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A statistical yield analysis is presented for gain-and index-coupled DFB laser structures, allowing a comparison of their single longitudinal mode (SLM) yield capabilities. For the yield calculations, we take into account the threshold gain difference A gL and the longitudional spatial hole burning (SHB).By comparing the experimental and theoretical yield of index-coupled DFB lasers, the significance of spatial hole burning for correct yield predictions is illustrated. For the purpose of comparison, yield calculations for various X/4-shifted DFB lasers (with low facet reflectivities) are presented in a novel way. The most emphasis, however, is on partly gain-coupled DFB lasers. First, estimations of practical K~~~~ (gain coupling coefficient) values for gain and for loss gratings are discussed. Then, for low facet reflectivities, the spatial hole burning corrected yield for various K~~~~ and Kindex (index-coupling coefficient) combinations is given. Results for cleaved facets are also presented. In both cases, a large increase of the spatial hole burning corrected yield has been found. For all structures, design criteria for the optimization of the spatial hole burning corrected yield are discussed.

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One way of suggesting that an NP problem may not be NP-complete is to show that it is in the class UP. We suggest an analogous new approach-weaker in strength of evidence but more broadly applicable-to suggesting that concrete NP problems are not NP-complete. In particular we introduce the class EP, the subclass of NP consisting of those languages accepted by NP machines that when they accept always have a number of accepting paths that is a power of two. Since if any NP-complete set is in EP then all NP sets are in EP, it follows-with whatever degree of strength one believes that EP differs from NP-that membership in EP can be viewed as evidence that a problem is not NP-complete. We show that the negation equivalence problem for OBDDs (ordered binary decision diagrams [22, 13]) and the interchange equivalence problem for 2-dags are in EP. We also show that for boolean negation [25] the equivalence problem is in EP NP , thus tightening the existing NP NP upper bound. We show that FewP [2], bounded ambiguity polynomial time, is contained in EP, a result that is not known to follow from the previous SPP upper bound. For the three problems and classes just mentioned with regard to EP, no proof of membership/containment in UP is known, and for the problem just mentioned with regard to EP NP , no proof of membership in UP NP is known. Thus, EP is indeed a tool that gives evidence against NP-completeness in natural cases where UP cannot currently be applied.