actual photon-counting statistics of SPADs deviate from the Poisson distribution.
The single-photon counting module (SPCM) used in this study, as a type of SPD, consists of a photomultiplier tube (PMT) and high-speed signal processing circuit, with its maximum counting rate limited by the pulse-pair resolution of the built-in circuit. Pulse-pair resolution refers to the minimum time interval required to distinguish each output pulse. The SPCM generates output pulses with a width of 10 ns and a pulse-pair resolution of 22ns, enabling recognition of only one detection event per output cycle. Following detection of a photon signal, the SPCM cannot respond to other arriving photons during the 22ns period, which is equivalent to the "dead time" of the SPCM.
Assuming that a light pulse with optical power $P_{r}$ is detected by an SPCM with quantum efficiency $\eta$, the photon counting rate when not considering dead time of the detector can be expressed as
where h is the Planck’s constant, and v denotes the optical frequency. The detection period is denoted by T. When the dead time of the detector is considered and denoted as $\tau$, the upper bound of the photon counting rate during the detection period [29] can be calculated as where $\lfloor \cdot \rfloor$ indicates rounding down. The probability of detecting n photons over a detection period [29,30] is then given byIn a $m$-OAM multiplexing underwater photon-counting communication system, a set of data symbols are divided into $m$ parts and transmitted simultaneously using $m$ channels. The receiver combines the photon counting data from all channels and retrieves the information using the modulation format. In this scenario, it is important to consider the potential impact of inter-channel crosstalk on the system’s performance, as the average photon counts $n_1$ and $n_0$ of channels may vary as a result. Inter-channel crosstalk is defined as the ratio of the average photon counts of channel $j$ to channel $i$ when channel $i$ sends symbol "1", and it is denoted by $c_{ij}$, which means the effect of channel $i$ on channel $j$. The symbols sent simultaneously are $b=b_1 b_2 \cdots b_m\left (b_1, b_2, \ldots, b_m \in \{0,1\}\right )$, the probabilities of sending "1" and "0" are equal, and the average photon counts of each channel are adjusted to $n_1^{initial}$ and $n_0^{initial}$ when sending information alone. The average photon counts of channel $k$ are updated as
Once the photon counting data from all channels has been collected and organized, the average photon counts for the symbol "1" and "0" can be expressed as follows:
The inter-channel crosstalk will affect the received optical power of each channel, which will result in different photon distribution $p_1(n)$ and $p_0(n)$. According to Eq. (4), the two average photon counts values also change. Thus we need to search suitable photon-counting statistics $p_1(n)$ and $p_0(n)$, whose average photon counts equal to updated $n_1$ and $n_0$ in Eq. (7) and Eq. (8), respectively. Accordingly, the BER of underwater photon-counting communication with $m$-OAM multiplexing can be deduced. When using the on-off keying (OOK) modulation, the BER is expressed as
For a symbol with photon counts $n$, the symbol is designated as "1" if LLR $\geq$ 0 and as "0" otherwise. The optimal decision threshold $n_t$ is the value of $n$ that satisfies the condition $p_1(n)=p_0(n)$. When using 2-pulse position modulation (2PPM), the BER can be expressed as
In this study, we demonstrate the implementation of 2-OAM multiplexing for underwater photon-counting communication. The corresponding average photon counts $n_1$ and $n_0$ are expressed as
Assuming that $n_1^{initial}$ ranges from 1 to 4, $n_0^{initial}$ = 0.01, $c_{12}$ = $c_{21}$ = $c_{0}$, the effects of inter-channel crosstalk on BER are shown in Fig. 1. The results indicate that the BER decreases as the number of photon counts $n_1$ increases. Additionally, it can be seen that the higher crosstalk ratio leads to the larger BER at the same level of photon counts.
Fig. 1. The effects of inter-channel crosstalk on BER for 2-OAM multiplexing UWOC with different modulation formats. (a) OOK. (b) 2PPM.
