Retardation effect in microstrips and microwave detection of spatial dispersion in superconductors

Effect of significant retardation of the phase velocity in a microwave microstrip resonator has been found and utilized for detection of spatial-dispersion phenomena in superconductors, which should be pronounced when the phase velocity became less than the Fermi velocity. The effect is explained by the influence of the fine fringes of a strip near of which the high values of curvature can appear for the system of coordinates introduced to find solutions. This leads to a spatial dependence of the phase velocity on the Lamé coefficients (metric coefficients) of the curvilinear system of coordinates and can decrease the velocity significantly. Comparative estimates of the spatial effects for single-crystal high-Tc (YBaCuO), Nb, and Cu samples were obtained from measurements of the resonant frequency depending on a position of the sample in the field.