## 3 Results  
### Simulation  
#### 3.1.1 Unidirectional Transmission  
In the simulation experiment, the influence of different beam parameters on the propagation result was investigated firstly by the forward transmission part of the IMC method. The medium in the simulation was set to Jerlov II type water, which is an oceanic water type and mostly free of extra colored dissolved organic matter from terrigenous sources, resulting in small signal attenuation, and the detailed values of \(c\) and \(\omega\) were 0.42 m\({}^{-1}\) and 0.89 [39] The scattering angle \(\theta\) was determined by the Henyey-Greensien (H-G) scattering phase function [40], where \(\gamma\) satisfies the uniform distribution of \([0,2\pi]\). To ensure that in underwater laser communication or detection applications, the laser transmitted through the channel can not only illuminate the core area, but also maximize the energy at the target or receiver, the impact of divergence angle and spot radius in the initial on spatial and temporal variation characteristics after unidirectional transmission was analyzed emphatically in the simulation. The target was located at different distances, transmission results of spatial broadening and temporal broadening on the target plane are shown in the figure below where the pulse width (full width at half maximum (FWHM)) was 4.5 ns, the divergence angles were 20, 60, 100 and 200 mrad, with the initial radius of 0.5, 2.5 and 10 mm (FWHM), respectively. The number of simulated photon packets was \(1\times 10^{8}\) and each packet contained 5.35 \(\times\)\(10^{5}\) photons (each photon has an energy of \(3.74\times 10^{19}\)\(J\) at a wavelength of 532 nm, thus, the total energy can be calculated as \(1\times 10^{8}\times 5.35\times 10^{5}\times 3.74\times 10^{-19}\)\(J=20\times 10^{-6}\)\(J\)).  
As the transmission length increased, the spot and pulse width of all beams were broadened, but it is worth noting that when the divergence angle was the same, the effect of the spatial broadening of lasers with different initial radius at the same length was extremely weak and could be ignored. While the changes of divergence angle bring contrasting results: when the distance was relatively short, the different divergence angles had significant differences in the effect of spatial broadening, the larger the divergence angle, the more obvious the broadening. With the increase in transmission distance, the results of smaller divergence angles gradually tended to be the same, such as 20 mrad (solid blue line) and 60 mrad (dashed blue line); however, larger divergence angles within a certain range maintained more distinct broadening than smaller ones, as shown by 200 mrad (densely dashdotted blue line) and 20 mrad in Figure 2. Conversely, as the red line shown in Figure 2,the temporal broadening effect of the laser was almost unaffected by the divergence angle and the initial radius. For simplicity, only the temporal broadening results of 20 and 200 mrad are shown here. Consequently, it was necessary to comprehensively consider the application scenario and experimental conditions to select the most appropriate initial parameters to ensure the best results.