Diffraction of a focused wave by an aperture: a new perspective

Area of Science:

• Optics and Photonics
• Mathematical Physics

Background:

• Accurate calculation of the diffracted field in the focal region of optical systems is crucial.
• Understanding the behavior of light near the focus is essential for lens design and performance analysis.

Purpose of the Study:

• To present a new, simplified approach for calculating the diffracted field along lines through the focal point of a lens.
• To apply this method to various aperture shapes, including circular, semicircular, and polygonal.
• To gain new insights into the asymptotic behavior and intensity zeros of the diffracted field.

Main Methods:

• Development of a new analytical method for calculating the diffracted field.
• Application of the method to circular apertures.
• Extension of the method to other aperture shapes like circular sectors, segments (semicircular, Hilbert mask), and polygons.
• Utilizing a one-dimensional Fourier transform for diffracted field computation.

Main Results:

• The presented method accurately calculates the diffracted field, even at observation points distant from the focus.
• The approach is successfully applied to a range of aperture geometries.
• New insights into the asymptotic behavior of the diffracted field and the existence of intensity zeros are revealed for different shapes.

Conclusions:

• The new approach provides an efficient and insightful way to analyze the focal region field.
• The method's applicability to diverse aperture shapes enhances its utility in optical studies.
• This work contributes to a deeper understanding of diffraction phenomena and their dependence on aperture geometry.