Discreteness of the real point emitters as a physical condition for diffraction

Area of Science:

• Optics and Photonics
• Mathematical Physics

Background:

• Diffraction phenomena are typically described using continuous models.
• The cross-spectral density is a standard mathematical tool for analyzing light propagation.

Purpose of the Study:

• To establish the physical conditions necessary for describing diffraction from aperture planes to the far field.
• To re-evaluate the role of mathematical continuity requirements in diffraction theory.
• To introduce new methods for characterizing physical point sources of light.

Main Methods:

• Analysis of the spectrum of classes of point emitters.
• Investigation of the zeroth-order class discreteness.
• Comparison with continuity requirements of cross-spectral density.

Main Results:

• The discreteness of the zeroth-order class is a necessary and sufficient physical condition for far-field diffraction.
• The continuity requirement of cross-spectral density is shown to be physically redundant.
• New insights into the physical understanding of diffraction are provided.

Conclusions:

• Physical point sources exhibit spectral discreteness crucial for diffraction.
• This work offers novel tools for designing efficient non-paraxial propagation algorithms.
• New criteria for characterizing physical point sources of light are established.