The electromagnetic field is the most pervasive underlying noumenon of nature. A large diversity of phenomena — from lightning to wind pressure, and from light to heat can be explained in terms of electromagnetic interactions and the forces thus created. That having been said, usually many of these derived phenomena have their own well developed models — geometric optics, thermodynamics, fluid mechanics, and so forth. These models are so well developed, that in most instances, it is not necessary, for the modeler, to dwell upon the “essential electromagnetic nature of all things”.
On the other hand, many technological and some natural processes are best modeled using the fundamental equations of electromagnetics. Electromagnetics is used in wireless transmission, sensing and imaging technologies such as radar, subsurface sensing, MRI, in microwave and induction heating, and in electrical components such as transformers. Electromagnetics is also important in modeling certain optical phenomena, where light interacts with physical structures having sub-microscopic features.
Following are some projects performed by us that involved direct calculation of electromagnetic effects:
CIRCUIT SIMULATION WITH EM COMPONENTS. A new methodology was developed to convert the PDEs governing linear electromagnetic components to ODEs, for fast and accurate simulation of EM components as electronic circuit components.
ELECTROMAGNETIC FEM. Built our own FEM EM solver to cross-check Mie scattering calculations, and to be able to perform scattering calculations for irregular shaped objects.
BIREFRINGENCE. Created models of uniaxial and biaxial birefringence. The biaxial birefringence model requires a modal decomposition of a non-linear equation, which was solved using a novel non-linear Rayleigh quotient method devised by us. These models were used to find birefringence parameters of actual samples. Read more…
EM MODES OF A WAVE GUIDE. EM modes of a wave guide were calculated using a ray tracing (instead of PDE) method. The rays are not energy rays, as used in geometric optics, but “wave” rays, like Huygens/Fermat light theory (or like Feynman's histories).