1. Introduction

Exploring ocean has been of great interest to man for many years for scientific, commercial, as well as military reasons [1–4]. Many emerging applications, such as surveillance, security and oil pipeline monitoring, demand high speed, stable, real-time data transmission. Traditionally, acoustic modulation has been used for underwater wireless communication because of its low attenuation enabling long-range of distance [5]. However, they suffer from major drawbacks in the form of limited transmission capacity and spectrum efficiency due to the limited bandwidth, the low propagation speed, the multi-path effect and the dimension of bulky antennas [6–8]. Alternatively, optical wave, especially for the blue-green region with relative low attenuation, enables higher capacity and spectrum efficiency for underwater wireless optics communication (UWOC) [9, 10]. Generally, the non-scattered portion of light beam attenuates exponentially according to Beer’s law,$P=P_{0}exp(-(a+b)z)$ where $P$ is the received power and $P_0$ is the initial power. The attenuation coefficient is the sum of the absorption coefficient ($a$) and the scattering coefficient ($b$). The values of $a$ and $b$ vary with the water type and light’s wavelength $\lambda$ [11, 12].

For further improvement of the data rate in UWOC, one potential approach is to transmit multiple orthogonal data-carrying beams employing the spatial domain of light, namely space division multiplexing (SDM). While twisted light, also known as orbital angular momentum (OAM) mode, offers such orthogonal spatial modal basis set which has been proved greatly potential in improving the transmission data rate [13–21]. Twisted light carrying OAM can be described by an azimuthal phase factor $exp(j\mathcal{l}\theta )$, where $\mathcal{l}$ is the topological charge and $\theta$ is the azimuth angle. OAM mode is the eigenmode or the synthesis of eigenmodes in free-space and optical fiber, so it can stably propagate in these media as well over underwater channels. OAM multiplexing is achieved for its orthogonality and multiple values. For example, terabit-scale capacity with high spectrum efficiency has reached both in free-space and fiber-based transmission link exploiting OAM multiplexing [14, 15]. Recently, OAM multiplexing technique has been introduced to UWOC link. J. Baghdady presented a 3-Gbit/s UWOC employing 2 OAM modes multiplexing [22] and Y. Ren impressively increased the UWOC transmission capacity to 40 Gbit/s (external modulation & frequency doubling) and 4 Gbit/s (directly modulated LD) by multiplexing 4 green OAM modes [23]. Besides, the channel stochastic degradations, e.g. absorption, scattering, and especially, the turbulence-induced fading [24, 25] may severely change the phase front of the propagating optical beam. There are some works on theoretical [26] and experimental [23] analyses on OAM-based UWOC systems showing that they are more promising in the short-distance (few meters to few tens meters) underwater scenarios to achieve high transmission capacity. In our previous works, we investigated the influence of bubbles and slight obstructions to underwater spatial modes (Gaussian, OAM and Bessel mode) [27] and demonstrated 1-to-4 OAM multicasting link [28] and water-air-water OAM transmission link [29]. However, in most of those reported works [22, 23, 27, 28], the light beam straightly passed through the water under the air-water interface. In some practical scenarios, there always have some obstacles such as underwater creatures and fixed rocks in the line of sight blocking the optical path. At the deep water, it is a potential way to employ multi-hop transmission through intermediate relay nodes [30–32] to solve the problem. While the link is set near the shore (in the vicinity of air-water interface), we propose another novel and simple method, which can provide more flexibility for underwater optical wireless communications using the total internal reflection.

In this letter, we present a non-line-of-sight underwater wireless optical transmission employing twisted light by the total internal reflection on the air-water interface. Natural phenomena such as the slight wind, the salinity (turbidity) and the vertical thermal gradient-induced turbulence will change the interface state and transmission link performance. For the beam drift, a large receiver aperture is one of the solutions to enlarge the field-of-view (FOV). As for twisted light communication link in the underwater scenario, large FOV is not enough for signal recovery because it needs more precise optical path alignment, especially for demodulation. Here, we propose and demonstrate a proof-of-concept adaptive feedback system at the receiver side for twisted light UWOC in such non-line-of-sight scenario to guarantee the signal quality.

