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Transition between free-space Helmholtz equation solutions with plane sources and parabolic wave equation solutions
R Mahillo-Isla1, M J Gonźalez-Morales, C Dehesa-Martínez
1Teoría de la Señal y Comunicaciones e Ingeniería Telemática, University of Valladolid, Paseo de Belén, 15, 47011, Valladolid, Spain. raumah@tel.uva.es
Summary
This study applies the slowly varying envelope approximation to Helmholtz equation radiation problems. It develops methods to find Helmholtz solutions using parabolic wave equation solutions, detailing necessary conditions.
Area of Science:
- Computational electromagnetics
- Wave propagation modeling
- Mathematical physics
Background:
- The Helmholtz equation is fundamental in describing wave phenomena.
- Solving radiation problems efficiently is a persistent challenge in physics and engineering.
- Existing methods may lack applicability for certain source types or geometries.
Purpose of the Study:
- To apply the slowly varying envelope approximation (SVEA) to Helmholtz radiation problems.
- To develop novel procedures for recovering Helmholtz equation solutions.
- To analyze the conditions required for the successful application of these procedures.
Main Methods:
- Application of the slowly varying envelope approximation (SVEA).
- Analysis of radiation problems involving planar single-layer and dipolar sources.
- Derivation of procedures linking Helmholtz and parabolic wave equation solutions.
Main Results:
- Procedures are established to recover Helmholtz equation solutions from parabolic wave equation evaluations.
- Specific conditions for the applicability of these recovery procedures are identified and discussed.
- The methodology is demonstrated for both single-layer and dipolar sources.
Conclusions:
- The SVEA offers a viable approach for solving Helmholtz radiation problems.
- The developed procedures provide a practical method for obtaining Helmholtz solutions.
- Understanding the conditions for applicability ensures the reliable use of these techniques.
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