Diagrammatic semiclassical laser theory

We derive semiclassical laser equations valid in all orders of nonlinearity. With the help of a diagrammatic representation, the perturbation series in powers of electric field can be resummed in terms of a certain class of diagrams. The resummation makes it possible to take into account a weak effect of population pulsations in a controlled way, while treating the nonlinearity exactly. The proposed laser theory reproduces the all-order nonlinear equations in the approximation of constant population inversion and the third-order equations with population-pulsation terms, as special cases. The theory can be applied to arbitrarily open and irregular lasers, such as random lasers.