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In this letter, Laguerre finite-difference time domain (FDTD) formulation for linear dispersive materials is proposed. Laguerre-FDTD is a time-domain method using Laguerre polynomials that ensures unconditional stability. Being free from Courant-Friedrich-Lewy (CFL) stability condition, Laguerre-FDTD is advantageous in the simulation of multiscale structures. The derived formulation has been implemented in 3-D and verified with a test structure containing frequency-dependent dispersive materials.