  We propose a new class of one-dimensional (1D) photonic waveguides: the
fractal photonic crystal waveguides (FPCWs). These structures are photonic
crystal waveguides (PCWs) etched with fratal distribution of grooves such as
Cantor bars. The transmission properties of the FPCWs are investigated and
compared with those of the conventional 1D PCWs. It is shown that the FPCW
transmission spectrum has self-similarity properties associated with the
fractal distribution of grooves. Furthermore, FPCWs exhibit sharp localized
transmissions peaks that are approximately equidistant inside the photonic band
gap.
