Antireflection of an absorbing substrate by an absorbing thin film at normal incidence

An absorbing substrate of complex refractive index n(2) - jk(2) at wavelength lambda can be coated by an absorbing thin film of complex refractive index n(1) - jk(1) and thickness d to achieve zero reflection at normal incidence. For given n(2),k(2) multiple solutions (n(1),k(1),d/lambda) are found that correspond to infinitely many distinct antireflection layers. This is demonstrated for a Si substrate at two wavelengths (6328 and 4420 A). The response of these absorbing antireflection layers to changes of the angle of incidence from 0 to 45 degrees and to changes of thickness of +/-10% is also determined and compared to the limting case of a nonabsorbing antireflection layer.