We develop a general formalism to treat reflection of spherical electromagnetic waves or, more precisely, dipole radiation from a spherical surface. Our main objective is interpretation of radio wave signals produced by cosmic ray interactions with Earth’s atmosphere which are observed by the Antarctica based ANITA detector after reflection off the ice surface. The incident wave is decomposed into plane waves and each plane wave is reflected off the surface using the standard Fresnel formalism. For each plane wave the reflected wave is assumed to be locally a plane wave. This is a very reasonable assumption and there are no uncontrolled approximations in our treatment of the reflection phenomenon. The surface roughness effects are also included by using a simple model. We apply our formalism to the radiation produced by the balloon-borne HiCal radio-frequency (RF) transmitter. Our final results for the reflected power are found to be in good agreement with data for all elevation angles. We also study the properties of reflected radio pulses in order to study their phase relationship with direct pulses. We find that for some roughness models the pulse shape can be somewhat distorted. However this is a rather small effect and is unable to provide an explanation for the observed mystery events by ANITA.

中文翻译：

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球面电磁波反射的一般处理及其对 ANITA 异常极性事件的影响


我们开发了一种通用形式来处理球形电磁波的反射，或更准确地说，处理来自球形表面的偶极子辐射。我们的主要目标是解释宇宙射线与地球大气层相互作用产生的无线电波信号，这些信号由南极洲的 ANITA 探测器在冰面反射后观测到。入射波被分解为平面波，并且每个平面波使用标准菲涅尔形式从表面反射。对于每个平面波，反射波被假定为局部平面波。这是一个非常合理的假设，并且在我们处理反射现象时不存在不受控制的近似。还通过使用简单的模型来考虑表面粗糙度的影响。我们将形式主义应用于气球载 HiCal 射频 (RF) 发射器产生的辐射。我们发现反射功率的最终结果与所有仰角的数据非常一致。我们还研究反射无线电脉冲的特性，以便研究它们与直接脉冲的相位关系。我们发现对于某些粗糙度模型，脉冲形状可能会有些扭曲。然而，这是一个相当小的影响，无法为 ANITA 观察到的神秘事件提供解释。