Effect of grating phase difference on single-mode yield incomplex-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 ΔΩ between index and gain gratings, (2) the coupling strength (ℵL)_i of gain grating, and (3) the coupling strength (ℵL)_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. ΔΩ=π/4 (and 3π/4) DFB lasers with HR-AR facets have the highest single-mode yield and should have ~0.6⩽(ℵL)_i⩽~1.5 and (ℵL)_r<~1.25 in order to obtain above 50% yields. Even above 90% yields can be obtained with the range of ~1.1⩽(ℵL)_i⩽~1.4 and ~0.5⩽(ℵL)_r ⩽~0.85. The superior yield characteristics of ΔΩ=π/4 (and 3π/4) DFB lasers, which is above 2.4 times higher than that of ΔΩ=0 (and π) DFB lasers, comes from their better field intensity uniformity. The results presented in this paper provide insight into the variation of the threshold gain difference and the optical field uniformity with ΔΩ, (ℵL)_r, (ℵL)_i, and (ρ_l, ρ_r)