Analytic properties of the electromagnetic Green's function are established and extended to a second complex frequency, introduced as a new degree of freedom, and to complex wavevectors. Next, Kramers-Kronig expressions for the inverse Helmholtz operator and the electromagnetic Green's function are derived by analogy with the permittivity. These Kramers-Kronig expressions are the starting point to propose a new method to obtain an expansion of Green's function on the leaky or quasinormal modes for open systems. This method is illustrated in the situation of a single dis-persive layer. Finally, the second frequency introduced as a new degree of freedom is exploited to characterize non-dispersive systems. Published by AIP Publishing.