2. Concept and principle

The concept and principle of underwater wireless optical link employing OAM mode are illustrated in Fig. 1. Considering the complicated environment under the water, in some scenarios line-of-sight optical link is not available. For instance, the fixed rocks and underwater creatures can obstruct the line-of-sight optical path. It is difficult to change the natural environment and it could be a potential way to exploit the non-line-of-sight optical path to overcome such limitation. We present a viable method using the total internal reflection at the air-water interface (Fig. 1(a)) and adaptive feedback system (Fig. 1(b)) at the receiver side to achieve the non-line-of-sight optical link. It is well-known that when the incident angle is larger than the critical angle of total internal reflection, all the light beam will reflect back to the water without transmission loss. The critical angle of the air-water interface is about 48.75° (the refractive index is about 1.33 for no matter fresh water or sea water). Hence, it is possible to achieve such total internal reflection non-line-of-sight optical link. Certainly, the reflected light beam will be fluctuated and drift as the state of air-water interface changes. The change of the surface orientation and the elevation of the sea-level manifests as the beam misalignment at the receiver side. Therefore, an adaptive feedback system is necessary to ensure a stable optical path, especially for OAM-based link. The adaptive feedback system includes two feedback closed-loop link because there are two dimensions of the displacement, one is the angle displacement which is the included angular between the drift beam and the original beam, and another is the lateral displacement which is the lateral position offset at the receiver plane. As depicted in Fig. 1(b), the blue line shows the original optical path at the receiver side. When the beam drifts, the output light (the red line) is not only offset in the lateral dimension but also the angular dimension as indicated in Fig. 1(b). We use the first mirror to adjust the light beam return to the original position at the second mirror (the yellow dotted line). Then the second mirror is used to adjust the light beam return to the original output position. Two fixed positions are enough to guarantee the stable output.

 

Fig. 1 Concept and principle of non-line-of-sight underwater optical link employing OAM mode.

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3. Experimental setup and results

The experiment was demonstrated in the laboratory and the setup is illustrated in Fig. 2. A 450-nm single mode pigtailed laser diode (LP450-SF15, Thorlabs) was set up on a mount (LDM9LP, Thorlabs) with integrated thermistor and TEC. The driven current was 37.68 mA (LDC205C, Thorlabs) and the thermistor was set as 10 k$\text{Ω}$ (TED200C, Thorlabs). The output single mode fiber was connected to a collimator to provide a blue Gaussian beam with the diameter of 2 mm. The first half-wave plate (HWP) was used to adjust the polarization for optimized mode modulation because the spatial light modulator (SLM) is a polarization-sensitive element based on the liquid crystal array. By loading a fork pattern, the combination of blazed grating and spiral phase [13–23, 27–29], on the SLM-1, a pure OAM mode was obtained in the first diffraction order. Another laser diode and SLM-2 were utilized to generate another OAM mode. The two OAM modes were combined by the beam splitter (BS-1). The transmit power was −2.67 dBm with the diameter of ~5 mm. Besides the desired mode, there were inevitable light beams in other diffraction orders due to the limited modulation efficiency and liquid crystal array which was spatially filtered by an iris. The underwater condition was imitated by a 2-m water tank with the height and width both of 40 cm. The filled tap water had the height of about 30 cm. The incident light before the tank and the output light after the tank both had the same height of about 25 cm. The total reflection point was at the middle of the water tank. So the incident angle to the air-water interface was about 87.14$°$. Blue light carrying OAM mode was obliquely incident on the surface with a large angle (greater than the critical angle) and reflected toward the receiver side by the total internal reflection. The beam size was ~5.5 mm at the air-water interface and ~6 mm at the receiver side. Any slight wind will give rise to water surface movement or wave action and a vertical thermal gradient will shift the reflection position. So we chose a large-diameter lens (3 inches, 76.2 mm) as the aperture of the receiver (Lens-1) to enlarge the FOV. The received power after Lens-1 was −6.51 dBm without turbidity. While the SLM-3 was placed nearby the focus point of the Lens-1. Therefore, once the light beam was received by the Lens-1, it could be guaranteed to be incident within the range of the screen of the SLM-3. Both SLM-3 and SLM-4 were set up with $90°$ rotation to increase the ability to handle the beam drift (the screen resolution is $1920\times 1080$). The reason was that the beam almost only drifted in the vertical direction due to the water wave only propagating along the longitudinal direction as observed. It should be resulted from the geometry of the water tank. Therefore the modulated polarizations of SLM-1 and SLM-3 (SLM-4) were orthogonal. We placed a HWP after BS-1 to rotate the polarization to the cross direction. Then the light beam could be modulated by both SLM-3 and SLM-4. Lens-1 (300 mm) and Lens-2 (100 mm) formed an inverse telescope to reduce the size of the light beam. The distance between Lens-1 and SLM-3 was about 250 mm. Lens-2 was set up 150 mm away from SLM-3. Lens-3 and Lens-4 formed another telescope with the same focal length of 200 mm. BS-2 was utilized to split the light beam carrying OAM modes into two paths with one incident on SLM-4 and another on Camera-1. The optical paths from Lens-3 to Camera-1 and Lens-3 to SLM-4 were the same (250 mm). After reflection by SLM-4, the light beam was split by BS-3 into two paths. One was incident on Camera-2 and the other was the output beam. The distance between SLM-4 and Lens-4 was 150 mm. So the first focal point was 50 mm after SLM-3 and the second one was 50 mm before SLM-4. On the other hand, our SLM screen can suffer up to 27 dBm laser power and the power we received was less than −6.51 dBm. Camera-1 and SLM-3 were connected as a closed loop while Camera-2 and SLM-4 were connected as another closed loop. The whole receiver within the dashed line in Fig. 2 functioned as an adaptive feedback system to correct the beam fluctuation and drift resulting. As shown in the bottom figure, there is a simply relationship that the light spots displacement in Lens-1 is about $\Delta D=2\Delta h\cdot sin(\theta )$, where the incident angle $\theta =ta{n}^{-1}(L/2h)$, $h$ is the level of water, $L$ is the length of tank, $\Delta h$ is the change of the water-level. In the experiment, $L$ was 2 m and $h$ was about 5 cm, so $\Delta D\approx 2\Delta h$. The maximum range was limited by the aperture of the Lens-1. As long as the light beam can be received by Lens-1, it can be steered by SLM-3 for further process. In the experiment, the diameter of the Lens-1 was 3 inches (76.2 mm). From the relationship above, the maximum range of $\Delta h$ is $\pm$ 19.05 mm.

