  We show that transverse-magnetic (TM) leaky modes can propagate further than
transverse electric (TE) modes in real-index dielectric waveguides. We compute
the density of states and find that while the TE spectrum contains only
overlapping resonances, the TM spectrum typically contains several isolated
peaks. By transforming the TM equation into a Schr\"{o}dinger-type equation, we
show that these isolated peaks arise due to $\delta$-function barriers at the
core-cladding interface. Our theory is useful for a range of applications,
including filtering TM modes from initially unpolarized light and transferring
information between distant waveguides.
