Starting from conventional rate equations describing the multimode operation of a laser with a broad homogeneous emission line, a system of approximately valid equations, suitable for both analytical and numerical studies of the spectral properties of laser radiation not too far from threshold, has been derived by introducing equations of motion for the spatial Fourier components of the inversion densityN(z, t), thus replacing the equation of motion forN(z, t)itself. Analytical solutions for steady-state operation were found and physically discussed in the following cases: (a) ring laser, (b) jet-stream laser with the active medium positioned either near one of the (Fabry-Perot) resonator mirrors or in the centre of the resonator, and (c) laser with a Fabry-Perot resonator completely filled with the active medium. The spectra thus calculated indicate that spatial hole burning is most efficient in providing mode co-existence in configuration (c), where it gives rise to a significant bandwidth. It is of minor importance, however, in case (b), where the spectrum differs only slightly from that of a ring laser, which is clearly free from hole-burning effects.
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