AI 中文总结
本文推导了包围柱面的三种等效线积分场表示，提出二维Schelkunoff-Franz表示，为无限周期结构的散射辐射研究提供了严格的惠更斯原理形式。
AI 中文摘要
本文研究了包围场源或散射体的无限长柱面的频域惠更斯原理及等效关系。假设场沿柱轴呈谐波依赖，推导了自由空间中包围柱外任意点场的三种等效线积分表示形式。其中一种形式类似亥姆霍兹-基尔霍夫标量衍射理论，积分包含纵向场分量及其法向导数；另一种形式包含纵向场和法向场分量，类似Stratton与Chu提出的三维边界积分表示，该形式无需计算场导数；此外，还提出了三维Schelkunoff-Franz表示的二维版本，其仅包含场的切向分量，符合场等效定理，可视为包围柱面的惠更斯原理的严格表述。三种线等效关系形式均为精确的，通过包围源区横截面的线上的等效场分布描述场。本文还从包围真实源的柱面上的虚拟线源发出的锥形波的角度，对惠更斯原理进行了物理解释，并给出了这些关系在近场和远场区域的特例。推导的表达式适用于研究沿一个方向无限且周期性的非常广泛类别的结构的散射与辐射问题。
英文摘要
Frequency-domain Huygens' principle and equivalence relations for an infinitely long cylindrical surface enclosing the field sources or scatterers are addressed. Assuming the harmonic dependence of the fields along the cylinder axis, we derive three equivalent versions of line-integral representations for the fields in free space at any point outside the enclosing cylinder. In one of the forms, similarly to the Helmholtz-Kirchhoff scalar diffraction theory, the integrals contain a longitudinal field component and its normal derivative. Another presented form contains longitudinal and normal field components, similarly to the three-dimensional boundary integral representations by Stratton and Chu. This form eliminates the need to calculate the field derivatives. Furthermore, we present a two-dimensional version of the three-dimensional Schelkunoff-Franz representation, which contains only tangential components of the fields, complies with the field equivalence theorem and can be regarded as a rigorous formulation of Huygens' principle for a cylindrical enclosing surface. All three forms of the line-equivalence relation are exact and describe the fields through equivalent field distributions on a line enclosing the cross section of the source region. A physical interpretation of Huygens' principle in terms of conical waves emanated by virtual linear sources on the cylindrical surface enclosing the true sources is given. Specialization of the relations to the intermediate and far-field zones are presented. The derived expressions are applicable for studies of scattering and radiation in a very general class of structures that are infinite and periodic along one direction.
