Probabilistic modelling of stochastic interactions between electromagnetic fields and systems

Rigorous deterministic models of physical phenomena are important for understanding the fundamental characteristics of interactions, but if we neglect the uncertainties in the various components of these models, the correspondence between predictions based on such models and real-life situations can be very weak. This article addresses the important question of how to account, rigorously, for uncertainties in classical macroscopic electromagnetic interactions between fields and systems of linear material (considering uncertainties in the field incident on the system as well as in the geometrical realisation of the system itself). In the first part, we develop the general ideas which lead to the expression of the variances of the observables of the problem in terms of field- and system covariance operators. In the second part, we study the covariance operator which characterises a stochastic system. In the third part, we investigate stochastic electromagnetic fields and present the definition of a canonical stochastic field of which the spatial covariance operator has the real part of the Green tensor function as kernel function. In the final part, we present an illustration by studying the interaction of a stochastic plane wave with a stochastic twisted pair of wires. To cite this article: B.L. Michielsen, C. R. Physique 7 (2006).