Nonlinear optical catastrophe from a smooth initial beam

Area of Science:

• Optics and Photonics
• Wave Phenomena
• Nonlinear Optics

Background:

• Diffraction is the bending of waves around obstacles.
• Gaussian beams are fundamental solutions to the paraxial wave equation.
• Catastrophe theory describes singularities in wave patterns.

Purpose of the Study:

• To experimentally observe and characterize an optical cusp diffraction catastrophe.
• To investigate the role of nonlinear and linear diffraction regimes in pattern formation.
• To analyze the resulting near-field and far-field beam structures.

Main Methods:

• Utilizing an initially smooth, elongated Gaussian beam with a 2:1 aspect ratio.
• Observing the beam propagation in both nonlinear and linear diffraction regimes.
• Analyzing the beam's spatial structure in the near-field and far-field using optical methods.

Main Results:

• Successfully observed an optical cusp diffraction catastrophe.
• Identified an elliptical annulus in the near-field diffraction pattern.
• Characterized a spatially complex astroid pattern in the far-field diffraction.

Conclusions:

• The optical cusp diffraction catastrophe can be generated from a simple elongated Gaussian beam.
• Both nonlinear and linear diffraction effects are crucial in shaping the observed optical patterns.
• The study provides experimental evidence for theoretical predictions of wave propagation singularities.