Spectral filtering effect of diffraction gratings with a lens coupling to optical fibers

We present a theoretical study of a spectral filter, which consists of a diffraction grating, a coupling lens, and an optical fiber. As the diffracted beam is highly dispersed spatially, coupling into an optical fiber naturally creates a Gaussian spectral filtering effect. Using ray transfer matrices, we derive simple equations to calculate the spectral filter bandwidth and the group velocity dispersion. This study offers insights for designing fiber-based spectral filters, particularly for mode-locked fiber lasers.