Cosine beam: diffraction-free propagation and self-healing.

Area of Science:

• Optics and Photonics
• Wave Phenomena
• Beam Propagation

Background:

• The cosine beam (CB) exhibits nondiffracting properties but is not physically realizable due to its infinite extent.
• Apodization pupils are employed to manage the transverse extent of beams, leading to practical realizations like cosine-Gauss (CG) and cosine-windowed beams.

Purpose of the Study:

• To analyze the nondiffracting characteristics of cosine-Gauss (CG) beams and their higher-order Hermite-cosine-Gauss (HCG) counterparts.
• To investigate the self-healing capabilities of HCG beams when encountering obstacles.

Main Methods:

• Analytical derivation of beam width and nondiffracting range for CG beams using second-order intensity moments.
• Superposition of two oppositely oblique Gaussian beams to form CG beams, extended to Hermite-Gauss (HG_n) beams for HCG_n beams.
• Experimental testing of HCG beam self-healing properties against varying obstruction sizes.

Main Results:

• Analytical expressions for CG beam width and nondiffracting range were derived.
• Higher-order Hermite-cosine-Gauss (HCG_n) beams were generated and their nondiffracting nature confirmed.
• The self-healing limit distance for HCG_n beams was quantified as a function of obstruction size and CG parameter.

Conclusions:

• CG and HCG beams are robust, nondiffracting beams with significant self-healing capabilities.
• The findings are relevant for structured light applications including particle manipulation, advanced imaging, and light sheet microscopy.
• This research provides a theoretical and experimental basis for utilizing these specialized beams in demanding optical systems.