色散聚焦波的德拜表示
Debye representation of dispersive focused waves
摘要：
我们报告基于矩阵的衍射积分，评估任何衍射限制轴对称复杂系统的焦点领域。这个衍射公式是德拜积分应用于有光阑聚焦光束的推广，可以适用于宽带问题。纵向色差可能会限制德拜公式的方便性，此外，还提供了焦点周围的有效性空间边界。当聚焦几何的菲涅耳数大大超过1时，为了保证聚焦区域完全进入德拜近似的有效区域，重新表述了菲涅耳数。我们已经应用基于矩阵的德拜积分的几个例子。具体地说，我们提出了一种具有强角色散和无纵向色差的光束聚焦光学系统。这种简单的形式主义为分析和设计具有任意角色散的聚焦光束留下了一扇敞开的大门。我们的结果对超短脉冲和多色非相干光源是有效的。
英文摘要：
We report on a matrix-based diffraction integral that evaluates the focal field of any diffraction-limited axisymmetric complex system. This diffraction formula is a generalization of the Debye integral applied to apertured focused beams, which may be accommodated to broadband problems. Longitudinal chromatic aberration may limit the convenience of the Debye formulation and, additionally, spatial boundaries of validity around the focal point are provided. Fresnel number is reformulated in order to guarantee that the focal region is entirely into the region of validity of the Debye approximation when the Fresnel number of the focusing geometry largely exceeds unity. We have applied the matrix-based Debye integral to several examples. Concretely, we present an optical system for beam focusing with strong angular dispersion and free of longitudinal chromatic aberration. This simple formalism leaves an open door for analysis and design of focused beams with arbitrary angular dispersion. Our results are valid for ultrashort pulsed and polychromatic incoherent sources.
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