Optical femtosecond self-channeling in gases, also called femtosecond filamentation, has become an important area of research in high field nonlinear optics. Filamentation occurs when laser light self-focuses in a gas owing to self-induced nonlinearity, and then defocuses in the plasma generated by the self-focused beam. The result of this process repeating itself multiple times is an extended region of plasma formation. Filamentation studies have been motivated by the extremely broad range of applications, especially in air, including pulse compression, supercontinuum generation, broadband high power terahertz pulse generation, discharge triggering and guiding, and remote sensing.

Despite the worldwide work in filamentation, the fundamental gas nonlinearities governing self-focusing had never been directly measured in the range of laser intensity up to and including the ionization threshold. This dissertation presents the first such measurements. We absolutely measured the temporal refractive index change of  O2, N2, Ar, H2, D2 and N2O caused by highfield  ultrashort  optical  pulses  with  single-shot  supercontinuum  spectral  interferometry,  cleanly separating  for  the  first  time  the  instantaneous  electronic  and  delayed  rotational  nonlinear response in diatomic gases.

We conclusively showed that a recent claim by several European groups that the optical bound  electron  nonlinearity  saturates  and  goes  negative  is  not  correct.  Such  a  phenomenon would preclude the need for plasma to provide the defocusing contribution for filamentation. Our results  show  that  the  `standard  model of filamentation', where the defocusing is provided by plasma, is correct.

Finally, we demonstrated that high repetition rate femtosecond laser pulses filamenting in gases can generate long-lived gas density `holes' which persist on millisecond timescales, long after the plasma has recombined. Gas density decrements up to ~20% have been measured. The density hole refilling is dominated by thermal diffusion. These density holes will affect all other experiments involving nonlinear high repetition-rate laser pulse energy absorption by gases.