Julián-Macías Israel, Martínez-Niconoff Gabriel, Silva-Ortigoza Gilberto, Rickenstorff-Parrao Carolina
J Opt Soc Am A Opt Image Sci Vis. 2024 Apr 1;41(4):686-693. doi: 10.1364/JOSAA.518866.
In the first part of this work, we introduce a monochromatic solution to the scalar wave equation in free space, defined by a superposition of monochromatic nondiffracting half Bessel-lattice optical fields, which is determined by two scalar functions; one is defined on frequency space, and the other is a complete integral to the eikonal equation in free space. We obtain expressions for the geometrical wavefronts, the caustic region, and the Poynting vector. We highlight that this solution is stable under small perturbations because it is characterized by a caustic of the hyperbolic umbilical type. In the second part, we introduce the corresponding solution to the Maxwell equations in free space.
在本工作的第一部分，我们介绍了自由空间中标量波动方程的一种单色解，它由单色非衍射半贝塞尔晶格光场的叠加定义，该叠加由两个标量函数确定；一个定义在频率空间上，另一个是自由空间中程函方程的完备积分。我们得到了几何波前、焦散区域和坡印廷矢量的表达式。我们强调，该解在小扰动下是稳定的，因为它具有双曲脐型焦散的特征。在第二部分，我们介绍了自由空间中麦克斯韦方程组的相应解。
