The finite-difference time-domain (FDTD) method is widely used to simulate the propagation of the electromagnetic wave, owing to its simplicity and robustness. Many applications, ranging from radar technology to bioelectromagnetism, have utilised broadband simulations using the FDTD method over recent years. However, the main drawback of the FDTD method is the difficulty in modelling electrically-fine geometrical features, including thin layers, curved surfaces and narrow slots. When the FDTD method is employed to resolve such geometrical features in a problem space, it requires very fine spatial sampling of the problem space, and thus it demands excessive computational resources in terms of memory and CPU time, due to the increase in the FDTD grid points and small time-step usage required to satisfy the Courant-Friedrichs-Lewy (CFL) condition. To enhance computational efficiency of the FDTD method, this thesis develops a subcell technique to model frequency-dependent thin layers in the FDTD method, where the frequency dependency is represented by the one-pole Debye model, and incorporated into the FDTD method by means of Auxiliary Differential Equation (ADE) formulation. The proposed technique relies on applying the integral form of the Maxwell-Ampere equation in a coarse cell containing electrically-fine geometrical features, and then advancing the field components in time using two different approaches; the first approach requires the solution of (M + 1)-order differential equation, where M is the number of frequency-dependent media in the cell, whereas the second approach requires the solution of M 2nd-order simultaneous equations. In this thesis, the latter approach is used in the numerical simulations when more than one Debye medium exists in a cell, due to the fact that the solution of high-order differential equations become intensely-parallel to the the number of frequency-dependent media in the cell. The obtained results from the numerical simulations are compared with analytical solutions, and with numerical references in both the time domain and frequency domain.