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Fractionalization of optical beams: I. Planar analysis
1Photonics and Mathematical Optics Group, Tecnológico de Monterrey, Monterrey, México. juliocesar@itesm.mx
Optics Letters
|June 5, 2007
Summary
Researchers introduce novel fractional-order beam solutions by applying fractional calculus to the paraxial wave equation, bridging existing integral-order solutions. This study focuses on fractionalizing Hermite-Gaussian beams.
Area of Science:
- Optics and Photonics
- Mathematical Physics
Background:
- The paraxial wave equation describes light propagation.
- Hermite-Gaussian beams are standard solutions in optics.
- Existing solutions are typically integral-order.
Purpose of the Study:
- To introduce new fractional-order beam solutions.
- To extend the concept of Hermite-Gaussian beams to fractional orders.
- To explore solutions intermediate to known integral-order solutions.
Main Methods:
- Application of fractional calculus tools.
- Fractionalization of the paraxial wave equation.
- Focus on Hermite-Gaussian beam structures.
Main Results:
- Novel fractional-order beam solutions were successfully introduced.
- These solutions act as intermediates between integral-order solutions.
- The fractionalization was demonstrated on Hermite-Gaussian beams.
Conclusions:
- Fractional calculus provides a new framework for beam solutions.
- Fractional-order beams offer a continuum between established optical modes.
- This approach expands the toolkit for analyzing wave propagation.
