  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 (neff).
The DOCP of the SPP field exhibits power-law scalability to the effective
refractive index in the 1D layered system, regardless of the material,
structural geometry, and excitation wavelength. The power-law scalability is
also confirmed in 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 towards 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 material. 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.
