To explore and exploit ocean resources, it is necessary to establish wireless communication networks between underwater and air platforms. In these wireless networks, data should be transmitted efficiently across the water-to-air (W2A) interface; reliable W2A communication links play a significant role in such data transmission. Although acoustic waves are the primary means for communication in water because of their long propagation distance (up to several kilometers), they are mostly reflected off when crossing the water surface. Moreover, the transmission rate of an acoustic communication system is relatively low (on the order of kb/s), which limits its application. Radio frequency waves are suitable for long distances (up to tens of kilometers) and high transmission rates (up to hundreds of Mb/s) of wireless communication in air, but they can only travel a few meters through water because of their high absorption and attenuation in underwater environments. Compared with acoustic and RF waves, optical waves can achieve long-distance wireless transmission in both water and air media; they provide a very high bandwidth, high transmission rate, and low latency and enable the use of advanced transceiver devices. Thus, the use of optical waves is a potential solution for communication across the W2A interface. However, when a light beam passes across the W2A interface, the propagating photons experience an unpredictable path deviation owing to the dynamic nature of the waves. Therefore, it is necessary to obtain the statistical properties of the physical responses of photons passing across different W2A interfaces, which can be used to characterize the correlation between the light beam drift and water wave dynamics.

This study focused on water-to-air visible light communication (W2A-VLC) through regular and random waves. The physical response of the propagating photons and corresponding link performances were evaluated by combining laboratory experiments with theoretical simulations. First, we built a laser diode (LD) transmission experiment and captured laser spots at the receiving end using a high-speed camera. The physical response of the propagating photons could be visualized by extracting the centroids of the laser spots, and a Monte Carlo simulation of the photon transmission was performed for comparative analysis. Second, by numerically fitting the centroid distribution, we further obtained the statistical properties of the photon responses under regular and random waves conditions. The inner dynamic processes of the statistical properties were also analyzed. Finally, we validated the narrow-beam characteristics from the perspective of wide-beam transmission through both theoretical simulations and experimental measurements. The statistical laws of the LD narrow beam were validated from the perspective of the LED wide beam.

The physical response of the propagating photons was first theoretically predicted based on Monte Carlo simulations. In the case of a calm water surface, the photons are mainly distributed around the coordinate center of the receiving end and present a circular structure. In the case of regular waves, the photons are distributed in a strip shape at the receiving end, whereas in the case of random waves, the received photons diffuse from the center to the periphery, and the distribution range significantly increases [Fig. 3(a)?(c)]. The experimental results of the photon responses are consistent with the Monte Carlo simulation patterns. The corresponding statistical features were analyzed further. For regular waves, the centroid points on the x-axis ( perpendicular to the wind) obey a normal distribution, whereas those on the y-axis (wind direction) obey a negatively skewed distribution with a skewed parameter of λ′=-2.5. For random waves, the distribution of the centroid points presents an approximately normal distribution (Fig. 4). We also justify the LD link characterization based on the simulation and real test of an LED transmitter. A Monte Carlo simulation of the LED wide-beam link was performed to obtain the light spot at the receiving end. The light spot on the calm water surface is a regular circle, and its brightness gradually decreases from the center. In the case of regular waves, the pattern of the light spot is elliptical. Conversely, in the case of random waves, the light spot still exhibits a circular outline, but the bright and dark areas in the light spot are irregularly distributed (Fig. 5). An experimental verification system for the LED link was designed to verify the simulation and extend the general statistical laws of the LD narrow beam (Fig. 6). The experimental results reveal that the photon diffusion and beam drift are mainly along the wind direction, consistent with the conclusion obtained for the LD narrow-beam link. Furthermore, the spatial distribution of the link gain values is consistent with the simulation pattern (Fig. 7).

In this study, narrow-beam light transmission through a wavy water-to-air (W2A) surface was evaluated. The physical response of the propagating photons and corresponding statistical characteristics were determined through a combination of lab experiments and theoretical simulations. We experimentally tested the LD narrow-beam link and obtained the photon-response characteristics. The test experiment reveals that, for regular waves, the photon response presents a negatively skewed distribution in the wind direction, whereas for random waves, the photon response shows a normal distribution. These statistical features imply an intrinsic dynamic correlation of the photon response with the wavy W2A surface and its driving forces. Because the LED transmitter can be treated as the integration of infinite LD lights over space, the narrow-beam link characteristics were validated using a wide-beam transmitter perspective. The simulation and real test of the LED transmitter confirm the characterization of the narrow-beam link under both regular and random waves.