Performance Improvement of Ultra-Short Distributed Feedback Fiber Lasers by Engineering of Coupling Coefficient Profiles

The performance of distributed feedback erbium-doped fiber lasers considering modified Gaussian profiles for coupling-coefficient variations in Bragg gratings is analyzed and compared to that of such lasers with conventional coupling-coefficient profiles, based on solving the generalized coupled-mode equations. With increasing and decreasing coupling coefficients near the cavity front-ends and
$\pi $
-phase-shift, respectively, the novel modified Gaussian profiles, are proved to represent not only flattened intra-fiber intensity distribution but also extremely-effective enhancement and reduction on the output power and linewidth, respectively. Moreover, using engineered profiles the lasing is even possible for small strengths for which the lasing is not accessible using constant profiles. Unidirectional operation of such a laser can be achieved using unbalanced modified Gaussian profiles by increasing and decreasing the strength of the half-grating on each side of the
$\pi $
-phase-shift while the total strength remains the same. To facilitate fabrication, 2-step profiles for coupling-coefficient variations, relying on approximations to the modified Gaussian and super-Gaussian profiles are also proposed and evaluated. For a 1-cm-long grating with an integrated strength of 6 and pumped with 250 mW, lasing is impossible using a constant-coupling profile, however, it is possible using the 2-step profiles. The lasers based on the 2-step profiles provide 90
$\mu \text{W}$
and 230
$\mu \text{W}$
output power with 28% and 19% decrease compared to those based on the original modified Gaussian and super-Gaussian profiles with the same length and strength. The corresponding enhancement in linewidth for the 2-step profiles is less than 5% in both cases.