The oscillation characteristics of a multimode laser are considered in detail. and for the first time saturation by all of the cavity modes is included. Analytical expressions are obtained for the mode amplitudes, linewidths, and over•all spectral characteristics of lasers operating above and below threshold. It is found that with increasing excitation the spontaneous emission spectrum is gradually resolved into a set of narrow discrete modes. Slightly above threshold the number of modes reduces in a homogeneoulsy broadened laser until only a single mode is oscillating strongly. The theoretical results are in agreement with experimental data that have been reported using semiconductor lasers. With inhomogeneous broadening the spectral width goes through a minimum near threshold.

A formalism is developed for describing the evolution of picosecond mode-locked pulses in synchronously pumped dye lasers. The finite phase memory of the molecular wave functions is included, and it is found that the resultant coherence effects can be dominant for operation close to exact synchrony. Considerations of the isotropic molecular orientational distribution and the finite vibrational relaxation times are also essential in obtaining quantitative agreement with experimental results.

Vector wave solutions are obtained for the propagation of beams of light in media having slow spatial variations of the gain, loss, or index of refraction. The formalism developed here is applicable to a wide range of problems, and an exa mple considered in detail is the propagation of off-axis beams in lenslike laser materials and optical waveguides. A procedure is also described for the diagnosis of localized dielectric inhomogeneities such as plasmas by means of Gaussian laser beams.

Sinusoidal-Gaussian beam solutions are derived for the propagation of electromagnetic waves in free space and in media having at most quadratic transverse variations of the index of refraction and the gain or loss. The resulting expressions are also valid for propagation through other real and complex lens elements and systems that can be represented in terms of complex beam matrices. The solutions are in the form of sinusoidal functions of complex argument times a conventional Gaussian beam factor. In the limit of large Gaussian beam size, the sine and cosine factors of the beams are dominant and reduce to the conventional modes of a rectangular waveguide. In the opposite limit the beams reduce to the familiar fundamental Gaussian form. Alternate hyperbolic-sinusoidal-Gaussian beam solutions are also found.

Detailed analytical expressions are developed for the output power and spectral characteristics of high-gain mirrorless laser amplifiers. With regard to intensity variations and spectral narrowing, such lasers are similar in behavior to conventional laser oscillators. A threshold transition region is apparent as saturation scts in. and spectral rebroadcning occurs in in homogeneously broadened laser systems. These solutions take full account of saturation by both the right and left propagating radiation, and the results agree with experiments that have been reported.