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A quarter-wave mirror, also called a Bragg mirror, is a dielectric mirror structure which consists of an alternating sequence of layers of two different optical materials, with each optical layer thickness corresponding to one-quarter of the wavelength for which the mirror is designed (here, the wavelength is taken to be the wavelength within the material, not the vacuum wavelength).
For a given wavelength and number of layer pairs, a quarter-wave mirror is the structure which can result in the highest reflectivity.
Quarter-wave stacks are also very basic building blocks of more complicated dielectric mirror structures.