Resonance modes in coplanar lines with integrated Josephson circuits

The propagation of microwave radiation in co-planar superconducting lines with Josephson circuits (microresonators) of various configurations is investigated. It is shown that dips in the frequency dependence of the transmission power of the waveguide line modes are associated with local modes of the circuit. The dependencies of shape and position of the dips on an external magnetic field and applied power are found. The calculation results can be used for developing modern cryoelectronic microwave superconducting devices.