Generalized Differential Transfer Matrix for Fast and Efficient Analysis of Arbitrary-Shaped Nonlinear Distributed Feedback Structures

A new, fast, and efficient approach based on the differential transfer matrix idea, is proposed for analysis of nonuniform nonlinear distributed feedback structures. The a priori knowledge of the most-likely electromagnetic field distribution within the distributed feedback region is exploited to speculate and factor out the rapidly varying portion of the electromagnetic fields. In this fashion, the transverse electromagnetic fields are transformed into a new set of envelope functions, whereupon the numerical difficulty of solving the nonlinear coupled differential equations is partly imparted to the analytical factorization of the fields. This process renders a new set of well-behaved nonlinear differential equations that can be readily solved. Strictly periodic, linearly tapered, and linearly chirped structures are analyzed to justify the accuracy and the efficiency of the proposed method.