<title>Analytical model of a two-stage Raman fiber laser considering intensity interactions in cascades</title>

Abstract

In the present work we have developed an analytical model which takes into account power distribution along the fiber in the two-stage Raman fiber laser thus enabling both qualitative and quantitative comparison with performed experiment. The model describes pump power depletion and intensity interactions in cascades that seem important in the experiment. It is shown that the cascade generation saturates (depletes) sequentially: depletion of residual pump power begins when the first Stokes generation starts, then the first Stokes power saturates when the second Stokes generation starts etc. We have also compared the resalts of calculations with measurements of intensities in cascades and residual pump power which confirm the model qualitatively. Good quantitative coincidence with the experiment is also reached but for this we have to take into account spectral broadening of the first Stokes wave with increasing pump power. The presented model adequately describes the thresholds, the differential efficiency for the first and the second Stokes waves generation, the saturation levels for the residual pump and the first Stokes wave powers.