Synthetic plasmonic lattice formation through invariant frequency comb excitation in graphene structures

Nonlinear surface-plasmon polaritons~(NSPPs) in nanophotonic waveguides excite with dissimilar temporal properties due to input field modifications and material characteristics, but they possess similar nonlinear spectral evolution. In this work, we uncover the origin of this similarity and establish that the spectral dynamics is an inherent property of the system that depends on the synthetic dimension and is beyond waveguide geometrical dimensionality. To this aim, we design an ultra-low loss nonlinear plasmonic waveguide, to establish the invariance of the surface plasmonic frequency combs~(FCs) and phase singularities for plasmonic peregrine waves and Akhmediev breather. By finely tuning the nonlinear coefficient of the interaction interface, we uncover the conservation conditions through this plasmonic system and employ the mean-value evolution of the quantum NSPP field commensurate with the Schr\"odinger equation to evaluate spectral dynamics of the plasmonic FCs~(PFCs). Through providing suppressed interface losses and modified nonlinearity as dual requirements for conservative conditions, we propose exciting PFCs as equally spaced invariant quantities of this plasmonic scheme and prove that the spectral dynamics of the NSPPs within the interaction interface yields the formation of plasmonic analog of the synthetic photonic lattice, which we termed \textit{synthetic plasmonic lattice}~(SPL).