Nearfield Focusing, propagating a field with a known spatial field phase

Hello,

There is a fantastic page demonstrating near field focusing using the Phased Array toolbox located here: https://www.mathworks.com/help/phased/ug/examine-the-response-of-a-focused-array.html

These example use an array of emitters to define the excitation that then solves into the near field focused field. If we have an already spatially-defined complex wave input field, is there a way to propagate the field in the same way to show it focusing? Or is it possible to 'fake' the field using an array of closely spaced emitters and weights?

[George]

Hi Paul, can you give a bit more information or some code showing what you mean by the spatially-defined complex wave input field?

[Paul Schmalenberg]

Hi George, if we take the 2D case (or 2D slice, such as the plot 'Single Steered and Focused Beam' in the link above), if we have the description or values for out of plane direction of Ez(x = 0, y) (and Ex, Ey = 0) for a certain frequency, is there a way to solve for the rest of (x,y)? Maybe as excitation by wire approximation?

I don't have any code at the moment, but I see solver pages like this: Solvers - MATLAB & Simulink (mathworks.com)

But is there a way to access these numerically? Or only through setting up antenna arrays with high level functions?

[David Goodmanson]

HI Paul, this sounds like the Kirchhoff vector integration theorem, where if the fields on a closed surface are known, the fields in the volume inside the surface can be calculated. It's not easy, a lot of the reason being due to approximations that are involved and how to justify them in a given situation.