Homogeneous gain profile

The essential characteristic of dye lasers is their broad homogeneous gain profile. 

If several modes are simultaneously absorbed, the factor N in (1.22a-1.22b) stands for the ratio of all coupled modes to those absorbed. If all modes have equal frequency spacing, their number N gives the ratio of the spectral width of the homogeneous gain profile to the width of the absorption profile. 

In the case of a homogeneous profile g(v —vo)> all molecules in the upper level can contribute to stimulated emission at the laser frequency Ua with the probability Bikpgiva I d), see (5.8). Although the laser may oscillate only with a single frequency v, the whole homogeneous gain profile a(v) = ANa v) saturates until the inverted population difference AN has decreased to the threshold value AAthr (Fig- 5.23a). The saturated amplification coefficient asat(v) at the intracavity laser intensity / is, according to Sect. 3.6,... 

Even when the net gain is sufficiently large to allow oscillation of, e.g., up to three spatially separated standing waves (p = 1,2, 3), only one mode can oscillate if the spectral width of the homogeneous gain profile is smaller than (2/3)(J/a)8v [5.33],... 

The unidirectional ring laser has the advantage that spatial hole burning, which impedes single-mode oscillation of lasers (Sect. 5.3.3), can be avoided. In the case of homogeneous gain profiles, the ring laser can utilize the total population in-... 

Fiq 5.14. Saturation of a homogeneous gain profile. The dashed curve is the line profile during the buildup time the dotted-dashed curve gives the stationary saturated profile... 

Fiq 5.16. Mode competition due to gain saturation of a homogeneous gain profile... 

A laser mode represents a standing wave in the laser resonator with a z-de-pendent field amplitude E(z) as illustrated in Fig.5.20a. Since the saturation of the inversion aN, discussed in the previous section, depends on the inten-sity I JE, the inversion saturated by a single laser mode will exhibit a spatial modulation aN(z) as drawn in Fig.5.20c. Even for a completely homogeneous gain profile, there are always regions of unsaturated inversion... 

For a homogeneous gain profile, the unsaturated gain per round is Gq = aNqB 22dhv/c, and we can write (5.76) as... 

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