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A completely open cavity, which is formed by three 60-degree wedges of a photonic crystal with negative effective index, is introduced. Such a realizable design for a completely open cavity (i.e., without any reflective wall in the radial direction) is the first of its kind ever been reported. Due to the negative effective refraction index of the photonic crystal and the high transmission at the photonic crystal/air interfaces, a closed path with zero optical path is formed for the resonance. The present open cavity is very suitable for use as a biosensor as it has large air wedges into which a liquid measurand can flow easily.