Laser filamentation in air via Mathieu modulation: ranging from trajectory-predesigned curved filament to quasi-soliton and ring light bullet.

We propose theoretically various kinds of filaments via the Mathieu modulation. Our results indicate curved filaments, in-phase and out-of-phase quasi-solitons and nonlinear light bullets can be formed successfully in air. Through calculated initial Mathieu accelerating beam (MAB), curved filament is able to propagate along a predesigned elliptical trajectory. By transforming the MAB into an axial symmetrical structure with in-phase and out-of-phase modulations, we obtain two kinds of quasi-solitons in air, respectively. The latter case can even propagate in a breathing fashion. With a ring structure of MAB, we successfully form a light bullet in air that generates a chain of intensity peaks over extended distances. These unique filaments can offer significant advantages for numerous applications, such as micro engineering of materials, THz radiation generation and attosecond physics.