Explicit expression of the pseudo-Brewster angle for anisotropic metamaterials

In the conventional optics, the pseudo-Brewster angle (PBA) mainly depends on the permittivity of the optical materials. However, the recent development of metamaterials in the optical wavelength has put magnetic permeability on equal footing. Thus, the conventional PBA needs to be revisited to include the permeability for metamaterial applications in the optical region. By taking into account the loss and anisotropy of the metamaterials, we present the explicit expression of PBA in terms of complex permittivity and permeability through rigorous analysis. Based on the explicit expression, some interesting features and potential applications of the PBA are discussed.