Tailoring Spin Angular Momentum of Light: Design Principles for Plasmonic Nanostructures

Abstract

Spin angular momentum (SAM), a fundamental property of light, is associated with the right-hand and left-hand circular polarizations. It has never been trivial to engineer a light beam with desired SAM, and especially at the frequency regime other than the visible region. A widely used approach is to build periodic arrays of plasmonic nanostructures that host two orthogonal dipole resonances. As the unit cell, its structure design is crucial, but the design principle remains obscure. We present a model of two orthogonal resonant Lorentz dipoles to quantitatively describe the creation of SAM in such plasmonic quarter-wave plates. The equal amplitude and $\ensuremath{\pi}/2$ phase difference are essential. The requirements can be achieved by structure modulation and, in addition, the amplitude can be manipulated by varying the polarization angle of incident waves. In practice, the resonant frequency difference of two dipoles $\mathrm{\ensuremath{\Delta}}\ensuremath{\omega}=|{\ensuremath{\omega}}_{A}\ensuremath{-}{\ensuremath{\omega}}_{B}|$, and their damping rate ${\ensuremath{\kappa}}_{A}$ and ${\ensuremath{\kappa}}_{B}$, should meet a basic criterion, such as $\mathrm{\ensuremath{\Delta}}\ensuremath{\omega}\ensuremath{\geqslant}\sqrt{{\ensuremath{\kappa}}_{A}{\ensuremath{\kappa}}_{B}}$. As an illustration, we design a cross-shaped circular polarization convertor, and show its structure and incident angle optimization. We find the optimal working frequency ${\ensuremath{\omega}}_{\mathrm{opt}}$ is roughly equal to $\sqrt{{\ensuremath{\omega}}_{A}{\ensuremath{\omega}}_{B}}$ at the critical condition $\mathrm{\ensuremath{\Delta}}\ensuremath{\omega}=\sqrt{{\ensuremath{\kappa}}_{A}{\ensuremath{\kappa}}_{B}}$. Our results provide good guidance on the design of SAM-enabled plasmonic devices for versatile applications.