(1) While, filamentation severely affects laser irradiation uniformity, which often encountered in indirect-drive research. Therefore, a proper smoothing method must be adopted.

(2) Developing process of filamentation and effect of characteristic parameters in underdense plasma have been studied using numerical simulation method.

(3) Instead they found that filamentation and complex patterns formed, varying with the gas identity, pressure, and strength of the electric and magnetic fields.

(4) Production and development of two-dimensional cylinder filamentation instability were presented clearly.

(5) The mechanism of filamentation formed by femtosecond pulse laser beam propagating in atmosphere is investigated.

(6) Filamentation refers to break up in the transverse direction, while modulation refers to the break up of an electromagnetic wave along its direction of propagation.

(7) It is shown that a dynamic equilibrium between optical self-focusing and plasma defocusing will be broken due to the MPA, which can induce instability of femtosecond filamentation.

(8) The results are consistent with theory and experiments of alien reports. It can provide reference for restraining filamentation.

(9) At the same time, it was showed that different laser wavelength or different electron background density could affect filamentation process.

(10) With the incidence power gradually increasing, the beam will undergo optical collapse due to intense focusing, and then the formation of femtosecond multiple filamentation(MF) can be obtained.

(11) Numerical results were derived on the developing process of filamentation under the situations of whether or not taking account of multiphoton absorption dissipation (MPA).

(12) Inner diameter of capillary has important effect on the spectrum broadening when used to restrict filamentation in high pressure gas.

(13) In the parametric amplification process, the pump light comes from the incident laser and the seed light from the generated supercontinuum by filamentation.