Ray-based diffraction calculations using stable aggregates of flexible elements.

Area of Science:

• Computational physics
• Wave propagation modeling
• Optics and electromagnetism

Background:

• Traditional ray-based methods often struggle to accurately model wave phenomena like diffraction.
• Accurate simulation of wave propagation is crucial in various fields, including acoustics and electromagnetics.
• Existing methods may fail at critical points such as caustics and shadow boundaries.

Purpose of the Study:

• To develop a robust ray-based wave propagation method that incorporates diffraction effects.
• To enhance the accuracy of wave field estimations, particularly at caustics and shadow boundaries.
• To provide a computationally efficient alternative for simulating wave phenomena.

Main Methods:

• Incorporation of diffraction effects into a ray-based technique named stable aggregates of flexible elements (SAFE).
• Assignment of Gaussian field contributions to individual rays, departing from independent beam solutions.
• Modeling diffraction by planar opaque obstacles using the Kirchhoff approximation and edge-diffracted rays.
• Derivation of the two leading asymptotic terms for complex amplitude contributions.

Main Results:

• The SAFE method successfully integrates diffraction effects into a ray-based framework.
• The derived method provides accurate field estimates even at caustics and shadow boundaries.
• Demonstrated validity through simulations of a focused wave in free space and propagation in a layered medium.

Conclusions:

• The stable aggregates of flexible elements (SAFE) method offers a validated approach for wave propagation with diffraction.
• The technique shows promise for accurate modeling in complex scenarios, including inhomogeneous media.
• This ray-based approach with diffraction provides accurate results where traditional methods may falter.