By combining the advantages of both a metallic metamaterial and a dielectric interlayer, we demonstrate the general mechanism to construct the dispersion-free metastructure, in which the intrinsic dispersion of the metallic structures is perfectly cancelled out by the thickness-dependent dispersion of the dielectric spacing layer. As examples to apply this concept, a broadband quarter-wave plate and a half-wave plate are demonstrated. By selecting the structural parameters, the polarization state of light can be freely tuned across a broad frequency range, and all of the polarization states on the Poincaré sphere can be realized dispersion free. DOI: 10.1103/PhysRevX.4.021026 Subject Areas: Metamaterials Metamaterials are the artificial structures assembled with subwavelength building blocks featuring some physical properties that do not exist in the natural world [1,2]. Over the past decade, developments in this area have been characterized by the realization of numerous novel optical properties, such as negative refractive indices [3][4][5], superlenses [6-8], etc. A two-dimensional metamaterial offers the possibility of controlling light with miniaturized devices, which are essential, especially for integrated photonics [9,10]. Furthermore, by engineering the phase discontinuity on an interface, one can fully steer light and accomplish unparalleled control of anomalous reflection and refraction [11][12][13][14][15] and realize different optical devices, such as optical vortex plates [11,16] and wave plates [17]. It has been well established that upon illumination of incident light, oscillating electric current can be excited on a metallic surface. The surrounding electromagnetic field is then modulated by the irradiation of oscillating surface electric current. At resonant frequency, this effect is so significant that a thin layer of metallic structure can effectively tune the state of light. However, the underlying Lorentz resonance in metal is highly dispersive in nature, which limits its application to a specific narrow wave band. Overcoming the dispersion of metamaterials is essential for wide optical applications. On the other hand, it is known that the dielectric material interacts with light by accumulating an optical path within a certain thickness. This feature is effective over a broad bandwidth and has already been applied in antireflection coating and other optical devices [18][19][20]. By integrating a metallic metastructure and a dielectric interlayer, it is possible to realize a dispersion-free broadband device on the subwavelength scale, where the strong response of the metallic structures helps to decrease the device size while the dielectric interlayer helps to eliminate the dispersion simultaneously in both the amplitude and the phase difference of the reflected or transmitted light.Thus far, much effort has been devoted to broaden the response frequency range of metallic metastructures [20][21][22][23][24][25][26][27][28][29][30][31][32][33]. For example, by superimposing different reson...