This paper reports a theoretical design of chirped mirrors in 1.3-μm double-section semiconductor lasers to achieve high reflectivity and dispersion compensation over a broad bandwidth. Analytic expressions for reflectivity, group delay and group delay dispersion are derived. We use for the first time chirped air/semiconductor layer pairs as mirrors for higher-order dispersion compensation in semiconductor lasers. Our optimised calculations demonstrate that the broad-band mirrors designed consist of a total of only 12 air/semiconductor layers and achieve a reflectivity higher than 99.8%, a smooth group delay and almost stable dispersion in the laser cavity over a 100-nm bandwidth. Due to a high index contrast of both types of the layers, n l = 1, n h~ 3.5, a high-reflectivity bandwidth of > 700 nm is obtained in 1.3-μm semiconductor lasers. We also compare our results with that of a commercial simulation program and show a good agreement between them. As a conclusion, we assume from the theoretical results that air/semiconductor layer pairs with varying thicknesses used at one end of double-section semiconductor lasers can lead to femtosecond optical pulse generation using mode-locking techniques. © Springer-Verlag 2005.