Groove-cell analysis of distributed feedback lasers

The propagation of waves in a groove cell is analyzed. This propagation is a function of transfer matrix, which contains the gain, together with the phase constant, the length of a groove cell, and the groove reflection coefficient. When the transfer matrix is cascaded the transmission of an optical field and the reflection coefficient of a distributed feedback structure can be determined even with unequal grooves and any groove number. With the help of an eigenvalue equation the threshold gain and phase constant of the resonator modes are determined for a symmetrical laser. The increase of threshold gain is demonstrated for an inhomogeneous laser with changed mean value of effective refractive index along the laser length. Bloch waves exist in a long grating (or a closed loop) of periodic grooves