Julián-Macías Israel, Sosa-Sánchez Citlalli Teresa, de Jesús Cabrera-Rosas Omar, Espíndola-Ramos Ernesto, Silva-Ortigoza Gilberto
J Opt Soc Am A Opt Image Sci Vis. 2020 Feb 1;37(2):294-304. doi: 10.1364/JOSAA.376545.
We show that $(\textbf{E},\textbf{H})=({\textbf{E}_0},{\textbf{H}_0}){e^{i[{k_0}S(\textbf{r})-\omega t]}}$(E,H)=(E,H)e is an exact solution to the Maxwell equations in free space if and only if ${{\textbf{E}_0},{\textbf{H}_0},\nabla S}${E,H,∇S} form a mutually perpendicular, right-handed set and $S(\textbf{r})$S(r) is a solution to both the eikonal and Laplace equations. By using a family of solutions to both the eikonal and Laplace equations and the superposition principle, we define new solutions to the Maxwell equations. We show that the vector Durnin beams are particular examples of this type of construction. We introduce the vector Durnin-Whitney beams characterized by locally stable caustics, fold and cusp ridge types. These vector fields are a natural generalization of the vector Bessel beams. Furthermore, the scalar Durnin-Whitney-Gauss beams and their associated caustics are also obtained. We find that the caustics qualitatively describe, except for the zero-order vector Bessel beam, the corresponding maxima of the intensity patterns.
我们证明，当且仅当${\textbf{E}_0,\textbf{H}_0,\nabla S}$构成相互垂直的右手系且$S(\textbf{r})$是程函方程和拉普拉斯方程的解时，$(\textbf{E},\textbf{H})=({\textbf{E}_0},{\textbf{H}_0}){e^{i[{k_0}S(\textbf{r})-\omega t]}}$是自由空间中麦克斯韦方程组的精确解。通过使用程函方程和拉普拉斯方程的一族解以及叠加原理，我们定义了麦克斯韦方程组的新解。我们表明矢量杜林光束是这种构造类型的特殊例子。我们引入了以局部稳定的焦散线、褶皱和尖点脊类型为特征的矢量杜林 - 惠特尼光束。这些矢量场是矢量贝塞尔光束的自然推广。此外，还得到了标量杜林 - 惠特尼 - 高斯光束及其相关的焦散线。我们发现，除了零阶矢量贝塞尔光束外，焦散线定性地描述了强度图案的相应最大值。
