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An erbium-doped fiber ring laser is presented. It consists of an inverse-Gaussian apodized fiber Bragg grating acting as a dual-wavelength passband filter, and an unpumped erbium-doped fiber serving as a saturable absorber. The proposed fiber laser can produce two stable lasing lines in which each of them operates in single-longitudinal-mode (SLM). This dual-wavelength SLM laser can generate a microwave signal at 10.502 GHz by beating the dual wavelengths at a photodetector.