3. Experimental setup
Figure 2 illustrates the experimental setup for the underwater photon-counting communication system employing 2-OAM multiplexing. The system employs two distinct OAM beams, each generated by modulating the phase of light emitted from one laser using separate spatial light modulators (SLMs). The FPGA board at the transmitter generates two 10MHz electrical signals that are transmitted to two 488nm semiconductor lasers (Cobolt MLD 488nm) as driving signals after waveform shaping and voltage conversion by a comparator. The beam from the collimator is initially converted into a horizontally polarized beam by a polarizer to match the polarization requirement of the SLM (Hamamatsu X13138-04). The beam then passes through a spatial filtering system consisting of two lenses (L1 = 100mm, L2 = 300mm) and an aperture (100$\mu$m) for beam expansion and spatial filtering, which optimizes the beam quality by blocking most of the high spatial frequency noise. As a result, the expanded beam has a spot diameter of approximately 7 mm. The two OAM beams ($OAM_{+3}$ and $OAM_{-3}$) are generated by loading specific phase patterns on the two SLMs, respectively. Finally, the two OAM beams are multiplexed and transmitted coaxially in the same water channel using a beam splitter (BS). To simulate stronger channel loss, several attenuators are used to adjust the transmitted optical power.
Fig. 2. Experimental setup of underwater photon-counting communication with 2-OAM multiplexing. (a) The schematic diagram. The signal generation, reception and processing are implemented by FPGA boards, which are connected to PCs via USB. SLM: spatial light modulator, QWP: 1/4 wave plate, BS: beam splitter. (b) Transmitter. (c) Water channel. (d) Receiver.
The multiplexed beam is transmitted through a 9 m water channel before reaching the receiver. To simulate the underwater channel, an acrylic water pipe filled with purified water is used, which has an inner diameter of 9 cm and is fixed with coated optical lenses on both ends. The measured attenuation coefficient of water is $c$=0.18/m, and the diameter of the main aperture at the receiver is approximately 10 mm. The beam is collected by an inverted beam expander with a collection efficiency of 89$\%$. A 1/4 waveplate (QWP) is used to convert the beam from horizontal polarization to circular polarization, and then the beam enters two optical paths through a 1:1 BS to achieve the separation of $OAM_{+3}$ and $OAM_{-3}$, respectively, with two Q-plates of order $q=3/2$ and $q=-3/2$. The demultiplexed beams have Gaussian-like profiles with bright spots in the center and are coupled into single-mode fibers. Finally, high-sensitivity photon detection is performed using the SPCM (Hamamatsu H12386-210), and the output signal is received by the FPGA board, which implements signal processing. The detection efficiency of SPCM at 488nm is approximately 18$\%$, the dark count is less than 100 counts/s, and the saturation count rate is about 35M counts/s, which is limited by the pulse-pair resolution and its own photosensitive material.
3.1 Generation and detection methods of OAM beam
We use specific spiral phase patterns to generate the OAM beams, and when a spiral phase pattern is loaded onto the SLM, the resulting output optical field can be expressed as
Q-plate is used to detect OAM beams. When a left-circularly polarized OAM beam with topological charge $l$ is incident on a Q-plate of order $q$, the output optical field is expressed as
Similarly, when a right-circularly polarized OAM beam with topological charge $l$ is incident on a Q-plate of order $q$, the output optical field is expressed as
The output beam is a left-circularly polarized OAM beam, which degenerates to a Gaussian-like beam when $q$ = -$l$/2.
3.2 FPGA design
The transmitter and receiver FPGA boards operate at a frequency of 100 MHz, providing a clock period of 10 ns. The pulse repetition frequency is 10 MHz, resulting in a pulse period of 100 ns. The entire system’s signal generation, reception, and processing functions are implemented using FPGA programming modules. Data frames are sent one by one, with each frame containing a frame head sequence (FHS), a frame estimation sequence (FES), and a data sequence (DATA). The frame structure is illustrated in Fig. 3(a), where the first 20 symbols "1010101010101010101010" are used for clock synchronization, and the last 8 symbols "1010101010" are used for frame synchronization in the FHS. The FES is utilized to estimate the average photon counts $n_1$ and $n_0$ for symbols "1" and "0". In OOK modulation, each time slot represents one symbol, with the time slot’s length equal to the pulse period. For 2PPM modulation, two time slots represent one symbol. In multiplexing communication, 8 bits are sent as a group, with the low 4 bits sent by LD1 and the high 4 bits sent by LD2. LD1 and LD2 send signals simultaneously.
Fig. 3. (a) Frame structure. (b) Signal processing steps at receiver. FIFO: first-in first-out buffer, UART: universal asynchronous receiver/transmitter.
