Reflectivity of Superimposed Bragg Gratings Induced by Longitudinal Mode Instabilities in Fiber Lasers

We report on reflectivity of transient Bragg gratings created in the active medium of a fiber laser with longitudinal mode instability. Despite the long history of laser physics, reflectivities of such gratings were theoretically studied and experimentally measured only recently. Based on the coupled-mode theory, we derived a theoretical model of superimposed Bragg gratings for a special case of mode instability known as spontaneous laser line sweeping (SLLS). SLLS fiber lasers exhibit a periodic wavelength drift over an interval of several nanometers, followed by a quick bounce backward, narrowband, and mostly single-frequency operation as well as pulsed output with pulse lengths on the order of microseconds. The refractive index modulation inside the active fiber is given by the Kramers–Kronig relations. For ytterbium, the refractive index change in the 1060-nm band is directly proportional to the metastable level population with a factor of
${\text{2.1}}\times {\text{10}}^{- 31}\,{\text{m}}^{3}$
. Taking into account realistic values of temporal damping of the gratings, significant reflectivity on the order of units to tens of percent is estimated. The reflectivity can be controlled by setting the SLLS laser parameters. Effect of the resonator length is shown as an example.