Subharmonic structures in Josephson tunneling

We studied the ac Josephson effect. The phase difference is expanded in a Fourier series. The Fourier components can be evaluated by solving the equations of motion. Truncation was applied to deal with the infinite products and series of Bessel functions. It is very efficient if the nonlinearity is not too large. We give some numerical results and derive the dc current response. The latter has a different form from previous works. The Shapiro steps were also studied with the same method and a more accurate step size estimation is given. © 1996 The American Physical Society.