We consider the excitation spectrum of a superconducting sphere embedded in a superconducting host. The sphere and host are assumed to have order parameters of the same magnitude, but different phases. For finite phase differences, we show that there exist states with energies below the superconducting gap. The energies of these states are studied as a function of the size of the superconducting sphere. We consider implications of these results for optical studies in high-temperature superconductors.
