  We propose the mechanism of active Faraday optical clock, and experimentally
demonstrate active Faraday optical frequency standards based on 852 nm narrow
bandwidth Faraday atomic filter by the method of velocity-selective optical
pumping of cesium vapor. The center frequency of the active Faraday optical
frequency standards is determined by the cesium 6 $^{2}S_{1/2}$ $F$ = 4 to 6
$^{2}P_{3/2}$ $F'$ = 4 and 5 crossover transition line. The optical heterodyne
beat between two similar independent setups shows that the frequency linewidth
reaches 996(26) Hz, which is 5.3 $\times$ 10$^{3}$ times smaller than the
natural linewidth of the cesium 852 nm transition line. The maximum emitted
light power reaches 75 $\upmu$W. The active Faraday optical frequency standards
reported here have advantages of narrow linewidth and reduced cavity pulling,
which can readily be extended to other atomic transition lines of alkali and
alkaline-earth metal atoms trapped in optical lattices at magic wavelengths,
making it useful for new generation of optical atomic clocks.
