We present an analytical study on the mutual injection mechanism of a spectral beam combining elements using ray tracing and diffraction integrals. We elucidate how mutual injection degrades the beam quality of combined lasers, while the feedback interinjection of the emitters oscillates in an external cavity. Because of the grating diffraction and feedback from the output plane mirror, the mutual injection beam establishes a stable positive feedback between the two emitters. The proposed theoretical model is also verified experimentally by comparing the output under different conditions.
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