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A new structure that can realize an all-optical equivalent two-tap negative tap photonic notch filter response is presented. It is based on a Sagnac fiber loop interferometer containing an optical phase modulator. An equivalent two-tap negative tap notch filter response is obtained by phase modulating the clockwise and counterclockwise propagating optical waves inside the Sagnac loop at different times. Results demonstrate a robust notch filter response using a narrow-linewidth optical source with no phase-induced intensity noise and no second-order harmonic component present at the output.