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Astigmatic transformations enable adiabatic connections for paraxial Gaussian beams. This study reveals a Talbot-effect-like evolution in superposition states, leading to pattern variations and revivals for structured light.

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Area of Science:

Optics and Photonics
Quantum Optics
Mathematical Physics

Background:

Paraxial Gaussian beams exist on modal spheres, with Hermite-Laguerre-Gaussian (HLG) modes representing feasible states.
Astigmatic unitary transformations facilitate adiabatic connections between these states on a single modal sphere.

Purpose of the Study:

To investigate the unitary modal evolution of complex structured Gaussian beams composed of HLG modes from different modal spheres using astigmatic transformation.
To understand the underlying beamforming mechanism responsible for pattern evolution in these complex states.

Main Methods:

Utilizing astigmatic unitary transformations to induce modal evolution in superpositions of HLG modes.
Employing Ince-Gaussian modes as a specific case for systematic analysis and experimental validation.
Analyzing the role of non-synchronized higher-order geometric phases in cyclic transformations.

Main Results:

A Talbot-effect-like modal evolution was observed in the superposition states of HLG modes due to geometric phases.
Specific geodesic loops in transformations led to pattern variations and revivals.
Experimental corroboration confirmed the theoretical predictions for Ince-Gaussian modes.

Conclusions:

A generic theory for modal conversion of structured Gaussian beams via astigmatic unitary transformation has been established.
This provides a novel method for actively shaping the spatial modal structure of light.
The findings offer potential for diverse applications in structured light technologies.