Radially polarized beams' phase filtering focal properties based on path integral analysis.

Area of Science:

• Optics and Photonics
• Electromagnetism
• Beam Focusing

Background:

• Radially polarized (RP) beams are crucial for applications requiring tight focusing.
• Analyzing the tight focusing of RP beams presents complex challenges.
• Existing methods may lack intuitive control over focal properties.

Purpose of the Study:

• To introduce the path integral (PI) method for analyzing the tight focusing of RP beams.
• To develop an intuitive phase filtering technique based on PI.
• To investigate the focal properties of RP beams using the new method.

Main Methods:

• Application of the path integral (PI) formalism to RP beam focusing.
• Development and implementation of a zero-point construction (ZPC) phase filtering technique.
• Analysis of focal properties for solid and annular RP beams before and after ZPC filtering.

Main Results:

• The PI method visually clarifies the contribution of each ray to the focal region.
• ZPC phase filtering allows for intuitive and precise selection of filter parameters.
• Superior focal properties were achieved by combining large numerical aperture (NA) annular beams with phase filtering.

Conclusions:

• The path integral method provides a powerful tool for understanding and manipulating RP beam focusing.
• The ZPC phase filtering technique offers an intuitive approach to optimize focal characteristics.
• Optimized RP beams using annular profiles and phase filtering hold promise for advanced optical systems.