Atomic optical stimulated amplifier with optical filtering of ultra-narrow bandwidth

Taking advantages of ultra-narrow bandwidth and high noise rejection performance of the Faraday anomalous dispersion optical filter (FADOF), simultaneously with the coherent amplification of atomic stimulated emission, we propose a stimulated amplified Faraday anomalous dispersion optical filter (SAFADOF) at cesium 1470 nm. The SAFADOF is able to significantly amplify very weak laser signals and reject noise in order to obtain clean signals in strong background. We show that for a weak signal of 50 pW, the gain factor can be larger than 25000 (44 dB) within a bandwidth as narrow as 13 MHz. Having the ability to amplify weak signals with low background contribution, the SAFADOF finds outstanding potential applications in weak signal detections.