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We have theoretically proposed a highly compact refractive-index sensor
consisted of edge-cavity and line-defect waveguide in two-dimensional photonic
crystal. The sensing object is completely outside of the single enclosed
surface of the sensor. The edge-cavity is designed by engineering the spatial
distribution of the cutoff frequency of edge modes. The coupling between the
edge-cavity and the waveguide is maximized by optimizing the radius of the rods
between them, so that the transmittance spectrum through the waveguide has a
sharp anti-peak. As the refractive index of the sensing object changes, the
resonant wavelength of the edge-cavity is changed, which in turn changes the
wavelength of the anti-peak. The sensitivity of the sensor is up to 40 nm/RIU,
and the footprint of the sensor is only 40 $\mu m^{2}$. Because the
transmittance spectrum is determined by the overlap between the sensing object
and the highly localized resonant mode, the sensor can also perceive spatial
distribution of refractive index in the sensing object.

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