Spatial hole burning

If the length L of the active medium is small compared to the resonator length (e.g., in cw dye lasers), it is possible to minimize the spatial hole- 

In terms of the spacing = c/2d of the longitudinal resonator modes, the spacing of the spatial hole-burning modes is 

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], 

In gas lasers the effect of spatial hole burning is partly averaged out by diffusion of the excited molecules from nodes to maxima of a standing wave. It is, however, important in solid-state and in liquid lasers such as the ruby laser or the dye laser. Spatial hole burning can be completely avoided in unidirectional ring lasers (Sect. 5.2.7) where no standing waves exist. Waves propagating in one direction can saturate the entire spatially distributed inversion. 

Single-mode operation could be achieved if the spectral gain profile is smaller than 2000 MHz. 

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 

Spatial hole burning Field distributions of two standing waves with slightly different wave lengths along the resonator axis and the resultant spatial modulation of the inversion due to gajn saturation 

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Using a coarse tuning element, the homogeneously broadened standing wave laser oscillates in one primary mode, and one or two secondary modes caused by spatial hole burning. The frequency spacing of the secondary modes from the primary mode is given by... 

Spatial hole burning Gain saturation by a singlefrequency standing wave Add proceeds primarAy... 

Fig.5.24a-d. Spatial intensity distribution for two standing waves with slightly different wavelengths X and A.2 (a), (b), and their corresponding saturation of the inversion AN z) (c). Explanation of spatial hole-burning modes in the active medium (d) with a small length L, close to a resonator mirror Ml (a< b)... 

In fact, such single-mode operation without further frequency-selecting elements in the laser resonator can be observed only in a few exceptional cases because there are several phenomena, such as spatial hole burning, frequency jitter, or time-dependent gain fluctuations, that interfere with the pure case of mode competition discussed above. These effects, which will be discussed below, prevent the unperturbed growth of one definite mode, introduce time-dependent coupling phenomena between the different modes, and cause in many cases a frequency spectrum of the laser which consists of a random superposition of many modes that fluctuate in time. 

Spatial hole burning can be avoided in the ring resonator (Fig. 5.78b). This facilitates stable single-mode operation and yields higher output powers. For example, a NaChOH color-center laser with a ring resonator yields 1.6W output power at X = 1.55 p.m when pumped by 6W of a cw YAG laser at X = 1.065 p.m [5.145]. 

I.V. Hertel, A. Stamatovic Spatial hole burning and oligo-mode distance control in CW dye lasers. IEEE J. QE-11, 210 (1975)... 

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-... 

For spectroscopic applications of multimode lasers one has to keep in mind that the spectral interval Av within the bandwidth of the laser is, in general, not uniformly filled. This means that, contrary to an incoherent source, the intensity /(v) is not a smooth function within the laser bandwidth but exhibits holes. This is particularly trae for multimode dye lasers with Fabry-Perot-type resonators where standing waves are present and spatial hole burning occurs (Sect. 5.3.4). 

For a Doppler width of Avd = 1 GHz the gain at the first adjacent spatial hole burning mode is g = goe / 26 o.06go- This mode does not reach the threshold. 

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