Output Power of Laser Resonators

Abstract

The differential equations (9.35) and (9.56) describing the amplification of the intensity inside the active medium are now used to derive the output power of stable resonators. In the resonator model used (Fig. 10.1) it is assumed that both the forward travelling beam with intensity I ⁺(z) and the backward traveling beam with intensity I ^-(z) cover the same area of the active medium. The complete overlap of the two counterpropagating beams is characteristic for stable resonators. During a round trip the intensity is decreased due to diffraction losses (loss factors V ₁ -V ₄ ), scattering, and absorption inside the medium (loss factor V _s ), and by output coupling. In steady state operation, these losses are compensated by the amplification process characterized by the small-signal gain coefficient g ₀ The next assumption we make is that no spatial hole burning is present meaning that at any plane inside the medium the intensity I(z) is given by the sum of the two intensities I ⁺(z) and I ^- (z). This is a reasonable approach for most lasers since the effect of spatial hole burning on the output power is smoothed out by atomic motion (gas lasers), energy migration, or axial multimode operation (solid state lasers). Furthermore, the mode is assumed to exhibit a flat-top intensity profile. The incorporation of the real mode structure will be discussed in Chapter 11.