Using the known "looking glass" transformation property (z -> 2 pi-z, y -> 27 pi-y) of the optical phase thickness z and y of matching layers of two-layer anti-reflection coating, together with the fact that optical characteristics of any film do not change after addition of a half-wavelength layer, we designed dual-band anti-reflection coatings transparent at any preset wavelengths lambda(1) and lambda(2). On the basis of this result common fractional anti-reflection coatings for second and higher harmonics generation using dispersionless coating materials are developed. Explicit analytical relationships between refractive indices of the layers and substrate are deduced. Since for second harmonic generation the dispersion of materials may be a factor we show how to compensate the known dispersion of the coating materials by special choice of dispersion of a suitable substrate. (c) 2007 Elsevier B.V. All rights reserved.