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Ray tracing in gradient-index media: a comparative analysis of discretization-based methods.

V Chávez-Islas, E Espíndola-Ramos, F H Maldonado-Villamizar

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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.

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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.