Pearcey beam tuning and caustic evolution

Area of Science:

• Optics
• Nonlinear Optics
• Mathematical Physics

Background:

• Pearcey beams are a type of optical beam with unique focusing properties.
• Catastrophe theory provides a framework for understanding the formation of singularities in physical systems.
• Controlling light-field structures is crucial for advanced optical applications.

Purpose of the Study:

• To modify Pearcey beams by introducing an additional phase factor for enhanced control over their light-field structure.
• To investigate the optical structure and evolution characteristics of the modified Pearcey beams, particularly their caustics.
• To derive analytical equations for the caustics of these engineered Pearcey beams.

Main Methods:

• Theoretical modification of Pearcey beams by adding a phase factor based on catastrophe theory.
• Derivation of analytical equations describing the caustics of the engineered beams.
• Experimental generation of the modified Pearcey beams using binary masks and the superpixel method.

Main Results:

• The modified Pearcey beams exhibit a more flexible and controllable light-field structure.
• Analytical equations for the caustics were derived, considering the engineered phase factor.
• Experimental generation successfully produced the theoretically designed beams.
• Theoretical analysis and numerical simulations showed that caustics remain unchanged but laterally shift with varying phase parameters during propagation.

Conclusions:

• The engineered Pearcey beams offer tunable caustic properties.
• The observed lateral shift of caustics has potential applications in optical manipulation.
• This work provides a method for designing and generating advanced optical beams with controllable characteristics.