Numerical solutions to paraxial wave equations
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In this thesis, we apply various numerical methods to solve ordinary differential equations and the paraxial wave equation. The numerical methods we applied to solving paraxial wave equation are the 4th order Runge Kutta method, the Crank-Nicolson method, the Leapfrog Crank-Nicolson method, and the splitting spectrum method. The advantage of the explicit RK4 method is the high order accuracy in time. We perform detailed comparison between these numerical methods.
The paraxial wave equation is derived from Maxwell's equation and we focus on the case of cubic Kerr nonlinearity presents, which is applied to study optical pulse propagation in nonlinear Kerr media.
The Leapfrog Crank-Nicolson method, being an implicit method, is the most cost efficient method and when choosing small step sizes can be the most accurate when applied to paraxial wave equations.