Modeling Gaussian Beam Focusing

I am trying to model beam focusing using machine learning algorithms in Python with the goal of building a model that learns to focus the beam to the smallest point possible. However, I am lost as to how to represent the physics behind beam focusing.

Looking online, I am thinking that the changing the beam focus (aka beam waist) would be the input and the beam radius + intensity would be the output, but I still fail to understand the connection between how changing the focus affects the output variables, so I am unable to piece together the model. Could somebody shed some light on the physical connection?

• Gaussian optics? Feb 7, 2021 at 17:26
• yes, gaussian optics Feb 7, 2021 at 17:35
• I know that your optics skills are not the best, but I think you need to be more specific. It's not clear what you are trying to do, what your inputs will be, what your outputs will be, what approximations you are willing to make. What is your model allowed to vary? etc Feb 7, 2021 at 18:10
• my model is trying to simulate the act of changing the focus of an electron microscope (input) and its effect on the radius and intensity of the resulting beam (output) to have the model gradually learn to focus to the smallest point possible. it seems from my reading that this is an optimization problem. is that correct? also, not exactly sure on what approximations can be made, but starting with a basic model of the beam propagation should be fine Feb 7, 2021 at 18:22
• focus and waist is the same concept btw. The terminology for lasers is typically: beam waist: one sided $1/e$ field ($1/e^2$ intensity), so basically the radius of the focus. Beam diameter=beam waist*2. In my comprehension of your problem, as you need to compare output (measured) vs input (also measured) you do not need machine learning and much simpler algorithms following one scan of the variables should be more than enough. If needed you can add a physical model to make it more robust/versatile. But of course, that's my opinion after reading the information you gave. Feb 8, 2021 at 11:12