A reflecting mirror for transforming the polarization of electromagnetic ) waves independently of the frequency of the waves and, thus, over an arbitrarily wide RF bandwidth includes two interleaved sets of planar arrays of resonant elements, both being orthogonally polarized, and each set comprising layers of the arrays which are arranged so that the layered elements of each set form a log-periodic configuration. The difference in phase between the reflection coefficient functions of the first and second sets of arrays is independent of the frequency of EM waves. Each of the arrays resonates at a different frequency and the arrays resonate over the frequency band of operation. A plane EM wave, the polarization of which has two vector components, strikes the mirror on the array having the shortest strips. The two polarization components of the wave travel into the mirror. Each component is reflected as it encounters strips of an array having a resonance which matches the resonant frequency of the component. The components being non-parallel to each other are reflected from different arrays which causes the components to change in phase relative to each other, thereby transforming the polarization of the wave.