Stability of isotropic self-similar dynamics for scalar-wave collapse

Arrest of Langmuir wave collapse by quantum effects

The arrest of Langmuir wave collapse by quantum effects, first addressed by Haas and Shukla [Phys. Rev. E 79, 066402 (2009)] using a Rayleigh-Ritz trial function method is revisited, using rigorous estimates and systematic asymptotic expansions. The absence of blow up for the so-called quantum Zakharov equations is proved in two and three dimensions, whatever the strength of the quantum effects. The time-periodic behavior of the solution for initial conditions slightly in excess of the singularity threshold for the classical problem is established for various settings in two space dimensions. The difficulty of developing a consistent perturbative approach in three dimensions is also discussed and a semiphenomenological model is suggested for this case.

Quantum and classical dynamics of Langmuir wave packets

The quantum Zakharov system in three spatial dimensions and an associated Lagrangian description, as well as its basic conservation laws, are derived. In the adiabatic and semiclassical cases, the quantum Zakharov system reduces to a quantum modified vector nonlinear Schrödinger (NLS) equation for the envelope electric field. The Lagrangian structure for the resulting vector NLS equation is used to investigate the time dependence of the Gaussian-shaped localized solutions, via the Rayleigh-Ritz variational method. The formal classical limit is considered in detail. The quantum corrections are shown to prevent the collapse of localized Langmuir envelope fields, in both two and three spatial dimensions. Moreover, the quantum terms can produce an oscillatory behavior of the width of the approximate Gaussian solutions. The variational method is shown to preserve the essential conservation laws of the quantum modified vector NLS equation. The possibility of laboratory tests in the next generation intense laser-solid plasma compression experiment is discussed.

Self-similar optical wave collapse: observation of the Townes profile

Analyses of many different types of nonlinear wave equations indicate that a collapsing wave will transform into a universal blowup profile regardless of its initial shape; that is, the amplitude of the wave increases as the spatial extent decreases in a self-similar fashion. We show experimentally that the spatial profile of a collapsing optical wave evolves to a specific circularly symmetric shape, known as the Townes profile, for elliptically shaped or randomly distorted input beams. These results represent the first experimental confirmation of this universal collapsing behavior and provide deeper insight into the high-power filamentation of femtosecond laser pulses in air.