We consider the construction and analysis of staggered high order spatial finite difference methods for Maxwell's equations in dispersive media. We present a novel expansion of the symbol of finite difference approximations, of arbitrary even order, of the first order spatial derivative operator. This alternative representation allows the derivation of a concise formula for the numerical dispersion relation for all even order schemes, including the limiting (infinite order) case. We further derive a closed-form analytical stability condition for these schemes as a function of the order of the method. Using representative numerical values for the physical parameters, we validate the stability criterion while quantifying numerical dissipation.