An absorbing substrate of complex refractive index n2 - jk2 at wavelength λ can be coated by an absorbing thin film of complex refractive index n1 - jk1 and thickness d to achieve zero reflection at normal incidence. For given n2,k2 multiple solutions (n1,k1,d/λ) are found that correspond to infinitely many distinct antireflection layers. This is demonstrated for a Si substrate at two wavelengths (6328 and 4420 Å). The response of these absorbing antireflection layers to changes of the angle of incidence from 0 to 45° and to changes of thickness of ±10% is also determined and compared to the limting case of a nonabsorbing antireflection layer.
R. M. A. Azzam, E. Bu-Habib, J. Casset, G. Chassaing, and P. Gravier, "Antireflection of an absorbing substrate by an absorbing thin film at normal incidence," Appl. Opt. 26, 719-722 (1987)