Using finite difference time domain (FDTD) method, we analyze static and dynamic response of non-uniform grating quarter-wavelength shift distributed feedback QWS-DFB laser with non-zero facet reflection coefficients, both for large signal transient and small signal modulation. By introducing a convex tapered grating structure for QWS-DFB laser (XTG-DFB), it is shown that single mode stability of laser enhances and laser is less sensitive to random phase of reflection coefficients. We also show that XTG-DFB laser has better small signal response in comparison with uniform grating QWS-DFB laser. (c) 2007 Elsevier Ltd. All rights reserved.