Canonical momentum based numerical schemes for hybrid plasma models with kinetic ions and massless electrons

We study the canonical momentum based discretizations of a hybrid model with kinetic ions and mass-less electrons. Two equivalent formulations of the hybrid model are presented, in which the vector potentials are in different gauges and the distribution functions depend on canonical momentum (not velocity). Particle-in-cell methods are used for the distribution functions, and the vector potentials are discretized by the finite element methods in the framework of finite element exterior calculus. Splitting methods are used for the time discretizations. It is illustrated that the second formulation is numerically superior and the schemes constructed based on the anti-symmetric bracket proposed have better conservation properties, although the filters can be used to improve the schemes of the first formulation.Comment: 24 pages, 8 figure

Pseudo-type-II tuning behavior and mode identification in whispering gallery optical parametric oscillators

Wavelength tuning of conventional mirror-based optical parametric oscillators (OPOs) exhibits parabolically-shaped tuning curves (type-0 and type-I phase matching) or tuning branches that cross each other with a finite slope (type-II phase matching). We predict and experimentally prove that whispering gallery OPOs based on type-0 phase matching show both tuning behaviors, depending on whether the mode numbers of the generated waves coincide or differ. We investigate the wavelength tuning of optical parametric oscillation in a millimeter-sized radially-poled lithium niobate disk pumped at 1 μm wavelength generating signal and idler waves between 1.7 and 2.6 μm wavelength. Our experimental findings excellently coincide with the theoretical predictions. The investigated whispering gallery optical parametric oscillator combines the employment of the highest nonlinear-optical coefficient of the material with a controlled type-II-like wavelength tuning and with the possibility of self-phase locking