In a method of amplifying optical input signals over a wide bandwidth, the optical input signals are applied to an optical waveguide made from a rare-earth-doped amorphous material (e.g., erbium-doped Bi₄Ge₃O₁₂ material). The optical input signals include optical signals having wavelengths over a range of approximately 125. Pump light is applied to the optical waveguide to cause the waveguide to provide optical gain to the optical input signals. The optical gain causes the optical signals to be amplified within the waveguide to provide amplified optical signals over the approximately 125-nanometer range, including, in particular, optical signals having wavelengths at one end of the range and optical signals having wavelengths at a second end or the range.