Circular Huygens Dipoles: Unidirectional Spin-Angular Momentum from Achiral Nanoparticles

Abstract

Simultaneous control over the directionality and spin of light at the nanoscale is a central goal in nanophotonics with applications ranging from quantum information to advanced biosensing. We introduce the concept of the Circular Huygens Dipole and numerically demonstrate its realization in a single Si nanocuboid. We show that the polarization of an incident linear wave controls the interference between co-located circular electric and magnetic dipoles excited in phase quadrature. This enables deterministic switching of the forward-scattered radiation between purely right- and left-circularly polarized states. The system also functions as a directional spin-to-linear polarization converter. Our findings establish a robust, passive method for reconfigurable spin-directional control in a simple, monolithic silicon nanostructure, opening avenues for chip-scale spin-optics, chiral quantum interfaces, and novel sensing platforms.

Figures (6)

• Figure 1: Principle of the Circular Huygens Dipole.  3D far-field radiation patterns for ideal point dipoles. Radius is proportional to intensity ($S_0$) and color indicates the degree of circular polarization ($S_3/S_0$). Stokes parameters are $S_0 = |E_\theta|^2 + |E_\phi|^2$ and $S_3 = 2\,\mathrm{Im}(E_\theta E_\phi^*)$. Handedness is defined from the source viewpoint. (a)-(d) Bidirectional radiation from fundamental right-handed ($p_{xy}^+, m_{xy}^+$) and left-handed ($p_{xy}^-, m_{xy}^-$) circular dipoles.  (e)–(h) Their interference yields four unique unidirectional spin states: (e) Forward RCP from $h_{xy}^+=p_{xy}^+ + i m_{xy}^+$. (f) Backward LCP from $h'_{xy}{}^-=p_{xy}^+ - i m_{xy}^+$. (g) Forward LCP from $h_{xy}^-=p_{xy}^- - i m_{xy}^-$. (h) Backward RCP from $h'_{xy}{}^+=p_{xy}^- + i m_{xy}^-$.
• Figure 2: Realization of Circular Huygens Dipoles in a Si Nanocuboid.  (a) Scattering geometry: Si nanocuboid ($L_x=128$, $L_y=94$, $L_z=440$ nm) under LP illumination at angle $\alpha$.  (b) Multipole magnitudes, identical for $\alpha=\pi/4$ and $3\pi/4$, show comparable strength of $p_x,p_y,m_x,m_y$ at $\lambda_0=660$ nm.  (c, d) For $\alpha=\pi/4$, phase differences of $\approx+90^\circ$ excite $p_{xy}^+$ and $m_{xy}^+$, realizing a Right-Handed Circular Huygens Dipole ($h_{xy}^+$) and producing forward RCP scattering.  (e, f) For $\alpha=3\pi/4$, phase differences flip to $\approx-90^\circ$, exciting $p_{xy}^-$ and $m_{xy}^-$ and yielding forward LCP scattering.
• Figure 3: Near-Field Origin of Circular Huygens Dipoles.  E- and H-field distributions in the central xy-plane at $\lambda_0=660$ nm.  (a, b) For $\alpha=\pi/4$, fields co-rotate clockwise (CW), exciting $p_{xy}^+$ and $m_{xy}^+$. The magnetic field leads the electric by $\approx+90^\circ$, realizing $h_{xy}^+ = p_{xy}^+ + i m_{xy}^+$.  (c, d) For $\alpha=3\pi/4$, fields co-rotate counter-clockwise (CCW), exciting $p_{xy}^-$ and $m_{xy}^-$. The magnetic field lags by $\approx-90^\circ$, realizing $h_{xy}^- = p_{xy}^- - i m_{xy}^-$.  These near-fields directly show how incident polarization controls dipole handedness and interferometric phase.
• Figure 4: Directional Linear Scattering from Circular Excitation.  (a) A Si nanocuboid under normally incident CP illumination.  (b) Excited multipole magnitudes are identical to the linear case (Fig. 2b).  (c, d) For RCP input, phased orthogonal electric and magnetic dipoles are excited that satisfy the linear Huygens condition, producing forward (-z) linearly polarized radiation.  (e, f) LCP input excites a complementary set of dipoles, again yielding directional linear scattering.
• Figure 5: Alternative Pathways to Directional Spin Emission and Basis Equivalence. (a)-(d) Radiation patterns of fundamental linear electric ($p_x, p_y$) and magnetic ($m_x, m_y$) dipoles. (e)-(h) Unidirectional, linearly polarized radiation from linear Huygens (forward, e-f) and Anti-Huygens (backward, g-h) dipoles. (i)-(l) Radiation from chiral dipoles ($\sigma_x^\pm, \sigma_y^\pm$), which produce circularly polarized toroidal patterns. (m)-(p) Synthesis of the four unidirectional, circularly polarized sources from Fig. 1 of the main text, demonstrating that each can be constructed from a superposition of linear Huygens or chiral dipoles.