title: Femtosecond pulse propagation in nitrogen: numerical study of (3 + 1)-dimensional extended nonlinear Schrödinger equation with shock-term correction.
abstract: We develop an accurate and efficient method for calculating evolution due to the extended nonlinear Schrödinger equation, which describes the propagation behavior of a femtosecond light pulse in a nonlinear medium. Applying Suzuki's exponential operator expansion to the evolution operator based on the finite-differential formulation, we realize the accurate and fast calculation that can be performed without large-scale computing systems even for (3 + 1)-dimensional problems. To study the correspondence between experiments and calculations, we calculate the propagation behavior of a femtosecond light pulse that is weakly focused in nitrogen gas of various pressures and compare the calculation results to the experimental ones. The calculation results reproduce the relative behavior of the spatial light pattern observed during the propagation. Additionally, the multiple-cone formation and interaction between two collimated pulses in nitrogen gas are also demonstrated as applications of the developed method.
authors.affiliation: Hamamatsu Photonics K.K., Central Research Laboratory, Hirakuchi, Hamakita-City, Shizuoka, 434-8601, Japan. taro@crl.hpk.co.jp
authors.forename: Taro
authors.initials: T
authors.lastname: Ando
authors.forename: Masatoshi
authors.initials: M
authors.lastname: Fujimoto