Rytov’s theory of thermally generated radiation is used to find the noise in two-dimensional
passive guides based on an arbitrary distribution of lossy isotropic dielectric. To simplify
calculations, the Maxwell curl equations are approximated using difference equations that also
permit a transmission-line analogy, and material losses are assumed to be low enough for modal
losses to be estimated using perturbation theory. It is shown that an effective medium
representation of each mode is valid for both loss and noise and, hence, that a one-dimensional
model can be used to estimate the best achievable noise factor when a given mode is used in a
communications link. This model only requires knowledge of the real and imaginary parts of the
modal dielectric constant. The former can be found by solving the lossless eigenvalue problem,
while the latter can be estimated using perturbation theory. Because of their high loss, the theory is
most relevant to plasmonic waveguides, and its application is demonstrated using single interface,
slab, and slot guide examples. The best noise performance is offered by the long-range plasmon
supported by the slab guide.