Solving the differential equation of light rays in Cartesian coordinates

This paper presents a method for solving the differential equation of light rays. We define functions which represent Cartesian coordinates and take the arc length as the independent variable. Then the ray equation can be transformed to convenient pattern by these defined functions. This proposed method avoids the complex transformation and interpolation in traditional techniques. So the coordinate value can be directly solved using the computational software. The solution procedure has been demonstrated by a ray tracing simulation in an axial gradient refractive-index media. And the computer code can be developed. Comparing with the analytical solution shows that the error of the proposed method is small.