Dynamics of underdamped Josephson junctions with non-sinusoidal current-phase relation

Results on analytical and computational investigations of high-frequency dynamics of Josephson junctions, characterized by non-zero capacitance and the second harmonic in the current-phase relation are presented. These attributes each have influence on the behaviour of integer Shapiro steps and lead to the formation of non-integer Shapiro steps. Analytic theory of the integer and non-integer Shapiro steps has been developed for the so-called high-frequency limit. The analytical and numerical results are compared with experimental data for hybrid heterostructures YBCO/Au/Nb. Detector response for the case of high fluctuation level has been considered as well.