Localization of Light: Dual Symmetry between Absorption and Amplification

We study the propagation of radiation through a disordered waveguide with a complex dielectric constant $\varepsilon$, and show that dual systems, which differ only in the sign of the imaginary part of $\varepsilon$, have the same localization length. Paradoxically, absorption and stimulated emission of radiation suppress the transmittance of the waveguide in the same way.