 

Fig. 2 Experimental setup for non-line-of-sight underwater wireless optical link employing twisted light based on total internal reflection. Col.: collimator; HWP: half-wave plate; SLM: spatial light modulation; BS: beam splitter; NDF: neutral density filter; X-Pol.: x-axis polarized direction; Y-Pol.: y-axis polarized direction.

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Before studying the adaptive feedback system, we recorded the original OAM mode transmission state. Figure 3 shows the intensity profiles for two different OAM modes with topological charges of + 5 and −5. At the transmitter side, the modulated OAM modes were perfect with doughnut profiles. After the total internal reflection at the air-water interface and propagation through the 2-m water tank, the captured intensity profiles still maintained high quality with little distortion on Camera-1. When loading a pure blazed grating phase pattern on SLM-3 and an inverse fork pattern (as the insets shown) on SLM-4, the demodulation intensity profiles (captured by Camera-2 and also known as the output beam) showed a bright spot (Gaussian-like) at the beam center, which could be further coupled into a single mode fiber for detection. While if the patterns on SLM-4 was same as the transmitted pattern, the topological charge of the OAM beam was doubled up to + 10 or −10 leading a bigger doughnut profile as shown in Fig. 3. The intensity profiles show that the total internal reflection at the water surface had a negligible impact on OAM mode. Additionally, we took these states as the original states for further feedback processes.

 

Fig. 3 Measured intensity profiles for OAM₊₅ and OAM_-5 at the transmitter side (Tx), receiver side (Rx) captured by Camera-1, and after demodulation by $\mathcal{l}$ = $\pm$5 patterns captured by Camera-2.

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To introduce the adaptive feedback system, we first theoretically show the relationship between the pattern loaded on SLM and the light-beam position on camera. As displayed in Fig. 4(a), in practice the shifted beam (blue spot) is apart from the original position (red spot) on the SLM. When loading a linear phase ramp pattern on SLM, the light beam can be diffracted to the original position on camera. For the sake of analysis, this process can be equivalent to another process as shown in Fig. 4(b), i.e. the incident light at the same position (red spot) on SLM (inverse pattern) is diffracted to an offset position (blue spot) on the camera with an azimuthal angle $\text{Ω}$. The position offset $\text{Δ}r$ can be decomposed to horizontal offset $\text{Δ}x$ and vertical offset $\text{Δ}y$ as depicted in Fig. 4(c). Similarly, the azimuthal angle is composed of horizontal angle ${\theta }_x$ and vertical angle ${\theta }_y$. On the other hand, the linear phase ramp pattern consists of two cross-direction blazed gratings with the period of $d_x$ and $d_y$. There is a well-known relationship that:

 

Fig. 4 Schemes for the relationship between the patterns loaded on SLM and the light-beam position on camera.

