To calculate the propagation length of surface plasmons numerically, you can use methods like finite element analysis (FEA) or finite difference time domain (FDTD) simulations. These techniques solve Maxwell's equations to model the behavior of electromagnetic waves interacting with materials at the nanoscale. By simulating the interaction of light with metal-dielectric interfaces, you can determine the distance over which surface plasmons propagate before being absorbed or attenuated. Additionally, you may need to consider factors such as the material properties of the metal and dielectric, wavelength of incident light, and surface roughness.