Inreflectance: a new function for the optimization of multilayers with absorbing materials

A new magnitude is unveiled from the fact that a multilayer can be optimized for the largest reflectance in a layer-by-layer sequence: This magnitude has been named inreflectance. Inreflectance equals the modulus of the complex reflectance once elevated to the inverse of the complex refractive index of the next outer layer, including the inclination term. The maximization of inreflectance at every internal layer, proceeding sequentially starting with the innermost layer, results in a multilayer with the largest reflectance. At a given layer in the multilayer, inreflectance is different from reflectance when the next outer material absorbs radiation, whereas the two magnitudes are coincident when the next outer layer is transparent. The outermost layer of the multilayer is intrinsically different from the internal layers, and its optimization is performed through reflectance and not through inreflectance. Every maximum of inreflectance is found at a layer thickness that is larger than that for the reflectance maximum. The new magnitude is illustrated with some examples in the extreme ultraviolet, a spectral range in which all materials absorb radiation. Inreflectance can also be used to design multilayers in which some layers have fixed thicknesses and the rest of the layers have to be optimized taking into account the fixed layers.