Objective  Due to the strong attenuation of electromagnetic waves by seawater and the complex and variable characteristics of ocean acoustic channels, a single communication method can not meet the long-distance communication needs of aerial platforms for underwater targets. Optical-to-acoustic technology can convert laser signals in the atmosphere into underwater acoustic signals, combining two optimal channels to overcome the bottleneck problems, that is, large attenuation of single electromagnetic waves in water and strong divergence in the atmosphere. And this technology does not require sound waves to be transmitted remotely through underwater channels, resulting in minimal interference to the signal and extremely high transmission efficiency. However, different incident angles play an important role in the photoacoustic conversion efficiency and confidentiality of air-underwater transboundary communication. And vaporization mechanism is more feasible than other mechanisms. Therefore, it is necessary to use numerical calculation methods to study the three-dimensional scattering characteristics of laser on rough sea surfaces at different sea conditions and incidence angles, in order to improve the confidentiality of optical-to-acoustic transboundary communication in vaporization mechanism and accurately grasp the variation characteristics of laser transmission energy intensity with incidence angle.

  Methods  To improve the accuracy of simulation results, mathematical model of three-dimensional laser scattering field on sea surface was established (Fig.1). To enhance the calculation efficiency, three-dimensional surface integral equation of laser on sea surface was solved with preconditioned conjugate gradient method. And the interface was divided into strong zone and weak zone according to the characteristics of incident light wave to enhance the computing efficiency (Fig.2). And different rough surface in different sea state are simulated (Fig.3). In order to obtain the three-dimensional energy distribution characteristics of the laser scattering field on a fluctuating water surface, we used the Monte Carlo method to statistically analyze the effects of different incident angles and sea conditions on the energy distribution of the scattering field. The number of Monte Carlo simulations was 5000 times. Finally, the simulation experimental system was established, and the simulation results were validated by indoor simulation experiment (Fig.8).

  Results and Discussions   The effect of different incident angles and different sea conditions on the energy distribution characteristics of scattering field and transmitting field are statistically analyzed (Fig.4-7). The simulation results show that the incident angle have important effect on the conversion efficiency and confidentiality of air-underwater transboundary communication. A simulation experimental system is built in the laboratory to test the conversion efficiency of optical-to-acoustic in vaporization mechanism at different incident angles and the experiment results are shown (Tab.1). The experiment results show that the optimal range of incidence angle is \theta _i \in 0^\circ ,60^\circ . The feasibility of transboundary communication with optical-to-acoustic in vaporization mechanism has been proven by the laser induced acoustic characteristic parameters at vertical incidence after convergence (Tab.2).

  Conclusions  It is found that as the incident angle increases, the water surface spot area and transmittance will change so that spot power density and convergence efficiency decrease continuously through the analysis of three-dimensional numerical calculation results and indoor simulation test results. When the incident angle is greater than 60°, the sound source level and photoacoustic conversion efficiency measured in the experiment begin to decrease significantly. The spectrum analysis results of the acoustic pulse signal show that the energy peaks of the acoustic pulse appeared at 126 kHz, 36.8 kHz, and 4.647 kHz, with most of the energy concentrated around 200 kHz. The experiment results show that the optimal range of incidence angle is \theta _i \in 0^\circ ,60^\circ . When the power density of the light spot decreases, the vaporization phenomenon on the water surface also weakens. Which means the power density of the water surface spot area cannot reach the vaporization threshold so as to make the vaporization phenomenon and the thermal expansion phenomenon happen together. The experimental result shows that the photoacoustic conversion efficiency is almost 10⁻³ in the above case.