Theory on distributed feedback /DFB/ lasers including strong modulations

A general theory on distributed feedback lasers is developed which includes weak and strong periodic modulations. The theory is based on a complex Hill wave equation which is treated by matrix methods. An infinite DFB medium is modeled as an infinite chain of four-terminals, where each period of the DFB structure is represented by a four-terminal. The dispersion relation of the infinite DFB structure is obtained from the corresponding infinite chain of four terminals, while the resonance condition of a finite DFB laser is calculated from the corresponsing finite chain terminated by free-space impedances. It is shown that an approximation for weak modulations is compatible with the dispersion relation obtained using the coupled-wave theory.