We present general criteria for crossing perpendicular waveguides with near
ly 100% throughput and 0% cross talk. Our design applies even when the wave
guide width is of the order of the wavelength. The theoretical basis for th
is phenomenon is explained in terms of symmetry considerations and resonant
tunneling and is then illustrated with numerical simulations for both a tw
o-dimensional photonic crystal and a conventional high-index-contrast waveg
uide crossing. Cross-talk reduction by up to 8 orders of magnitude is achie
ved relative to unmodified crossings. (C) 1998 Optical Society of America.