Gaussian Beam Plane Wave Expansion

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Hi, I just recently learnt that the paraxial gaussian beam equation is not really effective for a scatterer surrounded by inhomogeneous domains when using the scattered field formulation. it was proposed I use the plane wave expansion approach. for a 3D model, has anyone used the plane wave expansion approach using equations. I have attached my model of the paraxial approach. you can edit my model to suit the plane wave expansion method or if you have any example. That will be great.



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