Multimode Lasers and Gain Competition

The different gain saturation of homogeneous and inhomogeneous transitions strongly affects the frequency spectrum of multimode lasers, as can be understood from the following arguments  

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. 

In the case of a purely inhomogeneous gain profile, the different laser modes do not share the same molecules for their amplification, and no mode competition occurs. Therefore all laser modes within that part of the gain profile, which is above the threshold, can oscillate simultaneously. The laser 

Real lasers do not represent these pure cases, but exhibit a gain profile that is a convolution of inhomogeneous and homogeneous broadening. It is the ratio of mode spacing 5v to the homogeneous width that gov- 

The suppression of higher-order TEM modes can be achieved by a proper choice of the resonator geometry, which has to be adapted to the cross section and the length L of the active medium (Sect. 5.4.2). 

If only the axial modes TEMoo participate in the laser oscillation, the laser beam transmitted through the output mirrors has a Gaussian intensity profile (5.32), (5.42). It may stiU consist of many frequencies Va = qc/ 2nd) within the spectral gain profile. The spectral bandwidth of a multimode laser oscillating on an atomic or molecular transition is comparable to that of an incoherent source emitting on this transition  

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