Graded refractive index layers reduce the reflection and increase the coupling of light into a substrate by optical impedance matching at the interfaces. Due to the optical impedance matching, reflections at the interfaces are not possible for a broad wavelength range, rendering this type of anti-reflection coating a promising candidate for III/V multi-junction solar cells. Graded refractive index layers can be modeled using a transfer-matrix method for isotropic layered media. We derive the transfer-matrix method and we show calculations of the reflection from and the transmission into an AlInP layer coated with different anti-reflection coatings. We describe a new type of anti-reflection coating based on tapered semiconductor nanowires and we show reflection and transmission measurements of those kind of anti-reflection coatings on top of different substrates.