We demonstrate highly efficient transmission of light around sharp cor
ners in photonic bandgap waveguides. :Numerical simulations reveal com
plete transmission at certain frequencies, and very high transmission
(>95%) over wide frequency ranges. High transmission is observed even
for 90 degrees bends with zero radius of curvature, with a maximum tra
nsmission of 98% as opposed to 30% for analogous conventional dielectr
ic waveguides. We propose a simple one-dimensional scattering theory m
odel with a dynamic frequency-dependent well depth to describe the tra
nsmission properties.