本文提出了一种提高被动锁模光纤激光器计算效率的方法,该方法由对称分步傅立叶方法（SSFM）和全局误差局部能量（GELE）方法组成。该方法可将与全局误差相关的局部能量增量限制在一定范围内来控制步长。该方法具有自动步长调整机制。达到同程度的计算精度，本文方法的计算时间为255 s，而小的恒定步长SSFM方法需要3855 s。这表明本文方法可以将计算效率提高10余倍。本文方法还可以通过RK4IP、Adams、预测-校正等高阶算法进行扩展，以提高精度。

Underwater optical wireless communication, which is useful for oceanography, environmental monitoring, and underwater surveillance, suffers the limit of the absorption attenuation and Mie–Rayleigh scattering of the lights. Here, Bessel-like beams generated by a fiber microaxicon is utilized for underwater wireless propagation. Underwater, the cone angle for generating Bessel-like beams starts from 46°, which is smaller than that in air for Bessel-like beams. When the cone angle of the fiber microaxicons is about 140°, the depth of focus underwater, which is four times as long as the depth of focus in air, has enlarged about 28 µm, 36.12 µm, and 50.7 µm for 470 nm, 520 nm, and 632 nm visible lights. The transmission distance of the Bessel beams for visible lights has been simulated by using Henyey–Greenstein–Rayleigh phase function methods and spectral absorption by bio-optical model due to Monte Carlo methods. The results show that the propagation distance could reach 4000 m, which overcome the limit of the Mie–Rayleigh scattering and absorption attenuation underwater.