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Ray tracing in gradient-index media: a comparative analysis of discretization-based methods
Applied Optics
|March 17, 2026
Summary
Calculating light paths in gradient-index (GRIN) media is challenging. Optical path length discretization offers a highly accurate and robust numerical method for tracing rays in GRIN materials.
Area of Science:
- Optics and Photonics
- Computational Physics
- Materials Science
Background:
- Ray tracing in gradient-index (GRIN) media is computationally intensive.
- Analytical solutions are limited to specific refractive index profiles.
- Numerical methods are essential for practical GRIN applications.
Purpose of the Study:
- To present and compare three numerical ray-tracing methods for GRIN media.
- To evaluate the accuracy and limitations of different discretization schemes.
- To identify the most effective numerical approach for GRIN ray tracing.
Main Methods:
- Medium discretization: Dividing the GRIN medium into discrete layers.
- Geometric path length discretization: Segmenting the ray's physical path.
- Optical path length discretization: Discretizing the accumulated optical path.
- Iterative application of Snell's law for trajectory reconstruction.
Main Results:
- Optical path length discretization demonstrated superior accuracy compared to other methods.
- The Luneburg lens served as a benchmark with an exact analytical solution.
- The proposed optical path length method offers a robust framework for GRIN ray tracing.
Conclusions:
- Optical path length discretization is the most accurate and robust method for ray tracing in GRIN media.
- This approach surpasses the accuracy of traditional methods like the Runge-Kutta scheme.
- The findings provide a valuable tool for designing and analyzing optical systems with GRIN materials.
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