Photon-counting signals from the SPCM are utilized for time synchronization, frame match and data demodulation. The signal processing steps are shown in Fig. 3(b). Time synchronization is the first step, which establishes a common timing reference for the receiver and transmitter, allowing for accurate counting by determining the start and stop positions of each time slot. Frame synchronization follows, determining the initial position of each frame. Once time and frame synchronization are completed, the FPGA module counts photons in each 100 ns time slot after the FHS in real-time and stores the data in a FIFO module. The UART module then sends the photon data in the FIFO to the PC, and the PC software performs symbol decision and decoding.
4. Experimental results and discussion
4.1 Generated OAM beams
SLMs are utilized to generate $OAM_{+3}$ and $OAM_{-3}$ beams. The liquid crystal window of the SLM has a size of 1024 $\times$ 1280 pixels, with a single-pixel size of 12.5$\mu$m $\times$ 12.5$\mu$m, allowing for high-accuracy phase-only modulation. The forked phase patterns shown in Fig. 4(a),(b) correspond to $OAM_{+3}$ and $OAM_{-3}$ beams, respectively. These forked phase patterns are obtained by superimposing spiral phase and blazed grating phase, which eliminates the effect of zero-order diffraction noise. The intensity profiles of the generated OAM beams are shown in Fig. 4(c),(d). The spatial filtering system optimizes the quality of the Gaussian beam incident on the SLM, and the high-precision phase modulation of the SLM and fine optical alignment result in a uniform energy distribution for the final generated OAM beams.
Fig. 4. Phase patterns and intensity profiles of the generated OAM beams. (a) Phase pattern for $OAM_{+3}$. (b) Phase pattern for $OAM_{-3}$. (c) Intensity profile for $OAM_{+3}$. (d) Intensity profile for $OAM_{-3}$.
4.2 Detection of OAM beams and inter-channel crosstalk
The polarization characteristics of the generated OAM beams at the receiver are measured first. Since the Q-plate requires circular polarization, the optical polarization distributions before and after the QWP are measured using a linear polarizer as a checker. The checker is rotated, and the optical power after the checker is measured with a power meter. Figure 5(a),(b) shows the polarization characteristics of $OAM_{+3}$ and $OAM_{-3}$ beams before and after the QWP, respectively. As expected, the beam should have horizontal polarization before the QWP and circular polarization after the QWP, and the measured results confirm this. However, the actual polarization states are not perfect, and there is a slight deviation at the receiver, as can be seen in the figure.
Fig. 5. Optical polarization characteristics before and after QWP. (a) For $OAM_{+3}$ channel. (b) For $OAM_{-3}$ channel.
The detection and demultiplexing of OAM beams are achieved in this experiment using Q-plates. The received intensity profiles of the OAM beams are observed and recorded with a CCD camera. Figure 6(a) shows the intensity distribution of the multiplexed beam, which exhibits an excellent doughnut shape. Due to the relatively pure water channel and fine optical alignment, the $OAM_{+3}$ and $OAM_{-3}$ beams are overlapped nearly perfectly. Figure 6(b)-(d) depict the demultiplexing results of the superimposed beam, $OAM_{+3}$ and $OAM_{-3}$ beams on channel $ch_{+3}$. The demultiplexing results on channel $ch_{-3}$ are presented in Fig. 6(e)-(g). The demultiplexed patterns show several clear bright spots in the center, where the $OAM_{+3}$ and $OAM_{-3}$ beams are transformed into Gaussian-like beams by the inversion process of Q-plates.
Fig. 6. Demultiplexing results of OAM beams. (a) The received intensity profile of multiplexed beam. The demultiplexing results of (b) superimposed beam, (c) $OAM_{+3}$ beam and (d) $OAM_{-3}$ beam on channel $ch_{+3}$, and (e) superimposed beam, (f) $OAM_{-3}$ beam and (g) $OAM_{+3}$ beam on channel $ch_{-3}$.
In practice, the OAM beam experiences mode distortion and energy redistribution due to the random water channel and imperfect devices, leading to the performance degradation of OAM multiplexing UWOC system. After mode distortion, some of the energy in the original OAM mode is transferred to neighboring OAM modes, and the closer it is to the original mode, the more energy will be transferred. This energy transfer between OAM modes leads to an increase in BER, and the energy reduction of the original OAM mode causes additional energy loss, decreasing the received intensity. Therefore, the topological charges of the OAM modes used for communication should not be too close, but they should not be too large either due to the limitation of the receiving aperture. In this experiment, OAM beams with topological charges $l=\pm 3$ are selected to balance these factors.
