The effect of polarization on the propagation distance of leaky guided modes

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.