Zang Feng, Liu Lifeng, Deng Fusheng, Liu Yanhong, Dong Lijuan, Shi Yunlong
Opt Express. 2021 Aug 2;29(16):26048-26057. doi: 10.1364/OE.435518.
In this paper, we provide analytical solutions describing the dynamic behavior of the Pearcey-Gaussian beams propagating in free space. Based on the analytical solutions, explicit expressions governing the focusing distances of the Pearcey-Gaussian beams are found and verified by numerical simulations. For the linearly chirped Pearcey-Gaussian beam, it exhibits a uni-focusing behavior during propagation. Particularly, the focusing distance is independent on the linear chirp parameter and remains z = 2 unchanged. Of particular interest is that the quadratically chirped Pearcey-Gaussian beam focuses twice when the quadratic chirp parameter β < 0. The first and the second focusing distances are determined by z = 2/(1 - 4β) and z = -1/(2β), respectively. Furthermore, we numerically investigate the peak powers at the different focusing positions and find that as β increases, the peak powers at z and z linearly decrease. It is expected that the characteristics can be used for manipulating the focusing distances and the peak powers to generate an optical beam with high peak power by adjusting the chirp parameter β.
在本文中，我们提供了描述皮尔斯高斯光束在自由空间中传播时动态行为的解析解。基于这些解析解，找到了控制皮尔斯高斯光束聚焦距离的显式表达式，并通过数值模拟进行了验证。对于线性啁啾皮尔斯高斯光束，它在传播过程中表现出单聚焦行为。特别地，聚焦距离与线性啁啾参数无关，始终保持(z = 2)不变。特别有趣的是，当二次啁啾参数(\beta < 0)时，二次啁啾皮尔斯高斯光束会聚焦两次。第一次和第二次聚焦距离分别由(z = 2/(1 - 4\beta))和(z = -1/(2\beta))确定。此外，我们通过数值研究了不同聚焦位置处的峰值功率，发现随着(\beta)的增加，(z)处和(z)处的峰值功率线性下降。预计这些特性可用于通过调整啁啾参数(\beta)来控制聚焦距离和峰值功率，从而产生具有高峰值功率的光束。
