The electric field distribution and complex propagation constants of a multimode dielectric optical waveguide with complex index of refraction were calculated. A waveguide with a similar structure was fabricated by ion exchange into a glass substrate. The complex index of refraction region was provided by flowing a dye solution over the waveguide surface. Optical gain as high as 40%/cm was obtained. An experimental determination of the gain of various propagating modes was made and found to be in good agreement with theoretically calculated values.