Dipolar Huygens–Kerker radiation for surface waves

Abstract

Exotic dipolar radiation with zero light emission in one direction but maximal light emission in the opposite direction was envisioned by Huygens in 1690, and it could emerge in vacuum if the ratio between the source’s electric and magnetic dipole moments fulfills the Kerker condition as revealed by Kerker in 1983. Due to its intricate connection with both the Huygens principle and Kerker condition, this radiation phenomenon is suggested to be termed as dipolar Huygens–Kerker radiation, and at this moment, the ratio is termed as the Huygens–Kerker ratio. However, the dipolar Huygens–Kerker radiation remains underexplored in non-vacuum matters, inside which the source locates, especially for surface waves. Here we find that the dipolar Huygens–Kerker radiation of surface waves in principle could occur in non-vacuum matters and is essentially featured with the same normalized radiation pattern, which is closely related to the inclination factor that appears in the Fresnel–Kirchhoff diffraction theory. Moreover, the corresponding Huygens–Kerker ratio is intrinsically determined by the phase velocity of excited surface waves. To be specific, the Huygens–Kerker ratio is proportional to the phase velocity for transverse-magnetic surface waves but becomes inversely proportional to the phase velocity for transverse-electric surface waves.