Scalar theory of electromagnetic wave in a spherically symmetric radially anisotropic and inhomogeneous medium: Photonic atoms

摘要

Based on quantum mechanical angular momentum operators, we establish a scalar potential theory for describing electromagnetic wave in a spherically symmetric radially anisotropic and inhomogeneous dielectric medium. The developed scalar theory is validated by rederiving the prescription for spherical invisible cloaking against electromagnetic wave. As an application of the scalar potential theory, it is shown that under appropriate radial anisotropy conditions photons can be localized, in a manner that is analogous to the bounded electrons in atoms. We refer to such localized states as the photonic atoms in order to reflect their conceptual significance as an extension to the analogies between photons and electrons. The developed scalar potential theory is expected to be helpful in practice.