Catastrophe optics of sharp-edge diffraction

Area of Science:

• Optics
• Wave phenomena
• Mathematical physics

Background:

• Classical diffraction theory addresses wave interactions with apertures.
• Catastrophe optics offers a new framework for analyzing wave phenomena.
• Sharp-edge apertures present a long-standing challenge in diffraction analysis.

Purpose of the Study:

• To reformulate plane wave diffraction by sharp-edge apertures using catastrophe optics.
• To derive uniform analytical estimates for the diffracted wavefield near caustics.
• To validate the theoretical predictions through diffraction from parabolic apertures.

Main Methods:

• Application of catastrophe optics principles to diffraction problems.
• Integration of geometrical arguments within a wave optics context.
• Utilizing paraxial approximation for analytical estimations.

Main Results:

• Uniform analytical estimates of the diffracted wavefield near fold caustics were obtained.
• The results are expressed in terms of the Airy function and its derivative.
• The method provides accurate predictions for wavefield behavior.

Conclusions:

• Catastrophe optics offers a powerful new perspective on classical diffraction problems.
• The derived analytical estimates are reliable for predicting diffracted wavefields.
• Diffraction from parabolic apertures serves as a robust validation method.