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Summing Lax series for nonparaxial beam propagation
Riccardo Borghi1, Massimo Santarsiero
1Dipartimento di Elettronica Applicata, Istituto Nazionale per la Fisica della Materia, Università Roma Tre, Via della Vasca Navale 84, Rome I-00146, Italy. riccardo.borghi@uniroma1.it
Optics Letters
|June 5, 2003
Summary
This study enhances the Lax approach for nonparaxial electromagnetic beam propagation using a delta transformation. The method effectively calculates electric field components for highly nonparaxial beams.
Area of Science:
- Optics and Photonics
- Computational Electromagnetics
Background:
- The Lax approach is a standard method for studying electromagnetic beam propagation.
- Highly nonparaxial beams pose challenges for traditional approximations.
Purpose of the Study:
- To efficiently apply the Lax approach to strongly nonparaxial electromagnetic beams.
- To introduce a nonlinear resummation scheme for improved accuracy.
Main Methods:
- Applying a nonlinear resummation technique, the delta transformation.
- Utilizing the delta transformation on perturbative series from the Lax scheme.
- Evaluating transverse and longitudinal electric field components.
Main Results:
- The delta transformation effectively handles divergent perturbative series.
- The enhanced method accurately models highly nonparaxial beam propagation.
- Numerical results demonstrate the effectiveness for vectorial Gaussian beams.
Conclusions:
- The delta transformation significantly improves the applicability of the Lax scheme for nonparaxial beams.
- This approach offers a robust method for analyzing complex electromagnetic beam propagation.