Excitation of nonlinear beams: from the linear Talbot effect through modulation instability to Akhmediev breathers

The smooth transition between stable, Talbot-effect-dominated and modulationally unstable nonlinear optical beam propagation is described as the superposition of oscillating, growing and decaying eigenmodes of the common linearized theory of modulation instability. The saturation of the instability in form of breather maxima is embedded between eigenmode growth and decay. This explains well the changes of beam characteristics when the input intensity increases in experiments on modulation instability and breather excitation in spatial-spatial experimental platforms. An increased accuracy of instability gain measurements, a variety of interesting nonlinear beam scenarios and a more selective and well-directed breather excitation are demonstrated experimentally.