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When the alternating direction implicit-finite difference time domain method (ADI-FDTD) is applied to simulating photonic devices, full efficiency can not be achieved if reasonable accuracy is to be kept, due to numerical errors such as numerical dispersion. A simple modification to ADI-FDTD is proposed by calculating the envelope rather than the fast-varying field, so that errors are minimized. A factor of two-five in speed can usually be gained while retaining the same level of accuracy compared with conventional FDTD. The efficiency and the accuracy of this improved approach is demonstrated on several problems, from simple waveguide structures to complex photonic crystal structures.