well-known class of algorithms is based on a method proposed by Yee [@Yee66] and is called the finite-difference time-domain (FDTD) method. The FDTD method has matured during past years and various algorithms implemented for specific purposes are available by now [@Taflove; @Website]. These algorithms owe their popularity mainly due to their flexibility and speed while at the same time they are easy to implement. A limitation of Yee-based FDTD techniques is that the stability of the algorithms is conditional. The stability depends on the mesh size used to discretize space and the time step used to perform the time integration [@Taflove].

In this paper we present a family of unconditionally stable algorithms that solve the time-dependent Maxwell equations (TDME) through the application of orthogonal transformations. That this is possible follows from the representation of the TDME in matrix form. The exponential of a skew-symmetric matrix plays the role of the time-evolution operator of the EM fields. This time-evolution operator is orthogonal. The key to the construction of an unconditionally stable algorithm to solve the Maxwell equations is the observation that orthogonal approximations to this operator automatically yield unconditionally stable algorithms. The Lie-Trotter-Suzuki product formulae [@Suzuki8591] provide the mathematical framework to 