System performance can be significantly impacted by inter-channel crosstalk. In this study, we experimentally measured inter-channel crosstalk, which was defined in Section 2. The crosstalk from channel $ch_{+3}$ to channel $ch_{-3}$ is denoted as $c_{12}$, while the crosstalk from channel $ch_{-3}$ to channel $ch_{+3}$ is denoted as $c_{21}$. The measured results are presented in Fig. 7, indicating that the crosstalk is below −19 dB for both channels, and mostly below −20 dB. Theoretically, when the reception efficiencies of both channels are the same and fixed, changes in received optical intensity alone should not affect inter-channel crosstalk. However, as shown in Fig. 7, the crosstalk curves fluctuated within a small range with the average photon number, which may have been caused by random environmental disturbances.
Inter-channel crosstalk is primarily caused by mode degradation and polarization changes. Various random underwater disturbances, such as scattering, turbulence, bubbles, and flow, can destroy the OAM modes, causing phase distortion and energy transfer [20,26,31]. Additionally, the time-varying underwater environment and imperfect optics can slightly alter the polarization angle and linearity of the optical beam. Consequently, the polarization state of the OAM beam incident on the Q-plate is a superposition of left- and right-hand circular polarization, resulting in extra circular polarization that leads to inter-channel crosstalk.
4.3 Photon-counting statistics
The photon number distribution in a symbol period is closely related to the BER. Therefore, photon-counting statistics is analyzed in this study. A group of photon-counting data, corresponding to one frame, is randomly selected from the total experimental data. Counts corresponding to symbol "1" are identified from the selected data, and the average photon counts $n_1$ of the frame is calculated. The frequencies of different photon numbers are then counted, and a normalized frequency distribution histogram is plotted in Fig. 8. All photon counts are less than or equal to 5, which agrees with theoretical expectations. According to Eq. (2), the maximum photon counts $n_{max}=5$ in this experiment. The orange curve represents the predicted results using photon-counting theory with dead time effect, and it can be seen that the theory is consistent with the experiment. The green curve represents the ideal Poisson distribution with $n_1$ as the parameter, and the results indicate that treating photon-counting statistics as a Poisson distribution would lead to a large deviation from the actual distribution. In fact, due to the existence of dead time in detectors, the actual photon-counting statistics is a new distribution, which becomes narrower.
4.4 Communication performance
Figure 9 shows the BER performance of the experimental system using two modulation formats: OOK and 2PPM. The BER decreases as the average photon number $n_1$ increases. The orange and purple curves in Fig. 9 indicate the BER of 2-OAM multiplexing UWOC with OOK and 2PPM modulation, respectively. The BER of channel $ch_{-3}$ is chosen as the reference, i.e., the blue and yellow curves in Fig. 9. This is because theoretically there is no difference in choosing channel $ch_{+3}$ or $ch_{-3}$. When using 2PPM modulation, the BER is significantly lower than that using OOK modulation. The reason is that the method of demodulation by comparing the photon counts of two time slots has better error tolerance than the decision threshold. In the 2-OAM multiplexing experiment, the minimal BER for OOK is 1.26$\times 10^{-3}$ and for 2PPM is 3.17$\times 10^{-4}$ at $n_1 \approx 3.4$, both of which are lower than the FEC threshold of 3.8$\times 10^{-3}$. And when error correction coding is used, the BER can be greatly decreased. Some system parameters are listed in Table 1.
Fig. 9. The BER of 2-OAM multiplexing UWOC with OOK and 2PPM modulation. "OOK wo crosstalk" means UWOC using OOK with only one OAM channel, and "OOK w crosstalk" means UWOC using OOK with 2-OAM multiplexing. There are similar meanings for 2PPM modulation.
Table 1. Part of the system parameters.
