ac Josephson effect for asymmetric superconducting junctions

We calculate the ac and dc current-voltage (I-V) relation when a tunnel barrier is placed in the normal region of a superconductor–normal-metal–superconductor (S₁NS₂) junction, where the two superconducting contacts have different gaps (Δ₂>~Δ₁>~0). The voltages at which subharmonic gap structure (SGS) appears in the zero-temperature I-V are the same as previously found for the SGS in ballistic S₁NS₂ junctions at a finite temperature. Some of the SGS’s are strong enough to produce negative differential resistance. We determine the variation of the ac Josephson current with bias, junction transmissivity, gap ratio Δ₁/Δ₂, and junction length L. The ac Josephson current through a ballistic SNS junction can also be used to measure the superconducting phase difference φ.