A novel technique is presented in obtaining the performance characteristics of traveling-wave semiconductor optical amplifier (TWA) with tensile-strained-barrier multiple-quantum-well structure. In-out fiber ends of TWA are used to construct an external cavity resonator to produce big ripple on amplified spontaneous emission (ASE) spectrum. By this means, Hakki-Paoli method is adopted to obtain gain and differential gain spectra over a wide spectral range. From measured longitudinal mode spacing and peak wavelength shift due to increased bias current, we further calculate the effective refractive index, carrier-induced refractive index change and linewidth enhancement factor. Some special features about ASE mode spectrum shift and refractive index change above lasing threshold are revealed and explained.