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We numerically study a double-slit interferometer that detects the modification of local phase and amplitude signal due to a refractive index contrast in a nanoplasmonic sensor after the plasmonic wave has been coupled to the farfield. Specifically, the sensor consists of two elongated zero-mode waveguides (ZMW) which function to launch surface plasmons as well as transmit light directly into the farfield. The surface plasmon waves are coupled to the farfield by surface gratings which cover one quarter of a bull-eye antenna, with different transmission directions. In the farfield, the coupled plasmon waves interfere with the directly transmitted reference wave, which reveals a combination of the phase and amplitude modification by the asymmetry of refractive index in the lumen of the ZMW. We report a drastic increase in sensitivity over interferometers that only utilize the directly transmitted fraction., Comment: 18 pages, 12 figures