We study laser generation in 1D distributed feedback lasers with amplifying and lossy layers. We show that when the lasing frequency differs from the transition frequencies of the amplifying medium, loss induced lasing may occur due to the broadening of the resonator mode with increasing loss in the absorbing layers. This broadening leads to a shift in the lasing frequency towards the transition frequency. As a result, the cavity mode interaction with the amplifying medium is enhanced, and the lasing threshold is lowered.
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