Higher-Order Kerr Terms Allow Ionization-Free Filamentation in Gases

Higher-order Kerr terms allow ionization-free filamentation in gases.

We show that higher-order nonlinear indices (n(4), n(6), n(8), n(10)) provide the main defocusing contribution to self-channeling of ultrashort laser pulses in air and argon at 800 nm, in contrast with the previously accepted mechanism of filamentation where plasma was considered as the dominant defocusing process. Their consideration allows us to reproduce experimentally observed intensities a...

On negative higher-order Kerr effect and filamentation

Higher-order Kerr improve quantitative modeling of laser filamentation.

We test numerical filamentation models against experimental data about the peak intensity and electron density in laser filaments. We show that the consideration of the higher-order Kerr effect improves the quantitative agreement without the need of adjustable parameters.

Multipole solitary wave solutions of the higher-order nonlinear Schrödinger equation with quintic non-Kerr terms

We consider a high-order nonlinear Schrödinger (HNLS) equation with thirdand fourth-order dispersions, quintic non-Kerr terms, self steepening, and self-frequency-shift effects. The model applies to the description of ultrashort optical pulse propagation in highly nonlinear media. We propose a complex envelope function ansatz composed of single bright, single dark and the product of bright and ...

A Transfinite Knuth-Bendix Order for Lambda-Free Higher-Order Terms

We generalize the Knuth–Bendix order (KBO) to higher-order terms without λ-abstraction. The restriction of this new order to first-order terms coincides with the traditional KBO. The order has many useful properties, including transitivity, the subterm property, compatibility with contexts (monotonicity), stability under substitution, and well-foundedness. Transfinite weights and argument coeff...