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Simulation Scheme of Optical Systems

Propagation of light through an optical system can be described in terms of the Hamiltonian formulation. The time evolution of the propagating electromagnetic field is given by a Hamiltonian operator. Different optical components and waveguides correspond to different terms in the total evolution operator. Consecutive action of two or more components is not necessarily the sum of the actions of isolated components. This interaction of optical components is seen as commutators of the corresponding terms in the Hamiltonian. When the algebra of the operators is known the mutual action of the given components can be calculated using symbolic manipulation programs. This algorithm can be used whenever the propagating field can be approximated as plane waves.