Ray trajectory in a graded refractive index material with a Gaussian and Lorentzian profile

Abstract

We calculate the ray trajectory of light as it propagates along a medium with a Gaussian and Lorentzian graded index of refraction. The trajectory was determined by solving the differential equation obtained from Snell's Law applied to the interface with a varying index of refraction. For both the Gaussian and Lorentzian graded index of refraction, the ray trajectory follows a sinusoidal path whose frequency depends on the full width at half maximum of the graded index profile. The initial direction of the path of light inside the medium determines the amplitude of the sinusoid. We believe that calculating the trajectory of light inside a medium with a varying index of refraction may help students have a better understanding of waveguides.