Uniform asymptotics of paraxial boundary diffraction waves

Area of Science:

• Optics and Photonics
• Mathematical Physics

Background:

• Classical Fresnel diffraction theory.
• Paraxial formulation of boundary-diffracted-wave theory.

Purpose of the Study:

• To provide a geometrical interpretation of paraxial diffraction phenomena.
• To generalize Schwarzschild's uniform asymptotics to arbitrary smooth apertures.
• To explore diffraction patterns within the geometrical shadow of elliptic disks.

Main Methods:

• Utilizing the paraxial formulation of boundary-diffracted-wave theory.
• Applying catastrophe optics and geometrical interpretations.
• Analyzing diffraction patterns of opaque elliptic disks under plane wave illumination.

Main Results:

• Rediscovery of classical Fresnel diffraction results from a new perspective.
• Geometrical interpretation of Schwarzschild's uniform asymptotics for circular apertures.
• Generalization to arbitrarily shaped smooth apertures.
• Identification of the ellipse's evolute as a geometrical caustic for diffraction patterns.

Conclusions:

• The boundary-diffracted-wave theory offers a powerful geometrical framework for understanding diffraction.
• The study provides insights into saddle point mechanisms in diffraction patterns.
• The findings contribute to the understanding of wave propagation and diffraction phenomena.