  We present a robust iterative technique for solving complex transcendental
dispersion equations routinely encountered in integrated optics. Our method
especially befits the multilayer dielectric and plasmonic waveguides forming
the basis structures for a host of contemporary nanophotonic devices. The
solution algorithm ports seamlessly from the real to the complex domain--i.e.,
no extra complexity results when dealing with leaky structures or those with
material/metal loss. Unlike several existing numerical approaches, our
algorithm exhibits markedly-reduced sensitivity to the initial guess and allows
for straightforward implementation on a pocket calculator.
