Please post a full description and your questions.yashabyadav said:I am trying to apply finite difference scheme for Beam propagation method by following this paper.
I was wondering if anyone can share their code if they have implemented this method. I can share my code which is not working as expected and can get some insights if possible.
The finite difference method is a numerical technique used to approximate solutions to differential equations. It involves dividing the domain of the problem into a grid and using finite differences to approximate the derivatives in the equations.
In BPM (beam propagation method), the finite difference method is used to solve the Helmholtz equation, which describes the propagation of light through a medium. By discretizing the equation and using finite differences, we can approximate the electric field at each point in the grid.
The finite difference method is relatively easy to implement and can handle complex geometries and boundary conditions. It also allows for efficient computation of the electric field at each point in the grid, making it a popular method for simulating light propagation in optical systems.
While the finite difference method is a powerful tool, it does have some limitations. It can be computationally expensive for large grids and may not be suitable for problems with highly varying solutions. Additionally, it may not accurately capture sharp features in the electric field.
To implement the finite difference method for BPM, you will need to discretize the Helmholtz equation and apply the appropriate finite difference schemes to approximate the derivatives. You will also need to set up the grid and boundary conditions for your specific problem. There are many resources available online that can guide you through the implementation process.