The role of gain in an optical filter is advanced by good agreement between theory and experiment presented herein. The particular integrated photonic filter is composed of four semiconductor optical amplifiers and one four-port coupler located at the intersection of the amplifiers. The four-port coupler is realized using frustrated total internal reflection off a very thin slab of alumina embedded in the substrate. The delta function response of the filter is measured using an ultra-fast laser and cross-correlator, and the measured transfer functions agree well with a $z$-transform-based description of the device.
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