  A fundamental trade-off relation between the cross sectional confinement and
propagation length of an arbitrary mode of a general waveguide is presented.
This limit is a generalization of the well-known diffraction limit for guided
modes. The results provide a lower bound on propagation loss of plasmonic
waveguides which are attractive for their deep subwavelength mode dimensions.
We also introduce a material loss merit factor that sets a criterion for
comparing different plasmonic materials for achieving the best trade-off
between confinement and loss.
