Closed-form expressions for nonparaxial accelerating beams with pre-engineered trajectories

Area of Science:

• Optics and Photonics
• Wave Phenomena
• Beam Propagation

Background:

• Nonparaxial beams exhibit complex trajectories deviating from paraxial approximations.
• Controlling beam propagation along arbitrary paths is crucial for applications in optical manipulation and imaging.

Purpose of the Study:

• To introduce a general real-space method for generating nonparaxial accelerating beams.
• To enable the creation of beams with arbitrary predefined convex trajectories.
• To derive closed-form expressions for beam generation parameters.

Main Methods:

• Development of a real-space optical beam generation technique.
• Derivation of analytical solutions for phase profiles at the input plane.
• Mathematical formulation for arbitrary convex trajectories, including power-law and exponential curves.

Main Results:

• Closed-form expressions for the input phase required to generate nonparaxial accelerating beams.
• Demonstration of generating beams along circular, elliptic, parabolic, power-law, and exponential trajectories.
• Ability to tailor beam intensity profiles by modifying initial amplitude distributions.

Conclusions:

• The proposed method offers a versatile and exact approach for synthesizing nonparaxial accelerating beams.
• The findings extend the capabilities for controlling light propagation along complex, predefined paths.
• This work facilitates the design of novel optical beams for advanced applications.