Deviation of the Frantz-Nodvik equation for zig-zag optical path, slab geometry laser amplifiers

In slab-geometry laser amplifiers with zig-zag optical paths, multiple reflections within the slab cause the extracting optical beams to repeatedly fold over themselves. Because of this, some regions of the slabs are extracted by two overlapping beams. The theory for pulse propagation in laser amplifiers by L.M. Frantz and J.S. Nodvik (see J. Appl. Phys., vol.34. no.8, p.2346-9, 1963) is extended to include the effects of the zig-zag optical path. Simple equations for slabs which are either uniformly filled by the extracting beam or partially filled are derived. Extraction with spatial beam modulation due to interference is also examined