Curved optical tubes in a 4Pi focusing system

Area of Science:

• Optics and Photonics
• Three-Dimensional (3D) Light Field Engineering

Background:

• Conventional optical focusing systems typically generate simple focal spots, limiting the complexity of achievable light fields.
• Vortex beams possess unique annular focal intensity distributions, offering potential for constructing more intricate optical structures.

Purpose of the Study:

• To demonstrate the creation of curved optical tubes within a 4Pi focusing system.
• To investigate the properties of these optical tubes, specifically energy concentration along a 3D curve with a hollow cross-section.

Main Methods:

• Utilizing the annular focal spot of a vortex beam as a fundamental building block.
• Constructing optical tubes by arranging and transforming these building blocks (rotation and translation) to cover a desired central-axis curve.
• Calculating the spatial spectrum and input field of the optical tube via linear superposition of transformed building block spectra.

Main Results:

• Successful demonstration of curved optical tube formation in a 4Pi focusing system.
• Observation of energy concentration along prescribed 3D curves with hollow cross-sections.
• Generation of complex optical tube geometries, including torus, solenoid, and trefoil knot shapes, with good agreement to theoretical predictions.

Conclusions:

• The proposed method enables the creation of arbitrary curved optical tubes with unique energy localization properties.
• This technique offers a versatile platform for advanced optical field shaping and manipulation.
• The demonstrated ability to form complex 3D optical structures opens avenues for applications in optical trapping, microscopy, and material processing.