By using an analytical model and a finite element method, we investigate a new, very sensitive, superconducting traveling wave photodetector made by a fiber waveguide, which includes two high index layers and an active superconducting layer. A comparison with the corresponding superconducting box shaped waveguide shows that a larger width of the superconducting layer can be used to obtain single degenerate hybrid mode HE (11). The real part of the propagation constants in the fiber is smaller in comparison with that of the box-shaped waveguide with similar dimensions but the imaginary part of the propagation constant and the power absorption efficiency in superconducting layer are comparable with those of the corresponding box-shaped waveguide. The confinement regimes of the light and the power absorption efficiency in superconducting layer can be optimized by only acting on the fiber geometry.