As shown in Fig. 9, the BER curves of single OAM and 2-OAM multiplexing are close to each other for both OOK and 2PPM modulation, and the BER for 2-OAM multiplexing is slightly higher than that for a single OAM. This indicates that inter-channel crosstalk does not significantly affect the BER at the same optical intensity. Therefore, the effect of inter-channel crosstalk on communication is studied. Figure 10 shows the distribution of experimental $n_0$ for OOK and 2PPM modulation. The $n_0$ fluctuates within a small range, and the $n_0$ for 2-OAM multiplexing is generally larger than that for a single OAM. The mean values of $n_0$ are calculated and displayed in Fig. 10(a),(b). For OOK modulation, the difference between the two mean values is $\Delta _{O O K}=0.0591-0.0356=0.0235$, and for 2PPM modulation, the difference is $\Delta _{2PPM}=0.0861-0.0615=0.0246$. The fluctuations of $n_0$ are mainly caused by inter-symbol crosstalk. The experimental and theoretical BER comparisons for both OOK and 2PPM modulations are exhibited in Fig. 11 using Eq. (1)–(4) and Eq. (9)–(12). The noise intensity is set to be constant and equal to the mean values in Fig. 10(a),(b). It can be seen from Fig. 11 that the theoretical curves match with the experimental curves. Both experimental and theoretical results reveal that inter-channel crosstalk has a relatively small effect on the BER performance.
The noise counts $n_0$ are derived from three sources: background noise, inter-symbol crosstalk, and inter-channel crosstalk. Background noise contributes a small fraction of $n_0$ due to the use of single-mode fiber and appropriate blocking measures at the receiver, resulting in a counting rate of less than 400 counts/s. The previous results demonstrate that inter-channel crosstalk introduces a small number of noise counts. The main contributor to $n_0$ is inter-symbol crosstalk, which is related to time synchronization. If time synchronization is inaccurate, the start and stop positions of the counting period will be misaligned, and the photons corresponding to one symbol will be counted as another symbol. As a result, $n_0$ increases significantly and affects the separation of symbols "1" and "0".
In the case of weak signals, the receiving photon number experiences statistical fluctuations that follow a specific probability distribution, resulting in the BER. Various channel losses, such as water absorption and scattering, photon collection, Q-plate conversion, fiber coupling, and detector photoelectric conversion, cause significant signal loss and can lead to errors. Additionally, background light, dark counts, inter-symbol crosstalk, and inter-channel crosstalk are also sources of BER.
Furthermore, several attenuators are required to achieve single-photon level reception. When $n_1 \approx 3.4$, the loss of the attenuators is approximately 30 dB, and the total loss of the attenuators and the water channel is 37 dB. Without considering various underwater effects, the 37 dB total transmission loss is equivalent to transmitting over a distance of 283 m in Jerlov I type ($c$ = 0.03/m) seawater [32] according to Beer’s law. Theoretically, photon-counting communications could additionally resist approximately 68 dB water channel loss compared to APD with received power of about 100 microwatts [33,34]. Therefore, the photon-counting detection can overcome the disadvantage of high detection threshold of conventional UWOC and receive signals for reliable communication under weak light signals. The loss resistance of the system is boosted and the communication distance can be extended, and high-performance detectors can further promote the achievable distance. On the other hand, OAM modes can provide infinite orthogonal OAM states. Compared with polarization and wavelength multiplexing, OAM multiplexing is not limited by dimensionality and could be combined with polarization and wavelength multiplexing to further increase the data rate [24]. Meanwhile, there are still some problems that need to be conquered in the future research, such as the limitations of detection range, bandwidth for the photon-counting detection, and the influences of underwater turbulences, bubbles on the OAM beams, for the OAM multiplexing communication in underwater photon-counting links.
5. Conclusion
In this paper, we present a novel photon-counting communication scheme that utilizes OAM multiplexing. For multi-dimensional OAM multiplexing, the photon-counting statistics and BER models are provided by taking into account the effect of dead time on photon counting. The experimental results obtained demonstrate good agreement with the theoretical models. Specifically, we experimentally demonstrate a 2-OAM multiplexing underwater photon-counting communication scheme, achieving minimal BERs of 1.26$\times 10^{-3}$ and 3.17$\times 10^{-4}$ for OOK and 2PPM modulations, respectively, over a 9 m water channel. The proposed scheme offers a feasible solution for long-range and high-capacity UWOC, with promising applications in deep-sea calm environments. However, challenges related to the effects of turbulence and the long-distance transmission of OAM beams need to be investigated in future research.
Funding
Fundamental Research Funds for the Central Universities (202165008); National Natural Science Foundation of China (61575180, 61701464); Natural Science Foundation of Shandong Province (ZR2021ZD19).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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