Mathematical analysis of conducting and superconducting transmission lines

This paper is concerned with a mathematical study of guided propagation in the microstrip transmission lines used in microelectronics. In the first part, the case of a zero-thickness perfectly conducting strip is considered. Using a regularized formulation of Maxwell's equations, it is shown that finding guided modes amounts to the spectral analysis of a noncompact family of self-adjoint operators. The existence of guided modes is then proved thanks to the min-max principle. In the second part, we deal with the case of a zero-thickness superconducting strip. An asymptotic model derived from London's equation is studied and the existence of guided modes is deduced from the case of the perfectly conducting strip.