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As any slight wind may give rise to the water surface movement and wave action. We first investigated the influence of the wind and the frequency of the water wave. In the experiment, in order to make the light beam drift within the range of the receiver aperture (Lens-1), we produced slight wind by a gentle shaking half-meter away from the water tank. The slight wind caused the water wave to propagate along the water tank that made the light beam drift. We continuously recorded the beam drift at the Camera-1 with an interval of 1/30 second for 1000 pictures. Figure 5 shows the position variation for the center of the OAM beam. The results show that i) the beam had less drift in the X-axis and had a large displacement in the Y-axis (0.98 mm); ii) the frequency of the beam drift (or water wave) was about 2 Hz. As the Ref. 33 shown, the OAM link is sensitive to the lateral displacement and Rx angular error. As we observed, the lateral displacement should be within 0.1 mm to maintain good demodulation results. So we can estimate that the response rate should be above 40 Hz to handle such slight wind in the experiment. In real applications, the water wave has a higher frequency and larger amplitude, up to 100 Hz response rate might be more practical.

 

Fig. 5 Measured lateral displacement for Y-axis and X-axis at the Camera-1 resulted from the slight wind.

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As limited by the current equipment, e.g. low refresh rate for the SLM (60 Hz) and the camera (120 Hz), the presented system had relative high response time (~200ms). To prove the concept, we artificially changed the height of water surface at the interval of 10 mm by adding/taking some water to imitate the beam drift. When the air-water interface return back to flatness again, we tested the adaptive system. The correction was automatic but not real-time due to the 200-ms response time. The adaptive algorithm was to control two SLMs as flexible mirrors to change the light reflection according to the position offset on the two cameras. It aimed to fix the position to guarantee the stable output. Certainly, the equipment with higher response rate (>100 Hz) will handle the real-time dynamic beam drift in such scenario. It can be achieved by using fast steering mirrors (FSMs) and position sensor detectors (PSDs). The whole adaptive feedback system could be divided into two close-loop feedback processes. Camera-1 was placed at the position with the same optical path length compared with SLM-4 from BS-2. Therefore, the light beam incident on Camera-1 had the same position on SLM-4. Here a neutral density filter (NDF-1) was used for power attenuation before the camera (the same for NDF-2 and NDF-3). As shown in Fig. 6(a), in the feedback 1 (FB-1) process, we artificially changed the height of water surface at the interval of 10 mm by adding/taking some water to imitate the beam drift. Camera-1 captured the OAM mode profile and measured the position of the center in real time. The position offset $\Delta r^{\text{‘}}$ was then calculated and compared with the original position. According to the calculated relationship, the linear phase ramp with deduced grating period $-d_{x,\text{ y}}{}^{\text{‘}}$ was loaded on SLM-3 in real time. As a result, the offset position was corrected to the original position on Camera-1, which also meant the light beam was incident at the original position on SLM-4. In theory, one feedback process can hardly guarantee the complete coincidence of output optical path and original path for two dimensions of displacement. We further developed feedback 2 (FB-2) process and it could handle the problem because two points confirm a straight line. Camera-2 was also used for monitoring the position offset. Firstly, SLM-4 was loaded with an inverse fork pattern with a period of $d_{y0}$ (fork pattern consists of a spatial phase and a linear phase ramp) for OAM demodulation. When the height of air-water interface changed, the light offset the original position which made the OAM demodulation failed. After the FB-1 process, the light beam returns to the demodulation position on SLM-4, so the OAM mode could be demodulated with offset position as shown in Fig. 6(a) (the FB-2 process row 2). The images for offset position in the FB-2 process were captured after the whole process for the light is off the camera aperture during the process. Through the same calculation process, we obtained a corrected period value of $-d_{x,\text{ y}}{}^{\text{‘}}$. Then by adding this value on the original period $d_{y0}$, we generated a new fork pattern to correct the position offset with good demodulation results as shown in Fig. 6(a). Therefore, we achieve a stable output optical path with OAM demodulation.

 

Fig. 6 (a) The proposed adaptive feedback system divided into feedback 1 (FB-1) process and feedback 2 (FB-2) process. (b) Measured results for transmitting multiple OAM modes (OAM₊₅ + OAM_-5) through the adaptive feedback system.

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We also transmitted multiple OAM modes with the topological charge of + 5 and −5 to verify the multiplexing link as present in Fig. 6(b). We demonstrated two offset positions (above and below the original position). When adopting our proposed adaptive feedback system, the multiple OAM modes could be adjusted to the original position with relatively perfect demodulated profiles. It can be seen in Fig. 6(b) that when one OAM mode was demodulated, the other doughnut profile was enlarged that would benefit low crosstalk for the OAM multiplexing link.

