Laser theory without the rotating-wave approximation

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Abstract
The effect of counter-rotating terms in the interaction Hamiltonian on the photon statistics is investigated for a single-mode laser. The treatment is based on the Scully-Lamb model. A perturbation expansion is used to derive an equation of motion for the field-density matrix. The counter-rotating terms are found to lead to both transient and secular effects. With some reasonable approximations the steady-state photon-number distribution is derived and it is shown that the counter-rotating terms tend to raise the threshold of laser action and broaden the photon-number distribution. The relative size of these effects is found to be very small and depends on the square of the ratio of the atomic linewidth and the transition frequency.