Janus and Huygens Dipoles: Near-Field Directionality Beyond Spin-Momentum Locking

Unidirectional scattering from circularly polarized dipoles has been demonstrated in near-field optics, where the quantum spin-Hall effect of light translates into spin-momentum locking. By considering the whole electromagnetic field, instead of its spin component alone, near-field directionality can be achieved beyond spin-momentum locking. This unveils the existence of the Janus dipole, with side-dependent topologically protected coupling to waveguides, and reveals the near-field directionality of Huygens dipoles, generalizing Kerker’s condition. Circular dipoles, together with Huygens and Janus sources, form the complete set of all possible directional dipolar sources in the far- and near-field. This allows the designing of directional emission, scattering, and waveguiding, fundamental for quantum optical technology, integrated nanophotonics, and new metasurface designs.

Figure 1

(a) Triad of vectors (time-averaged power flow, reactive power, and spin vector) associated to any guided mode, each related to one of the three sources in the schematics (b). (b) Schematics of the sources and their relative vectors. The top left panel depicts a circularly polarized electric dipole, superposition of two orthogonal linear electric dipoles $\mathbf{p}$ with complex amplitudes 1 and $i$, representing their quadrature phase relation. This circular dipole is associated with a transverse spin vector shown in the panel. A similar notation is used throughout the table, using $\mathbf{m}$ for magnetic dipole moments. The spin (red), Poynting (yellow), and reactive power (blue) vectors are associated to different directional dipolar sources, and each of them behaves differently under parity ($P$) and time-reversal ($T$) symmetry transformations. Notice that, with respect to time-reversal, $\mathbf{E}$ fields are even while $\mathbf{H}$ fields are odd. Moreover, the operation of taking the real part of respective vectors is time even while taking the imaginary part is time odd.

Figure 2

Magnetic field radiated by (a) a circularly polarized electric dipole $\mathbf{p}=(1,0,i)$, $\mathbf{m}=(0,0,0)$; (b) a Huygens antenna $\mathbf{p}=(0,0,1)$, $\mathbf{m}=(0,-c,0)$; (c),(d) a Janus dipole $\mathbf{p}=(\pm 1,0,0)$, $\mathbf{m}=(0,ic,0)$ in noncoupling (c) and coupling (d) orientation, in close proximity ($z_0=0.1\lambda$) to a dielectric slab (index $n=2$ and thickness $t=\lambda /4$) (e) Schematic of field components excited by each source. The insets show the orientation of the dipoles and the far field radiation diagrams. These fields have been simulated using comsol multiphysics.

Figure 3

Amplitude of the electric field generated by (a) a circular dipole, (b) a Huygens antenna, and (c) a Janus dipole embedded in the center of a metal-air-metal waveguide, with $ϵ=-1.5+0.02i$ and $\mu =1$. The distance between the two waveguides is $0.7\lambda$. These fields have been simulated using comsol multiphysics.