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    Area of Science:

    • Optical Physics
    • Beam Optics
    • Wavefront Engineering

    Background:

    • Singular beams are crucial in optics for applications like optical trapping and microscopy.
    • Controlling the topological charge of singular beams is essential for advanced optical manipulation.
    • Existing methods for generating singular beams often lack flexibility in topological charge control.

    Purpose of the Study:

    • To introduce a novel type of singular beam with a controllable topological charge.
    • To investigate the generation mechanism using spatial phase modulation.
    • To analyze the propagation dynamics and verify the topological charge experimentally.

    Main Methods:

    • Spatial phase modulation using tangent and linear functions on angular and radial coordinates, respectively.
    • Numerical simulations to study beam propagation and evolution.
    • Experimental verification using a Shack-Hartmann wavefront sensor.

    Main Results:

    • Successfully generated singular beams with tunable topological charge.
    • Observed a warped intensity profile due to radial phase modulation.
    • Experimental results confirmed the simulated topological charge values.

    Conclusions:

    • The proposed method provides a flexible way to generate singular beams with controllable topological charge.
    • The combination of angular and radial phase modulation offers unique beam characteristics.
    • This work validates the theoretical model with experimental evidence.