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We describe a stable lightwave synthesized frequency sweeper (LSFS) using a Fabry-Perot (FP) cavity composed of two Faraday rotator mirrors (FRMs). In the former half of this paper, we numerically simulate the behavior of amplified spontaneous emission (ASE) noise accumulations, and show that angular deviations of the FRMs can cause instability in the frequency sweep span. We also show that the span is stabilized by placing a polarizer in one of the FRMs because the FP cavity then works as a single-polarization cavity with a small transmittance fluctuation. Experimental results confirming the stability of this LSFS are provided in the latter half of this paper.