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To model open-domain problems with Drude, Lorentz, and Debye media, the complex frequency-shifted perfectly matched layer (CFS-PML) is adopted to truncate the Crank-Nicolson Douglas-Gunn finite-difference time-domain (CNDG-FDTD) region. The auxiliary differential equation (ADE) and the bilinear Z-transform (BZT) methods are incorporated separately into the implementations of CNDG-CFS-PML formulations, while the ADE, piecewise linear recursive convolution (PLRC), and trapezoidal recursive convolution (TRC) methods are utilized to model dispersive media. The proposed formulations can not only circumvent the stability condition, but have the advantages of the CFS-PML in attenuating the evanescent waves and reducing the late-time reflection. Three numerical examples have been carried out to validate these formulations. The simulation results show that the proposed CNDG-CFS-PML algorithm is efficient in absorbing performance and saving more computational time compared with the conventional FDTD method, which leads to extensive applicability and acts as a very good prospect.

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We systematically investigate ultrafast dynamic nonlinear mechanisms of photonic crystals (PhCs) with femtosecond (fs) pumping via the transmission change of a signal pulse. The pumping causes a nonlinear decrease (or increase) in the dielectric constant of the PhC material. A new phenomenon of the asymmetric change in the transmission spectra was observed in the gap region and the band-gap edge modes. For the band region, a sloped change in the transmission spectra was observed, and for the transition region, a hybrid of the two was observed. In addition, a universal dynamic picture of the fs nonlinear responses of the PhC was constructed.