This work presents a numerical framework for modeling and solving time-modulated responses of complex bianisotropic metasurfaces. First, Lorentz-dispersive surfaces are implemented as impedance sheet models for the surface-wave-assisted transmissive bianisotropic metasurface, and the results are validated with prior analytical solutions. Next, a finite-difference time-domain (FDTD)-based numerical solution for time-modulated media is developed within the MIT Electromagnetic Equation Propagation (meep) framework using a sampled time-varying material function approach, and is verified through comparisons with circuit-based numerical methods, analytical solutions, and a reference FDTD solver. The results show good agreement in terms of harmonic frequencies, power levels, and phase-coherent transmission response. The method is then applied to simulate the time-modulated metasurface modeled with Lorentz-dispersive multilayers, demonstrating nonreciprocal transmission and unidirectional absorption under relatively low-frequency modulation. The proposed numerical approaches offer efficient and practical frameworks for modeling complex electromagnetic media in the time domain and for performing dynamic full-wave simulations, providing a viable solution path for analyzing functionalities such as isolation, unidirectional amplification, and absorption—phenomena that are difficult to achieve in time-invariant systems.

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• Metasurfaces
• Non-reciprocal transmission
• Dynamical systems
• Killing symmetry
• Bloch-Floquet theorem
• Effective medium approach
• Electromagnetic field calculations
• Finite-difference time-domain method
• Methods in electromagnetism
• Numerical approximation & analysis
• Numerical techniques
• Transfer matrix method