Principles of distributed feedback and distributed Bragg-reflector lasers

Wave propagation in periodic waveguides is analyzed by decomposing the eigen Bloch waves into traveling-wave components. It is shown that the principal components consist of a primary forward wave, a primary backward wave, and their Bragg-scattered secondary waves. One important parameter is the coupling constantsdue to Bragg scattering, which relates the secondary wave to the respective primary wave. Laser threshold condition is then obtained by applying the continuity of tangentialEandHat the two boundaries. The results thus obtained are general and applicable to thin-film lasers with various waveguide structures. The laser threshold condition of thin-film Bragg lasers is expressed in terms of two effective reflection coefficients for easy comparison with conventional lasers. For appreciable reflection, a significant change either in the propagation constant or in the coupling constant is required. Two basic types of thin-film Bragg lasers are distributed-feedback (DFB) lasers in which Bragg scattering is confined to the active medium and distributed-Bragg-reflector (DBR) lasers in which Bragg scattering is limited to regions beyond the active medium. The threshold gain, frequency control, and mode selectivity for both types are analyzed and the analyses are applied to GaAs and Nd lasers. It is shown that DBR lasers should have a lower threshold gain and a better mode selectivity than DFB lasers. For distributed-feedback effect to play a significant role in thin-film Bragg lasers, the product kLintmust be greater than unity whereKis the distributed-feedback coefficient and Lintis the interaction length. Advantages for having periodic structures outside the active medium so as to relax constraints onkand Lintare also discussed.