Quantum theory of a simple laser

Marlan O. Scully, Muhammad Suhail Zubairy

In this chapter, we present a theory of the laser based on the Heisenberg–Langevin approach. This is a different, but completely equivalent approach to the density operator approach discussed in the previous chapter. In general, the density operator approach is better suited to study the photon statistics of the radiation field whereas the Heisenberg–Langevin approach has certain calculational advantages in the determination of phase diffusion coefficients, and consequently laser linewidth. In Section 12.1, a simple approach to determine laser linewidth based on a linear theory is presented. This analysis is especially interesting and useful in that it includes atomic memory effects, something that is difficult to do within a density matrix theory. In Sections 12.2–12.4, we consider the complete nonlinear theory of the laser and rederive all the important quantities related to the quantum statistical properties of the radiation field. A simple Langevin treatment of the laser linewidth including atomic memory effects† The full nonlinear quantum theory of the laser discussed in the previous chapter yields most of the interesting quantum statistical properties of the radiation field. In many problems of interest, however, we do not need such an elaborate treatment. For example, as we saw in the previous chapter, the natural linewidth of the laser can be determined from a linearized theory of the laser. That is, the full nonlinear theory serves to determine the amplitude of the field but the phase fluctuations about this operating point are described by a linear theory.

Pierre Meystre, Murray Sargent

Pierre Meystre, Murray Sargent

S. V. Petrushkin, Самарцев Виталий Владимирович

The loss mechanism to account for the loss of laser photos from the cavity due to absorption by the second dopant inside the laser rod is investigated. We introduced a system of three-level ions as a dissipative subsystem and considered that photons can be lost through their coupling to this quantum subsystem. The conventional quantum laser theory is then expanded for this special case.

Pierre Meystre, Murray Sargent

J.C. Penaforte, B. Baseia

A simple model of a one-dimensional optical cavity having output coupling is used to develop a fully quantized linear laser theory. The present model and procedure, which work directly within the continuous spectrum, allow us to find a simple treatment that leads to explicit solutions for the field inside and outside the laser cavity. The threshold condition for laser light onset is obtained by assuming the field operating in a single collective mode and the usual adiabatic hypothesis. A development that removes this later restriction is also discussed and outlined.