Date of Award


Degree Name

Doctor of Philosophy


Computational Science


Raymond C. D. Rumpf


3D printing is revolutionizing the manufacturing industry and is now being considered in the electronics industry. The creation of the worldâ??s first 3D volumetric circuit has made a way to make circuits smaller, lighter, into unconventional form factors and exploit physics like anisotropy more effectively than planar geometries can. While this is exciting, many problems must be solved to make 3D volumetric circuits more efficient. One of these problems is electromagnetic interference and mutual coupling between the circuit components that are expected to increase in high-frequency 3D circuits. Spatially variant anisotropic metamaterials (SVAMs) could be a solution to overcome this difficulty, but research in this area is not possible without an algorithm that can generate SVAMs in 3D circuits. In this dissertation, an algorithm is developed and integrated into CAD software that can generate SVAMs for 3D circuits.There are no formulations available in the literature that consider general complex constitutive parameters in the external regions for the transfer matrix method (TMM). It is possible to handle certain special cases, such as reflection from a lossy dielectric, however, the standard TMM cannot calculate transmittance into a lossy dielectric. The TMM is combined with scattering matrices and named as transfer matrix method with scattering matrices (TMMSM) and modified to work with the complex medium. To verify the results from TMMSM, analytical equations were derived to calculate the power quantities at the interface between two complex mediums. A simpler conservation equation for transverse electric (TE) and transverse magnetic (TM) polarizations has been derived which accounts for both complex permittivity and complex permeability. The consideration of complex permeability in the formulation is important for simulating metamaterials and this is not addressed anywhere in the existing literature. The derivation also shows that the standard Fresnel coefficients are valid for a general complex medium, but the correct sign of the wave impedance needs to be chosen to calculate the Fresnel coefficients accurately. A condition has also been found to calculate the Fresnel coefficients correctly without fully resolving the sign of wave impedance. In this dissertation, the results of TMMSM and the analytical derivation for scattering analysis at the interfaces between complex mediums were compared. Additionally, the analytical results and TMMSM results were cross-checked with results from other sources to ensure that the methods are accurate.




Recieved from ProQuest

File Size

120 p.

File Format


Rights Holder

Asad Ullah Hil Gulib