电子光学中保角变换的一般框架
A general framework for conformal transformations in electron optics
摘要：
log-pol变换的实现最近在带电物质涡旋的电子光学中引入了一个新的推动力，允许在线性和轨道角动量（OAM）状态之间进行共形映射并测量它们。这种坐标变换属于Hossack变换的一般框架，最近已经通过静电元件有效地实现了。在这封信中，我们表明，这是一个一般的属性，这些共形变换产生的谐波相位元素，因此承认在电子光学方案中的静电实现。我们考虑一种新的保角映射，圆扇区变换，这是最近推出的OAM乘法和除法在光学，并讨论它是如何表示拉普拉斯方程的一般解，显示出类比的生成相元素与投影多极场和线性电荷分布。此外，我们证明了它的能力，执行多极波前的排序，发现一种新颖有效的方法来测量的强度和方向的偶极子场在一个快速，紧凑和直接的方式。
英文摘要：
The implementation of log-pol transformation has recently introduced a new boost in electron optics with charged matter vortices, allowing to map conformally between linear and orbital angular momentum (OAM) states and to measure them. That coordinate change belongs to the general framework of Hossack's transformations and it has been recently realized efficiently by means of electrostatic elements. In this letter we show that it is a general property of those conformal transformations to be produced by harmonic phase elements and therefore to admit an electrostatic implementation in the electron optics scenario. We consider a new kind of conformal mapping, the circular-sector transformation, which has been recently introduced for OAM multiplication and division in optics, and discuss how it represents a general solution of Laplace's equation, showing the analogy of the generating phase elements with projected multipole fields and linear charge distributions. Moreover, we demonstrate its capability to perform the sorting of multipole wavefronts, discovering a novel and effective method to measure the strength and orientation of a dipole field in a fast, compact and direct way.
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