The dark spots of Arago

Area of Science:

• Optics and Photonics
• Quantum Optics
• Laser Physics

Background:

• Laguerre-Gaussian beams are fundamental solutions in paraxial optics, characterized by orbital angular momentum.
• The Arago spot is a well-known phenomenon observed when a plane wave is diffracted by a circular obstacle.

Purpose of the Study:

• To investigate the diffraction and propagation of Laguerre-Gaussian beams with varying azimuthal indices past a circular obstacle.
• To analyze the behavior of the Arago spot under different beam and obstacle alignments.
• To understand the influence of the azimuthal index on the resulting diffraction patterns.

Main Methods:

• Experimental investigation using laser setups to generate and manipulate Laguerre-Gaussian beams.
• Numerical simulations employing diffraction theory and computational optics methods.
• Systematic variation of the azimuthal index and the degree of misalignment between the beam and obstacle.

Main Results:

• For aligned centers, non-zero azimuthal index beams produce a central dark spot of Arago, unlike the bright spot for zero index.
• As the beam and obstacle centers become misaligned, the central dark spot's structure changes.
• Higher incident azimuthal indices lead to the fragmentation of the central dark spot into multiple dark regions.

Conclusions:

• The phase singularity of Laguerre-Gaussian beams dictates the formation of the central dark spot of Arago.
• The azimuthal index plays a crucial role in the stability and fragmentation of the dark spot under misalignment.
• This study provides insights into the complex light-matter interactions involving structured light beams and obstacles.