See the Pattern: Casimir forces, measurng and calculating 3D fields efficiently, Gravitational energy density and engineering
See the Pattern: Casimir Effect – What causes this force? at https://www.youtube.com/watch?v=OgJj49ws478
See the Pattern,
To represent 3D fields, it is relatively easy to find many orthogonal representations. For atoms and molecules the groups often start from the Schrodinger equation, or the nonlinear Schrodinger equation. It is also possible to use 3D Fourier and wavelets. There are many choices.
Those “plates” are the wrong shapes and likely the wrong properties for real nanoscopic, picoscopic and femtoscopic objects and regions. But there are mathematical and computational methods for any shapes now.
The Coulomb force in 1/r^2, but the magnetic dipole force is 1/r^4. And the magnetic force is a vector. But it is well understood and documented. The corresponding potentials are 1/r and 1/r^3. At close distances, the forces between two particles having electric charge and magnetic moments usually required calculating the full multipole expansion. If you think of the 3D fields involved, then the time dependent field at ever point can often be represented in one of the many orthogonal basis sets. And often those are readily available on the Internet, and often packaged in to many of the tools. Python seems to have gained popularity, but there are many more.
I hope you will look more deeply at tools and data people are using when they do “real” calculations.
The energy density of the Earth’s gravitational field is about equal to the energy density of a magnetic field of about 380 Tesla. In black body terms, that is roughly 1500 electron Volts per particle, so it has a peak in the soft x-ray region, extends through the XUV, but covers all frequencies. As you found the frequencies larger than the object are not so easy to use to represent the fields of those small things.
But, you can use two large wavelengths (very close in frequency) where the difference fits into the right range. The “high harmonic generation” methods are what people use for laser and plasma excitation of energy densities in the XUV and soft x-ray region. And all of those are candidates for directly measuring and modifying fields, which I classify under “gravitational engineering” methods for the Internet as a whole.
Richard Collins, The Internet Foundation