Scaling behavior of the degree of circular polarization of surface plasmon polariton

Surface plasmon polaritons (SPPs) carry transverse optical spin within the evanescent field, which has enabled the demonstration of various chiral light-matter interactions in classical and quantum systems. To achieve high spin selectivity in the interactions, the elliptical polarization of the evanescent field should be made circular, but the engineering principle of the degree of circular polarization (DOCP) of SPPs has been lacking. In this study, we theoretically and numerically investigate the scaling behavior of the DOCP of the SPP field with respect to the modal effective refractive index (n_eff). The DOCP of the SPP field exhibits power-law scalability to the effective refractive index in the one-dimensional (1D) layered system regardless of the material, structural geometry, and excitation wavelength. The power-law scalability is also confirmed in two-dimensional (2D) waveguide structures for in-plane and out-of-plane SPP fields, but the scaling exponents vary depending on the distance from the waveguide boundaries by the reduced symmetry of the given system. Due to Lorentz reciprocity, the power-law scalability can be extended to the coupling directionality of chiral emitters toward the plasmonic waveguide. To this end, we propose a chiral photonic platform for enhanced light-valley interaction, which utilizes simultaneous enhancement of the DOCP and coupling directionality. An incident SPP can excite a chiral emitter with high spin selectivity that unidirectionally couples the emitted light into the plasmonic waveguide, depending on the valley polarization of excitons in 2D materials. Our work provides a ground rule for designing chiral nanophotonic systems and paves the way for the exploration of scale-free phenomena of electromagnetic waves.