Because the underwater environment is relatively complicated and many factors can influence the OAM mode. Here we further comprehensively study the vertical thermal gradient-induced turbulence and the turbidity effect. A vertical thermal gradient will shift the reflection position. We measured the influence of the vertical thermal gradient as shown in Fig. 7(a). We sunk a heater at the bottom of the water tank with the set temperature 28°C. The final temperature was 25°C and the measured temperature at the water-air interface was 24.5°C. That meant the vertical thermal gradient was about 0.5°C/30 cm (the water-level was 30 cm). In fact, such vertical thermal gradient is much larger than the real situation. We adopted a 3-inch (76.2-mm) Lens (Lens-1 in Fig. 2) to enlarge the field-of-view (FOV). As we observed, the beam drift was still within the range of the Lens-1 and all SLMs at the receiver side. Figure 7(a) displays the displacement caused by the vertical thermal gradient-induced turbulence. The received beams’ maximal displacement at the Camera-1 was estimated to be 0.15 mm. Such degree of the lateral displacement could be corrected by the proof-of-concept feedback- enabled adaptive system. However, as we observed, the beam distortion may be much worse resulting from the vertical thermal gradient induced turbulence.

 

Fig. 7 Measured lateral displacement and beam distortion at the Camera-1 resulting from (a) the vertical thermal gradient-induced turbulence, (b) the 0.5 ‰ salinity, and (c) the both influences of (a) and (b). (d) The measured relationship between the power loss and the salinity.

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To imitate the turbidity effect, we added the artificial sea salt with different quantities into the water tank. The artificial sea salt contains Na⁺, Mg²⁺, Ca²⁺, K⁺, Sr⁺ and other 40 kinds of microelements. After heating and stirring, the salt was totally dissolved in the water. The whole weight of the water was about 250 kg. We added the artificial sea salt 62.5 g each time. The salinity was roughly calculated which was equal to the weight rate of the sea salt and the water. We investigated the relationship between the power loss and the salinity. The power loss was measured by using an optical power meter (PM100D, Thorlabs) and a photodiode power sensor (S130C, Thorlabs). The result was shown in Fig. 7(d). It can be seen that the power loss linearly increases with the salinity. In a real situation, the salinity of the fresh water is less than 0.5 ‰ [34] which means the power loss is less than 2.5 dB/m as we measured. Seawater typically has a mass salinity of around 35 ‰ [34], although lower values are typical near coasts where rivers enter the ocean. From the measured data, one can roughly predict that the power loss in the sea water is about 40 dB/m. Then we measured the lateral displacement at the Camera-1. We recorded 1000 pictures at an interval of 1/30 second and calculated the center position. The result was presented in Fig. 7(b). We measured the lateral displacement at the salinity of 0.5 ‰. The beam could maintain a relatively stable position and the beam distortion was acceptable compared with the effect of vertical thermal gradient-induced turbulence. Additionally, we also measured the lateral displacement at the Camera-1 subjected to both the vertical thermal gradient-induced turbulence and the 0.5 ‰ salinity. The result was displayed in Fig. 7(c). Compared with the case only suffering from the vertical thermal gradient-induced turbulence, the beam drifted more violent and the displacement range was wider. Meanwhile, the observed beam distortion was worse. To correct the beam distortion, additional adaptive optical system with a wave-front sensor could be one potential option [35, 36].

4. Conclusion

In summary, we proposed and demonstrated a non-line-of-sight optical link under the water using the total internal reflection at the air-water interface. Single/multiple OAM mode(s) was/were transmitted and we imitated the beam fluctuation and drift by changing the water-level. A feedback-enabled adaptive system including two phase-only SLMs was verified to correct the optical path alignment (both lateral displacement and angular error). Linear phase ramp pattern was loaded on SLMs which was calculated according to the offset position on cameras in real time. The proof-of-concept adaptive feedback system was proved to be effective. Moreover, we studied the degrading effects of the slight wind effect, the salinity (turbidity) effect, and the vertical thermal gradient-induced turbulence effect. The results showed that the water wave caused the most beam drift, the thermal gradient caused the most distortions, and the salinity caused the most power loss.

Additionally, in the proof-of-concept experiment, the response rate of the demonstrated feedback system was mainly limited by the SLM, the camera and the communication between two closed-loop feedback processes. The whole response time for the current adaptive system was about 200 ms. It was the reason why we changed the water-level through adding/taking water from the tank. However, the system has been proved in concept. There are many methods to increase the response rate. For example, when replacing the SLMs and cameras by the FSMs and PSDs, the response rate can easily reach more than 100 Hz [37] that will make the system more practical in a real-life application. The proposed system can offer an effective method to handle the change of water surface in principle. The equipment can be easily replaced to meet the practical non-line-of-sight underwater optical wireless communications.