An air waveguide of left-handed photonic crystal （PhC） formed by holographic lithography is proposed. The symmetry mismatch between the incident wave and the Bloch modes of the holographic PhC is used to guide light efficiently. By properly designing the waveguide, backscattering loss can be significantly reduced. Due to the unique advantages of holographic photonie crystals, the serious problems of material loss and fabrication difficulty in left-handed material waveguides are also avoided. Furthermore it is shown that high transmission efficiency is easily achieved in the frequencv region with effective refraction index near zero. These features may extend the possible guiding ability of holographic photonic crystal waveguide and its promising potential in the application of photonic integrated circuits.
