Effect of grating phase difference on single-mode yield in complex-coupled DFB lasers with gain and index gratings

In complex-coupled DFB lasers with both index and gain gratings, I have studied the effect of the phase difference between index and gain gratings on the single-mode yield considering the threshold gain difference (side-mode suppression ratio) and the optical field uniformity (spatial hole burning). I have obtained the optimum values of: (1) the phase difference /spl Delta//spl Omega/ between index and gain gratings, (2) the coupling strength (/spl aleph/L)/sub i/ of gain grating, and (3) the coupling strength (/spl aleph/L)/sub r/ of index grating, in order to obtain a high single-mode yield regardless of the relative positions of both facets, The used theory is based on the coupled-mode theory and includes the spatial hole burning correction and the standing wave effect. /spl Delta//spl Omega/=/spl pi//4 (and 3/spl pi//4) DFB lasers with HR-AR facets have the highest single-mode yield and should have /spl sim/0.6/spl les/(/spl aleph/L)/sub i//spl les//spl sim/1.5 and (/spl aleph/L)/sub r/