Propagation-invariant wave fields with finite energy

Area of Science:

• Optics and Photonics
• Wave Physics
• Mathematical Physics

Background:

• Propagation-invariant wave fields are crucial for applications requiring stable beam structures.
• Existing models like Bessel beams and self-imaging phenomena have limitations in generality and applicability.
• The paraxial regime offers a simplified yet powerful framework for studying wave propagation.

Purpose of the Study:

• To generalize the concept of propagation invariance within the paraxial regime.
• To introduce and characterize a novel generalized self-imaging effect for wave fields.
• To establish connections between this generalized effect and known optical phenomena.

Main Methods:

• Derivation of necessary and sufficient conditions for the generalized self-imaging effect.
• Representation of these conditions in the Gauss-Laguerre modal plane.
• Analysis of relationships with classical self-imaging, rotating beams, and eigen-Fourier functions.

Main Results:

• Demonstration of a generalized self-imaging effect characterized by finite transverse self-images at varying scales and orientations.
• Confirmation that these generalized fields possess finite energy, enabling accurate generation.
• Inclusion of Bessel beams and Gauss-Laguerre beams within this unified framework, revealing a key relationship between them.

Conclusions:

• The generalized self-imaging effect provides a unifying framework for various paraxial propagation-invariant wave fields.
• This framework simplifies the understanding and generation of complex optical beams.
• The study highlights a significant link between paraxial Bessel beams and Gauss-Laguerre beams under this generalized effect.