Fig. 1: Locked transmission phase in a homogeneous antireflection coating.

a Schematic diagram of a layer of anisotropic homogeneous medium with thickness d, relative permittivity \(\tilde{\varepsilon }\) and permeability \(\tilde{\mu }\) in free space. An oblique incidence with the incident angle α is considered. b Schematic diagram of a layer of anisotropic homogeneous medium located on the interface between the free space and a dielectric with relative permittivity \({\varepsilon }_{g}\). c Calculated transmittance T as a function of \(m=\sqrt{{\varepsilon }_{y}-\,\sin^{2} \alpha/{\mu}_{z}}\) and \(n=\sqrt{{\mu}_{x}}\), where \({\mu}_{x}\), \({\mu }_{{{{\rm{z}}}}}\) and \({\varepsilon }_{y}\) are the x and z components of the relative permeability and the y component of relative permittivity of the homogenous layer. White and black dashed lines depict the contour plots of transmission phases of \(\pi /2\) and \(-\pi /2\), respectively. Black solid lines represent contour plot of the transmittance of 0.99. Here, d, \(\alpha\)and \({\varepsilon }_{g}\) are set as \(0.1{\lambda }_{0}\), 45° and 4.4, where \({\lambda }_{0}\) is the wavelength in free space.