Accelerating finite-energy generalized Olver beams

Area of Science:

• Optics and Photonics
• Mathematical Physics

Background:

• The paraxial wave equation (PWE) describes light propagation in many optical systems.
• Existing solutions often lack versatility in controlling beam properties during propagation.

Purpose of the Study:

• To introduce a new, general finite-energy beam solution to the PWE.
• To analyze the propagation characteristics of this novel beam.
• To demonstrate control over beam properties like diffraction resistance and trajectory.

Main Methods:

• Derivation of the finite-energy generalized Olver beam using an exponential differential operator on PWE solutions.
• Analytical calculation of field distributions.
• Numerical simulations to study beam propagation, intensity, centroid, and variance.
• Investigation of parameter influence on self-acceleration, sidelobes, and mainlobe stability.

Main Results:

• The proposed finite-energy generalized Olver beam demonstrates diffraction-resistant propagation along curved trajectories under specific conditions.
• Tunable control over self-acceleration, sidelobe profiles, and central mainlobe stability is achieved by adjusting transformation parameters.
• The study provides analytical expressions for field distributions and propagation dynamics.

Conclusions:

• The finite-energy generalized Olver beam offers a versatile platform for controlling optical beam properties.
• This novel beam solution shows promise for applications requiring diffraction-resistant and precisely controlled light propagation.