Figure 6
From: Controlling the dynamic range of a Josephson parametric amplifier

Resonance frequencies of the first three modes as a function of Josephson energy. The solid line results from the exact numerical solution of Eq. (27) while the dashed line shows the linearized solution in Eq. (29). The bare resonance frequency is chosen to be 7 GHz and the impedance of the transmission line resonator 50 Ω.