Two-dimensional fast marching for geometrical optics

Area of Science:

• Computational electromagnetics
• Wave propagation modeling
• Numerical methods in physics

Background:

• Accurate solutions to Maxwell's equations are crucial for understanding wave phenomena.
• Existing methods can be computationally intensive for complex geometries and inhomogeneous media.
• Geometrical optics approximations offer efficiency but require careful implementation.

Purpose of the Study:

• To develop a fast and accurate method for determining geometrical optics solutions to Maxwell's equations.
• To handle inhomogeneous 2D media and TM polarized electric fields efficiently.
• To accurately discretize scatterer boundaries and computational domains.

Main Methods:

• Solving the eikonal equation using the fast marching method.
• Employing a computer graphics technique for direct and inverse ray tracing.
• Solving the transport equation in its integral form.

Main Results:

• The algorithm accurately determines geometrical optics solutions in complex scenarios.
• It successfully models plane wave scattering from two perfectly conducting circular cylinders, accounting for multiple scattering.
• It demonstrates the advantage of inverse ray tracing for Luneburg lens simulations.

Conclusions:

• The developed approach provides a fast and accurate method for geometrical optics solutions.
• It effectively handles complex scattering phenomena and inhomogeneous media.
• The choice between direct and inverse ray tracing depends on the specific application, with inverse tracing preferred for Luneburg lenses.