Ray tracing in a finite-element domain using nodal basis functions

Area of Science:

• Optics and Photonics
• Computational Physics
• Materials Science

Background:

• Ray tracing is crucial for optical design and analysis.
• Traditional methods struggle with complex refractive index gradients and surface irregularities.
• Finite-element methods offer a powerful framework for discretizing complex geometries.

Purpose of the Study:

• To develop a novel finite-element method for accurate ray tracing in heterogeneous optical media.
• To precisely model ray trajectories influenced by severe refractive index gradients.
• To accurately compute refraction at interfaces with interpolated surface deformations.

Main Methods:

• Ray-trajectory equations were formulated in a local element coordinate frame.
• Full finite-element interpolation determined instantaneous index gradients for ray path integrals.
• Finite-element methodology interpolated surface deformations and normal vectors for refraction calculations.
• The method was applied to a finite-element model of an optic with a severe refractive index gradient.

Main Results:

• The finite-element ray tracing method successfully handled severe refractive index gradients.
• Calculated ray paths showed good agreement with the closed-form gradient ray-path integral approach.
• The method accurately computed refraction angles at surfaces with interpolated deformations.

Conclusions:

• The presented finite-element method provides an accurate and robust approach for ray tracing in complex optical systems.
• This methodology is particularly effective for media with significant refractive index variations and irregular surfaces.
• The findings support the use of finite-element analysis for advanced optical modeling and simulation.